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lsblx2nm | chemistry | thermodynamics | first-law-of-thermodynamics | Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following : | [{"identifier": "A", "content": "$\\mathrm{q}=0, \\Delta \\mathrm{T}=0, \\mathrm{w}=0$"}, {"identifier": "B", "content": "$\\mathrm{q}=0, \\Delta \\mathrm{T} \\neq 0, \\mathrm{w}=0$"}, {"identifier": "C", "content": "$\\mathrm{q} \\neq 0, \\Delta \\mathrm{T}=0, \\mathrm{w}=0$"}, {"identifier": "D", "content": "$\\mathr... | ["A"] | null | <p>Let's analyze what happens during a free (or unrestrained) expansion of an ideal gas under adiabatic conditions:</p>
<ul>
<li>Adiabatic process : By definition, in an adiabatic process, no heat is transferred between the system and its surroundings. Thus, $ q = 0 $.</li>
<br/><li>Free expansion : In a free expans... | mcq | jee-main-2024-online-1st-february-morning-shift | 4,210 |
jaoe38c1lsc6kh74 | chemistry | thermodynamics | first-law-of-thermodynamics | <p>If three moles of an ideal gas at $$300 \mathrm{~K}$$ expand isothermally from $$30 \mathrm{~dm}^3$$ to $$45 \mathrm{~dm}^3$$ against a constant opposing pressure of $$80 \mathrm{~kPa}$$, then the amount of heat transferred is _______ J.</p> | [] | null | 1200 | <p>The process involves an ideal gas expanding isothermally, meaning temperature ($$T$$) remains constant. In an isothermal process for an ideal gas, the change in internal energy ($$\Delta U$$) is zero:</p>
<p>$$\Delta U = 0$$ because temperature is constant.</p>
<p>According to the first law of thermodynamics, $$\Del... | integer | jee-main-2024-online-27th-january-morning-shift | 4,211 |
jaoe38c1lsdabhe3 | chemistry | thermodynamics | first-law-of-thermodynamics | <p>If 5 moles of an ideal gas expands from $$10 \mathrm{~L}$$ to a volume of $$100 \mathrm{~L}$$ at $$300 \mathrm{~K}$$ under isothermal and reversible condition then work, $$\mathrm{w}$$, is $$-x \mathrm{~J}$$. The value of $$x$$ is __________.</p>
<p>(Given R = 8.314 J K$$^{-1}$$ mol$$^{-1}$$)</p> | [] | null | 28721 | <p>It is isothermal reversible expansion, so work done negative</p>
<p>$$\begin{aligned}
& \mathrm{W}=-2.303 \mathrm{nRT} \log \left(\frac{\mathrm{V}_2}{\mathrm{~V}_1}\right) \\
& =-2.303 \times 5 \times 8.314 \times 300 \log \left(\frac{100}{10}\right) \\
& =-28720.713 \mathrm{~J} \\
& \equiv-28721 \mathrm{~J}
\end{al... | integer | jee-main-2024-online-31st-january-evening-shift | 4,212 |
1lsgz55cl | chemistry | thermodynamics | first-law-of-thermodynamics | <p><img src="data:image/png;base64,UklGRlgSAABXRUJQVlA4IEwSAADwGAGdASoAA6sCP4HA22S2MK2nIpLZMsAwCWlu+CU6y3sMud/zRkp1+mf+L6r7mLkLwN2+/t3G0wF1f/O2//9Yvv/eyn//6hy4DSaMq3bQQqiA4G+FyY3QtKpjdC0qmN0LSn7ULWOK5I6PzjIhSi2fNd0XlFKLZ813ReUUotnzXdF5RTIV3MhMK5cWVQnlxrHui8opRbPmu6LyilFs+a7ovKKUWz5sanI03Si2fNd0KYbF9nzXdF5RSi2fNd0XlFKLZ... | [] | null | 200 | <p>Work done is given by area enclosed in the P vs V cyclic graph or V vs P cyclic graph.</p>
<p>Sign of work is positive for clockwise cyclic process for V vs P graph.</p>
<p>$$\begin{aligned}
& W=\frac{1}{2} \times(30-10) \times(30-10)=200 \mathrm{~kPa}-\mathrm{dm}^3 \\
& =200 \times 1000 \mathrm{~Pa}-\mathrm{L}=2 \m... | integer | jee-main-2024-online-30th-january-morning-shift | 4,213 |
lv40vb8u | chemistry | thermodynamics | first-law-of-thermodynamics | <p>$$\Delta_{\text {vap }} \mathrm{H}^{\ominus}$$ for water is $$+40.79 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ at 1 bar and $$100^{\circ} \mathrm{C}$$. Change in internal energy for this vapourisation under same condition is ________ $$\mathrm{kJ} \mathrm{~mol}^{-1}$$. (Integer answer) (Given $$\mathrm{R}=8.3 \mathrm{~JK}^{... | [] | null | 38 | <p>To find the change in internal energy for the vaporization of water under the given conditions, we'll use the following relationship between enthalpy change ($$\Delta_{\text{vap}} H$$) and internal energy change ($$\Delta_{\text{vap}} U$$):</p>
<p>$$\Delta_{\text{vap}} H = \Delta_{\text{vap}} U + P \Delta V$$</p>
... | integer | jee-main-2024-online-8th-april-evening-shift | 4,215 |
lv5gt4tb | chemistry | thermodynamics | first-law-of-thermodynamics | <p><img src="data:image/png;base64,UklGRjIKAABXRUJQVlA4ICYKAADwrQCdASoBAgADP4G+2GY2LyynINDZasAwCWlu+D88jXjS/Xywi4aVmNwvj6ttP7ObuPl/m+fQjMlv//1VkzF+rP1Z+rP1Z+rP1Z+rPzoLSefchm5vHuCKYj2+qGQbVe8oKMECVjfTNwPnJmvXxa63eQOWej+V7ykuH7DY6fYiu8ZOaJ95Q7Xcsmse+gofDzp+52feUlxHjeAOpNTvOke2PSTwYYpcVeBiptV7ykt/bJ5/3lJb+7VtWVonyAhFMR7gh... | [] | null | 55 | <p>$$\begin{aligned}
& \mathrm{V}_1=100 \mathrm{~L} \\
& \mathrm{~V}_2=10 \mathrm{~L} \\
& \mathrm{~W}=-\mathrm{nR} \operatorname{Tl} \frac{\mathrm{V}_2}{\mathrm{~V}_1} \\
& =-1 \times 0.08206 \times 291.15 \times 2.303 \log \frac{10}{100} \\
& =55 \mathrm{~L} \text { atm } \\
&
\end{aligned}$$</p> | integer | jee-main-2024-online-8th-april-morning-shift | 4,216 |
lvc586b1 | chemistry | thermodynamics | first-law-of-thermodynamics | <p>An ideal gas, $$\overline{\mathrm{C}}_{\mathrm{v}}=\frac{5}{2} \mathrm{R}$$, is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is $$298 \mathrm{~K}$$ and $$5 \mathrm{~atm}$$, respectively then the final temperature is _________ $$\math... | [] | null | 274 | <p>$$-1\left(2 V_1-V_1\right)=n \times \frac{5 R}{2}\left(T_2-T_1\right)$$</p>
<p>$$\begin{aligned}
& -\mathrm{V}_1=\frac{5}{2}\left(n R T_2-5 \mathrm{~V}_1\right) \\
& -\mathrm{V}_1=2.5\left(\mathrm{nRT_{2 } )}-12.5 \mathrm{~V}_1\right. \\
& 11.5 \mathrm{~V}_1=2.5\left(\mathrm{nRT_{2 } )}\right. \\
& 11.5 \times \frac... | integer | jee-main-2024-online-6th-april-morning-shift | 4,217 |
IvJk60A3K13igIgC | chemistry | thermodynamics | fundamentals-of-thermodynamics | The heat required to raise the temperature of body by 1 K is called : | [{"identifier": "A", "content": "specific heat"}, {"identifier": "B", "content": "thermal capacity"}, {"identifier": "C", "content": "water equivalent"}, {"identifier": "D", "content": "none of these"}] | ["B"] | null | The heat required to raise the temperature of body by $$1K$$ is called thermal capacity or heat capacity. | mcq | aieee-2002 | 4,218 |
geVNizGmSr5wzrQTu1BCR | chemistry | thermodynamics | fundamentals-of-thermodynamics | An ideal gas undergoes isothermal expansion at constant pressure. During
the process : | [{"identifier": "A", "content": "enthalpy increases but entropy decreases."}, {"identifier": "B", "content": "enthalpy remains constant but entropy increases."}, {"identifier": "C", "content": "enthalpy decreases but entropy increases."}, {"identifier": "D", "content": "Both enthalpy and entropy remain constant.\n"}] | ["B"] | null | <p>In an isothermal expansion process, the temperature of the system remains constant throughout the process. Since, for an ideal gas, U depends only on temperature, we have $$\Delta$$U = 0. The enthalpy change of the system in isothermal expansion is also zero as</p>
<p>$$\Delta$$H = $$\Delta$$U + nR$$\Delta$$T = 0 + ... | mcq | jee-main-2017-online-9th-april-morning-slot | 4,219 |
zhdEqLEqSaZ3Mq4lqjot1 | chemistry | thermodynamics | fundamentals-of-thermodynamics | For diatomic ideal gas in a closed system, which of the following plots does not correctly describe the relation between various thermodynamic quantities?
| [{"identifier": "A", "content": "<img src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734266205/exam_images/n6do1g5svocqofc0txny.webp\" style=\"max-width: 100%; height: auto;display: block;margin: 0 auto;\" loading=\"lazy\" alt=\"JEE Main 2019 (Online) 12th January Morning Slot Chemistry - Thermodynamics Que... | ["D"] | null | C<sub>P</sub> does not changes with change in pressure. | mcq | jee-main-2019-online-12th-january-morning-slot | 4,221 |
Ufp1cmP4rAycaLyo00Wmd | chemistry | thermodynamics | fundamentals-of-thermodynamics | The combination of plots which does not represent isothermal expansion of an ideal gas is –
<br/><br/><img src="data:image/png;base64,UklGRkgVAABXRUJQVlA4IDwVAABQDQGdASr5AgADP4G+12Y2LywnIdFZIsAwCWlu+F6ogK169xNF3f5r/W+9x/B/83axL+bSXs7xL74v2mXoyp/rJlTPP//Pn0J/tWPmwDdVgRXgXtWRLRbfasiHYQkHt3qZEtFt9qx+dm5YnSbEbljJcT8Es/NKT... | [{"identifier": "A", "content": "A and D"}, {"identifier": "B", "content": "B and D"}, {"identifier": "C", "content": "B and C"}, {"identifier": "D", "content": "A and C"}] | ["B"] | null | For isothermal process of ideal gas,
<br><br>PV = constants = K
<br><br>$$ \therefore $$ P = $${k \over v}$$
<br><br>So, the graph between P and $${1 \over v}$$ is straight line passing through the origin. So, graph (A) is correct.
<br><br>As PV = K so the P and V curve is hyperbola. So, graph (B) is wrong.
... | mcq | jee-main-2019-online-12th-january-evening-slot | 4,222 |
AIptkfEbUM5X7S2PuA8A1 | chemistry | thermodynamics | fundamentals-of-thermodynamics | Among the following, the set of parameters that
represents path function, is :<br/>
(A) q + w<br/>
(B) q<br/>
(C) w<br/>
(D) H–TS<br/> | [{"identifier": "A", "content": "(B) and (C)"}, {"identifier": "B", "content": "(A) and (D)"}, {"identifier": "C", "content": "(B), (C) and (D)"}, {"identifier": "D", "content": "(A), (B) and (C)"}] | ["A"] | null | (A) q + w = $$\Delta $$E, state function
<br><br>(B) q, Path function
<br><br>(C) w, Path function
<br><br>(D) H – TS = G, State function | mcq | jee-main-2019-online-9th-april-morning-slot | 4,223 |
dKxseaqgpKvic9iQK0jgy2xukf7tfwiq | chemistry | thermodynamics | fundamentals-of-thermodynamics | For one mole of an ideal gas, which of these
statements must be true?
<br/>(a) U and H each depends only on temperature
<br/>(b) Compressibility factor z is not equal to 1
<br/>(c) C<sub>P, m</sub> – C<sub>V, m</sub> = R
<br/>(d) dU = C<sub>V</sub>dT for any process<br/> | [{"identifier": "A", "content": "(a), (c) and (d)"}, {"identifier": "B", "content": "(a) and (c)"}, {"identifier": "C", "content": "(c) and (d)"}, {"identifier": "D", "content": "(b), (c) and (d)"}] | ["A"] | null | For 1 mole of ideal gas :
<br><br>1. Both internal energy (U) and Enthalpy (H)
depends on temperature
<br><br>2. Compressibility factor Z = 1
<br><br>3. C<sub>P, m</sub> – C<sub>V, m</sub> = R
<br><br>4. dU = C<sub>V</sub>dT for all process | mcq | jee-main-2020-online-4th-september-morning-slot | 4,224 |
1ktftv51n | chemistry | thermodynamics | fundamentals-of-thermodynamics | Two flasks I and II shown below are connected by a valve of negligible volume.<br/><br/><img src="data:image/png;base64,UklGRjoTAABXRUJQVlA4IC4TAACwaACdASp0AcgAPm0wlUgkIqIhJHDLQIANiWlu4WjeRvJfRUpuge/DP84/lf7DeA39w/pv7Pf17yJfPv2b+o/tR/ZPZb/cOkQ+R/Vf51vfv45/XP9//gPnD+ef4f+X/tH/d/Sv3r/zH8z9gL01/eP5F/Yv9Z/cP3V9r3/E/i39V8HW... | [] | null | 84 | Applying; (n<sub>I</sub> + n<sub>II</sub>)<sub>initial</sub> = (n<sub>I</sub> + n<sub>II</sub>)<sub>final</sub><br><br>$$\Rightarrow$$ Assuming the system attains a final temperature of T (such that 300 < T < 60)<br><br>$$\Rightarrow$$ $$\left( {\matrix{
{Heat\,lost\,by} \cr
{{N_2}\,of\,container} \cr
... | integer | jee-main-2021-online-27th-august-evening-shift | 4,225 |
1l56ysjmb | chemistry | thermodynamics | fundamentals-of-thermodynamics | <p>When 5 moles of He gas expand isothermally and reversibly at 300 K from 10 litre to 20 litre, the magnitude of the maximum work obtained is __________ J. [nearest integer] (Given : R = 8.3 J K<sup>$$-$$1</sup> mol<sup>$$-$$1</sup> and log 2 = 0.3010)</p> | [] | null | 8630 | $$
\begin{aligned}
\mathrm{W}_{\mathrm{rev}} &=-2.303 ~\mathrm{nRT} ~\log _{10}\left(\frac{\mathrm{V}_{2}}{\mathrm{~V}_{1}}\right) \\\\
&=-2.303 \times 5 \times 8.3 \times 300 \times \log _{10}\left(\frac{20}{10}\right) \\\\
& \simeq-8630 \mathrm{~J}
\end{aligned}
$$ | integer | jee-main-2022-online-27th-june-evening-shift | 4,226 |
1l57rgtgz | chemistry | thermodynamics | fundamentals-of-thermodynamics | <p>Match List-I with List-II.</p>
<p><style type="text/css">
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
.tg th{border-color:black;border-style:solid;b... | [{"identifier": "A", "content": "(A) - (III), (B) - (II), (C) - (IV), (D) - (I)"}, {"identifier": "B", "content": "(A) - (II), (B) - (III), (C) - (IV), (D) - (I)"}, {"identifier": "C", "content": "(A) - (II), (B) - (III), (C) - (I), (D) - (IV)"}, {"identifier": "D", "content": "(A) - (II), (B) - (I), (C) - (III), (D) -... | ["B"] | null | (A) For a spontaneous process $$\Delta $$G<sub>T,P</sub> < 0 <br/><br/>
(B) $$\Delta $$P = 0 $$ \to $$ Isobaric process, $$\Delta $$T = 0 $$ \to $$ Isothermal process<br/><br/>
(C) $$\Delta $$H<sub>reaction</sub> = ($$\Sigma $$ Bond energies of reactants) -
($$\Sigma $$ bond energies of products) <br/><br/>
(D) $$\Del... | mcq | jee-main-2022-online-27th-june-morning-shift | 4,227 |
1l5w6o92s | chemistry | thermodynamics | fundamentals-of-thermodynamics | <p>1.0 mol of monoatomic ideal gas is expanded from state 1 to state 2 as shown in the figure. The magnitude of the work done for the expansion of gas from state 1 to state 2 at 300 K is ____________ J. (Nearest integer)</p>
<p>(Given : R = 8.3 J K<sup>$$-$$1</sup> mol<sup>$$-$$1</sup>, ln10 = 2.3, log2 = 0.30)</p>
<p... | [] | null | 1718 | $$
\begin{aligned}
&w=-2.303 ~ n R T ~ \log \frac{V_{2}}{V_{1}} \\\\
&P_{1} V_{1}=P_{2} V_{2} \Rightarrow \frac{V_{2}}{V_{1}}=\frac{P_{1}}{P_{2}}=\frac{6}{3}=2 \\\\
&w=-2.303 \times 1 \times 8.3 \times 300 \times \log (2) \\\\
&w=-1718.1 \mathrm{~J}
\end{aligned}
$$ | integer | jee-main-2022-online-30th-june-morning-shift | 4,228 |
1l6mbw6fr | chemistry | thermodynamics | fundamentals-of-thermodynamics | <p>Which of the following relation is not correct?</p> | [{"identifier": "A", "content": "$$\\Delta \\mathrm{H}=\\Delta \\mathrm{U}-\\mathrm{P} \\Delta \\mathrm{V}$$"}, {"identifier": "B", "content": "$$\\Delta \\mathrm{U}=\\mathrm{q}+\\mathrm{W}$$"}, {"identifier": "C", "content": "$$\\Delta \\mathrm{S}_{\\text {sys }}+\\Delta \\mathrm{S}_{\\text {surr }} \\geqslant 0$$"}, ... | ["A"] | null | If $\mathrm{U}+\mathrm{Pv}$ (By definition)<br/><br/>
$\Delta 14=\Delta \mathrm{U}+\Delta(\mathrm{Pr})$ at constant pressure<br/><br/>
$$
\Delta \mathrm{H}=\Delta \mathrm{U}+\mathrm{P} \Delta \mathrm{V}
$$ | mcq | jee-main-2022-online-28th-july-morning-shift | 4,229 |
1ldsc8dmu | chemistry | thermodynamics | fundamentals-of-thermodynamics | <p>Which of the following relations are correct?</p>
<p>(A) $$\mathrm{\Delta U=q+p\Delta V}$$</p>
<p>(B) $$\mathrm{\Delta G=\Delta H-T\Delta S}$$</p>
<p>(C) $$\Delta \mathrm{S}=\frac{q_{rev}}{T}$$</p>
<p>(D) $$\mathrm{\Delta H=\Delta U-\Delta nRT}$$</p>
<p>Choose the most appropriate answer from the options given below... | [{"identifier": "A", "content": "A and B only"}, {"identifier": "B", "content": "B and C only"}, {"identifier": "C", "content": "C and D only"}, {"identifier": "D", "content": "B and D only"}] | ["B"] | null | <p>(A) $$\mathrm{\Delta U=q-p\Delta V}$$</p>
<p>(B) $$\mathrm{\Delta G=\Delta H-T\Delta S}$$</p>
<p>(C) $$\mathrm{\Delta S=\frac{q_{rev}}{T}}$$</p>
<p>(D) $$\mathrm{\Delta H=\Delta U+(\Delta nRT)}$$</p>
<p>Hence, (B) and (C) relations are correct.</p> | mcq | jee-main-2023-online-29th-january-evening-shift | 4,231 |
1ldwvix1n | chemistry | thermodynamics | fundamentals-of-thermodynamics | <p>Following figure shows spectrum of an ideal black body at four different temperatures. The number of correct statement/s from the following is ____________.</p>
<p><img src="data:image/png;base64,UklGRqwWAABXRUJQVlA4IKAWAABQGwGdASoAA1cCP4G+2GU2L7+nIlHpu/AwCWlu+DrogMx5NlvH6e/4GNg4S6+Pbt7hcRRD+V89JYyd//vVJ96Ch7cSy4Ya2... | [] | null | 2 | A. $\mathrm{T}_{1}>\mathrm{T}_{2}>\mathrm{T}_{3}>\mathrm{T}_{4}$
<br/><br/>
B. It is incorrect as particles do not undergo simple harmonic motion.
<br/><br/>
C. It is correct
<br/><br/>
D. It is incorrect
<br/><br/>
E. It is correct | integer | jee-main-2023-online-24th-january-evening-shift | 4,232 |
1lgp1vctk | chemistry | thermodynamics | fundamentals-of-thermodynamics | <p>What happens when methane undergoes combustion in systems A and B respectively?</p>
<p><img src="data:image/png;base64,UklGRggPAABXRUJQVlA4IPwOAACQvgCdASoAA2IBP4G+12Q2MCwmo3HZ6sAwCWlu/B5enzB53NGSnD6F/XfvfyS7NTtll7w0u382TWyOqOPo0J3gNvWsQL2ApUTV+3rNEq0GdjRl5bbrZrAUqJq/b1rEC9gKVE1ft3UMBZspKL2LSg4/+5i1ZmR62vQY7+dtHAuPFz... | [{"identifier": "A", "content": "<style type=\"text/css\">\n.tg {border-collapse:collapse;border-spacing:0;}\n.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;\n overflow:hidden;padding:10px 5px;word-break:normal;}\n.tg th{border-color:black;border-style:solid... | ["B"] | null | When methane undergoes combustion in systems A (adiabatic system) and B (diathermic container), the outcomes are as follows:
<br/><br/>
<b>System A (adiabatic system):</b> In an adiabatic system, no heat exchange occurs between the system and its surroundings. As methane undergoes combustion, which is an exothermic pro... | mcq | jee-main-2023-online-13th-april-evening-shift | 4,233 |
1lgsz4e5k | chemistry | thermodynamics | fundamentals-of-thermodynamics | <p>The total number of intensive properties from the following is __________<br/><br/> Volume, Molar heat capacity, Molarity, $$\mathrm{E}^{\theta}$$ cell, Gibbs free energy change, Molar mass, Mole</p> | [] | null | 4 | Intensive properties are independent of the amount of the substance. They don't change with the size or mass of a sample. Examples include temperature, pressure, density, and concentration.
<br/><br/><b>Intensive properties :</b>
<br/><br/>1. Molarity : Molarity is a measure of concentration, defined as the number of... | integer | jee-main-2023-online-11th-april-evening-shift | 4,234 |
lv7v3ocj | chemistry | thermodynamics | fundamentals-of-thermodynamics | <p>The heat of combustion of solid benzoic acid at constant volume is $$-321.30 \mathrm{~kJ}$$ at $$27^{\circ} \mathrm{C}$$. The heat of combustion at constant pressure is $$(-321.30-x \mathrm{R}) \mathrm{~kJ}$$, the value of $$x$$ is __________.</p> | [] | null | 150 | <p>$$\mathrm{C}_6 \mathrm{H}_5 \mathrm{COOH}(\mathrm{s})+\frac{15}{2} \mathrm{O}_2(\mathrm{~g}) \longrightarrow 7 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{I})$$</p>
<p>$$\begin{aligned}
& \Delta \mathrm{H}=\Delta \mathrm{U}+\Delta \mathrm{n}_9 R T \\
& \Delta \mathrm{H}=-321.30-\frac{1}{2} \mathrm{R... | integer | jee-main-2024-online-5th-april-morning-shift | 4,235 |
96sFRl1xHh7Lww4E | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | For the reactions<br/>
2C + O<sub>2</sub> $$\to$$ 2CO<sub>2</sub>; $$\Delta H$$ = -393 J<br/>
2Zn + O<sub>2</sub> $$\to$$ 2ZnO; $$\Delta H$$ = -412 J | [{"identifier": "A", "content": "carbon can oxidise Zn"}, {"identifier": "B", "content": "oxidation of carbon is not feasible"}, {"identifier": "C", "content": "oxidation of Zn is not feasible"}, {"identifier": "D", "content": "Zn can oxidise carbon"}] | ["D"] | null | $$\Delta H$$ negative shows that the reaction is spontaneous. Higher negative value for $$Zn$$ shows that the reaction is more feasible. | mcq | aieee-2002 | 4,236 |
1XMTpaNC2M3DXEaK | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | If at 298 K the bond energies of C - H, C - C, C = C and H - H bonds are respectively 414, 347, 615 and 435 kJ/mol, the value of enthalpy change for the reaction<br/>
H<sub>2</sub>C = CH<sub>2</sub>(g) + H<sub>2</sub>(g) $$\to$$ H<sub>3</sub>C - CH<sub>3</sub>(g) at 298 K will be : | [{"identifier": "A", "content": "- 250 kJ"}, {"identifier": "B", "content": "+ 125 kJ"}, {"identifier": "C", "content": "- 125 kJ"}, {"identifier": "D", "content": "+ 250 kJ"}] | ["C"] | null | $$C{H_2} = C{H_2}\left( g \right) + {H_2}\left( g \right) \to C{H_3} - C{H_3}$$
<br><br>Enthalpy change $$=$$ Bond energy of reactants $$-$$ Bond energy of products.
<br><br>$$\Delta H = 1\left( {C = C} \right) + 4\left( {C - H} \right) + 1\left( {H - H} \right) - $$
<br><br>$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,... | mcq | aieee-2003 | 4,237 |
nthNWg6NbhKkFNtk | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | The enthalpy change for a reaction does not depend upon : | [{"identifier": "A", "content": "use of different reactants for the same product"}, {"identifier": "B", "content": "the nature of intermediate reaction steps"}, {"identifier": "C", "content": "the differences in initial or final temperature of involved substances"}, {"identifier": "D", "content": "the physical states o... | ["B"] | null | Enthalpy change for a reaction does not depend upon the nature of intermediate reaction steps. | mcq | aieee-2003 | 4,238 |
yAuIYD3VZdr8bSk4 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | The enthalpies of combustion of carbon and carbon monoxide are -393.5 and -283 kJ mol-1
respectively. The enthalpy of formation of carbon monoxide per mole is : | [{"identifier": "A", "content": "110.5 kJ"}, {"identifier": "B", "content": "-110.5 kJ"}, {"identifier": "C", "content": "-676.5 kJ"}, {"identifier": "D", "content": "676.5 kJ"}] | ["B"] | null | $$\left( i \right)\,\,\,C + {O_2}\rightleftharpoons C{O_2},$$
<br><br>$$\,\,\Delta H = - 393.5\,kJmo{l^{ - 1}}$$
<br><br>$$\left( {ii} \right)\,\,\,CO + {1 \over 2}{O_2}\rightleftharpoons\,C{O_2},$$
<br><br>$$\,\,\,\,\,\,\,\,\Delta H = - 283.0\,kJmo{l^{ - 1}}$$
<br><br>Operating $$(i)-(ii),$$ we have
<br><br>$$C + {... | mcq | aieee-2004 | 4,239 |
H0gde6CcofVD3KwM | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | Consider an endothermic reaction, X $$\to$$ Y with the activation energies E<sub>b</sub> and E<sub>f</sub>
for the backward and forward reactions, respectively. In general : | [{"identifier": "A", "content": "E<sub>b</sub> < E<sub>f</sub>"}, {"identifier": "B", "content": "E<sub>b</sub> > E<sub>f</sub>"}, {"identifier": "C", "content": "E<sub>b</sub> = E<sub>f</sub>"}, {"identifier": "D", "content": "There is no definite relation between E<sub>b</sub> and E<sub>f</sub> "}] | ["A"] | null | Enthalpy of reaction $$\left( {\Delta H} \right) = {E_{{a_{\left( f \right)}}}} - {E_{{a_{\left( b \right)}}}}$$
<br><br>for an endothermic reaction $$\Delta H = + ve$$
<br><br>Hence for $$\Delta H$$ to be negative
<br><br>$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ ... | mcq | aieee-2005 | 4,240 |
28ftA6VnOxdFyHH4 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | Consider the reaction: N<sub>2</sub> + 3H<sub>2</sub> $$\to$$ 2NH<sub>3</sub> carried out at constant temperature and
pressure. If $$\Delta H$$ and $$\Delta U$$ are the enthalpy and internal energy changes for the
reaction, which of the following expressions is true? | [{"identifier": "A", "content": "$$\\Delta H$$ > $$\\Delta U$$"}, {"identifier": "B", "content": "$$\\Delta H$$ < $$\\Delta U$$"}, {"identifier": "C", "content": "$$\\Delta H$$ = $$\\Delta U$$"}, {"identifier": "D", "content": "$$\\Delta H$$ = 0"}] | ["B"] | null | $$\Delta H = \Delta U + \Delta nRT$$
<br><br>for $$\,\,\,{N_2} + 3{H_2} \to 2N{H_3}$$
<br><br>$$\,\,\,\Delta {n_g} = 2 - 4 = - 2$$
<br><br>$$\therefore$$ $$\,\,\,\Delta H = \Delta U - 2RT\,\,\,$$
<br><br>or $$\,\,\,\Delta U = \Delta H + 2RT$$
<br><br>$$\therefore$$ $$\,\,\,\Delta U > \Delta H$$ | mcq | aieee-2005 | 4,241 |
J24XjW5J82brwjD0 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | If the bond dissociation energies of XY, X<sub>2</sub> and Y<sub>2</sub> (all diatomic molecules) are in the ratio of 1:1:0.5 and $$\Delta H_f$$ for the formation of XY is -200 kJ mole<sup>-1</sup>. The bond
dissociation energy of X<sub>2</sub> will be : | [{"identifier": "A", "content": "100 kJ mol<sup>-1</sup> "}, {"identifier": "B", "content": "200 kJ mol<sup>-1</sup>"}, {"identifier": "C", "content": "300 kJ mol<sup>-1</sup> "}, {"identifier": "D", "content": "800 kJ mol<sup>-1</sup>"}] | ["D"] | null | $${X_2} + {Y_2} \to 2XY,$$ $$\Delta H = 2\left( { - 200} \right).$$
<br><br>Let $$x$$ be the bond dissociation energy of $${X_2}.$$
<br><br>Then $$\Delta H = - 400$$
<br><br>$$ = {\xi _{x - x}} + {\xi _{y - y}} - 2{\xi _{x - y}}$$
<br><br>$$ = x + 0.5x - 2x$$
<br><br>$$ = - 0.5x$$
<br><br>or $$\,\,\,x = {{400} \over ... | mcq | aieee-2005 | 4,242 |
U3iyY5LnDKq3TzEE | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | ($$\Delta H - \Delta U$$) for the formation of carbon monoxide (CO) from its elements at 298 K is : (R = 8.314 J K<sup>–1</sup> mol<sup>–1</sup>) | [{"identifier": "A", "content": "\u20131238.78 J mol<sup>\u20131</sup>"}, {"identifier": "B", "content": "1238.78 J mol<sup>\u20131</sup>"}, {"identifier": "C", "content": "\u20132477.57 J mol<sup>\u20131</sup> "}, {"identifier": "D", "content": "2477.57 J mol<sup>\u20131</sup>"}] | ["B"] | null | For the reaction, $${C_{\left( s \right)}} + {1 \over 2}{O_{2\left( g \right)}} \to CO$$
<br><br>$$\Delta H = \Delta U + \Delta nRT$$
<br><br>or $$\,\,\,\,\,\Delta H - \Delta U = \Delta nRT$$
<br><br>$$\Delta n = 1 - {1 \over 2} = {1 \over 2};\,\,$$
<br><br>$$\Delta H - \Delta U = {1 \over 2} \times 8.314 \times 298$$... | mcq | aieee-2006 | 4,243 |
8gNZYH52f4fjzzVb | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | The standard enthalpy of formation $$\Delta _fH^o$$ at 298 K for methane, CH<sub>4</sub>(g), is –74.8 kJ mol<sup>–1</sup>. The additional information required to determine the average energy for C – H bond formation would be : | [{"identifier": "A", "content": "the dissociation energy of H<sub>2</sub> and enthalpy of sublimation of carbon"}, {"identifier": "B", "content": "latent heat of vapourization of methane "}, {"identifier": "C", "content": "the first four ionization energies of carbon and electron gain enthalpy of hydrogen"}, {"identifi... | ["A"] | null | The standard enthalpy of formation of $$C{H_4}$$ is given by the equation :
<br><br>$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$C\left( s \right) + 2{H_2}\left( g \right) \to C{H_4}\left( g \right)$$
<br><br>In order to calculate average energy for C – H bond formation
we shoul... | mcq | aieee-2006 | 4,244 |
W9PpzCB9wILwglIR | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | The enthalpy changes for the following processes are listed below : <br/><br/>
Cl<sub>2</sub>(g) = 2Cl(g), 242.3 kJ mol<sup>–1</sup><br/>
I<sub>2</sub>(g) = 2I(g), 151.0 kJ mol<sup>–1</sup> <br/>
ICl(g) = I(g) + Cl(g), 211.3 kJ mol<sup>–1</sup><br/>
I<sub>2</sub>(s) = I<sub>2</sub>(g), 62.76 kJ mol<sup>–1</sup> <br/><... | [{"identifier": "A", "content": "\u201314.6 kJ mol<sup>\u20131</sup> "}, {"identifier": "B", "content": "\u201316.8 kJ mol<sup>\u20131</sup>"}, {"identifier": "C", "content": "+16.8 kJ mol<sup>\u20131</sup>"}, {"identifier": "D", "content": "+244.8 kJ mol<sup>\u20131</sup>"}] | ["C"] | null | $${{\rm{I}}_2}\left( s \right) + C{l_2}\left( g \right) \to 2{\rm{I}}Cl\left( g \right)$$
<br><br>$$\Delta A = \left[ {\Delta {{\rm{I}}_2}\left( s \right) \to {l_2}\left( g \right) + \Delta {H_{{\rm I} - l}} + \Delta {H_{C{\rm I} - Cl}}} \right] - $$
<br><br>$${\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern... | mcq | aieee-2006 | 4,245 |
nwZbzAAAv8f0WATD | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | Assuming that water vapour is an ideal gas, the internal energy change $$\left( {\Delta U} \right)$$ when $$1$$ mol of water is vapourised at $$1$$ bar pressure and $${100^ \circ }C$$ (Given : molar enthalpy of vapourisation of water at $$1$$ bar and $$373$$ $$K$$ $$ = 41\,kJ\,mo{l^{ - 1}}\,$$
<br/>and $$R = 8.3\,J\,m... | [{"identifier": "A", "content": "$$41.00\\,kJ\\,mo{l^{ - 1}}$$ "}, {"identifier": "B", "content": "$$4.100\\,kJ\\,mo{l^{ - 1}}$$ "}, {"identifier": "C", "content": "$$3.7904\\,kJ\\,mo{l^{ - 1}}$$ "}, {"identifier": "D", "content": "$$37.904\\,kJ\\,mo{l^{ - 1}}$$ "}] | ["D"] | null | Given
<br><br>$$\Delta H = 41\,kJ\,mo{l^{ - 1}}$$
<br><br>$$ = 41000\,J\,mo{l^{ - 1}}$$
<br><br>$$T = {100^ \circ }C = 273 + 100$$
<br><br>$$ = 373\,K,n = 1$$
<br><br>$$\Delta U = \Delta H - \Delta nRT$$
<br><br>$$ = 41000 - \left( {2 \times 8.314 \times 373} \right)$$
<br><br>$$ = 37898.88\,J\,mo{l^{ - 1}}$$
<br><br... | mcq | aieee-2007 | 4,246 |
8RPGAzlQzMaIOhtP | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated
below: <br/>
$${1 \over 2}C{l_2}(g)$$ $$\buildrel {{1 \over 2}{\Delta _{diss}}{H^\Theta }} \over
\longrightarrow $$ $$Cl(g)$$ $$\buildrel {{\Delta _{eg}}{H^\Theta }} \over
\longrightarrow $$ $$C{l^ - }(g)$$ $$\buildrel {{\De... | [{"identifier": "A", "content": "+152 kJ mol<sup>\u22121</sup>"}, {"identifier": "B", "content": "\u2212610 kJ mol<sup>\u22121</sup>"}, {"identifier": "C", "content": "\u2212850 kJ mol<sup>\u22121</sup>"}, {"identifier": "D", "content": "+120 kJ mol<sup>\u22121</sup>"}] | ["B"] | null | The energy involved in the conversion of
<br><br>$${1 \over 2}C{{\rm}_2}\left( g \right)\,\,$$ to $${\mkern 1mu} {\mkern 1mu} {\mkern 1mu} C{l^{ - 1}}\left( {aq} \right)$$ is given by
<br><br>$${\mkern 1mu} \Delta H = {1 \over 2}{\Delta _{diss}}H_{C{l_2}}^{\left( - \right)} + {\Delta _{eg}}H_{Cl}^{\left( - \right... | mcq | aieee-2008 | 4,247 |
KYX8L2SMD3SvNEjD | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | On the basis of the following thermochemical data : <br/>($$\Delta _fG^oH^+_{(aq)}$$ = 0)<br/><br/>
H<sub>2</sub>O(l) $$\to$$ H<sup>+</sup>(aq) + OH<sup>-</sup>(aq); $$\Delta H$$ = 57.32 kJ<br/>
H<sub>2</sub>(g) + $${1 \over 2} O_2(g) \to$$ H<sub>2</sub>O(l); $$\Delta H$$ = -286.20 kJ<br/><br/>
The value of enthalpy o... | [{"identifier": "A", "content": "-22.88 kJ "}, {"identifier": "B", "content": "-228.88 kJ "}, {"identifier": "C", "content": "+228.88 kJ "}, {"identifier": "D", "content": "-343.52 kJ "}] | ["B"] | null | Given, for reaction
<br><br>$$(i)$$ $$\,\,\,\,\,\,{H_2}O\left( \ell \right) \to {H^ + }\left( {aq.} \right) + O{H^ - }\left( {aq.} \right);$$
<br><br>$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\Delta {H_r} = 57.32\,kJ$$
<br><br>$$(ii)$$ $$\,\,\,\,\,\,{H_2}\left( g \right) + {1 \over 2}{O_2}\left( g \right)... | mcq | aieee-2009 | 4,248 |
cTIvQgMIyWL58Sob | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | The standard enthalpy of formation of NH<sub>3</sub> is –46.0 kJ mol<sup>–1</sup>. If the enthalpy of formation of H<sub>2</sub> from its atoms is –436 kJ mol<sup>–1</sup> and that of N2 is –712 kJ mol<sup>–1</sup>, the average bond enthalpy of N–H bond in NH<sub>3</sub> is : | [{"identifier": "A", "content": "\u2013964 kJ mol<sup>\u20131</sup>"}, {"identifier": "B", "content": "+352 kJ mol<sup>\u20131</sup>"}, {"identifier": "C", "content": "+ 1056 kJ mol<sup>\u20131</sup>"}, {"identifier": "D", "content": "\u20131102 kJ mol<sup>\u20131</sup>"}] | ["B"] | null | $${N_2} + 3{H_2} \to 2N{H_3}\,$$
<br><br>$$\,\Delta H = 2 \times - 46.0\,\,kJ\,mo{l^{ - 1}}$$
<br><br>Let $$x$$ be the bond enthalpy of $$N-H$$ bond then
<br><br>[<b>Note :</b> Enthalpy of formation or bond formation enthalpy is given which is negative but the given reaction involves bond breaking hence values shoul... | mcq | aieee-2010 | 4,249 |
kq7naEdLF4URf35Q | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | The heats of combustion of carbon and carbon monoxide are –393.5 and –283.5 kJ mol<sup>–1</sup>, respectively. The
heat of formation (in kJ) of carbon monoxide per mole is : | [{"identifier": "A", "content": "676.5"}, {"identifier": "B", "content": "-676.5"}, {"identifier": "C", "content": "\u2013110"}, {"identifier": "D", "content": "110.5"}] | ["C"] | null | Given
<br><br>$$C\left( s \right) + {O_2}\left( g \right) \to C{O_2}\left( g \right);$$
<br><br>$$\Delta H = - 393.5\,\,kJ\,mo{l^{ - 1}}......\left( i \right)$$
<br><br>$$CO\left( g \right) + {1 \over 2}{O_2}\left( g \right) \to C{O_2}\left( g \right);$$
<br><br>$$\Delta H = - 283.5\,kJ\,mo{l^{ - 1}}\,\,\,\,\,....\le... | mcq | jee-main-2016-offline | 4,251 |
9z1xsGvNOMCeubLi | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | Given, $${C_{(graphite)}} + {O_2} \to C{O_2}(g)$$;<br/><br>
$${\Delta _r}{H^o}$$ = - 393.5 kJ mol<sup>-1</sup><br/><br>
$${{\rm H}_2}(g)$$ + $${1 \over 2}{O_2}(g)$$$$\to {{\rm H}_2}{\rm O}(l)$$<br/><br>
$${\Delta _r}{H^o}$$ = - 285.8 kJ mol<sup>-1</sup><br/><br>
$$C{O_2}(g)$$ + $$2{{\rm H}_2}{\rm O}(l) \to$$ $$C{H_4}(... | [{"identifier": "A", "content": "+144.0 kJ mol<sup>\u20131</sup>"}, {"identifier": "B", "content": "\u2013 74.8 kJ mol<sup>\u20131</sup>"}, {"identifier": "C", "content": "-144.0 kJ mol<sup>\u20131</sup>"}, {"identifier": "D", "content": "+ 74.8 kJ mol<sup>\u20131</sup>"}] | ["B"] | null | C(graphite) + O<sub>2</sub>(g) $$ \to $$ CO<sub>2</sub> (g);
<br>
$${\Delta _r}{H^o}$$ = - 393.5 kJ mol<sup>-1</sup> .............(1)<br><br>
$${{\rm H}_2}(g)$$ + $${1 \over 2}{O_2}(g)$$$$\to {{\rm H}_2}{\rm O}(l)$$<br>
$${\Delta _r}{H^o}$$ = - 285.8 kJ mol<sup>-1</sup> .........(2)<br><br>
$$C{O_2}(g)$$ + $$2{{\rm H}... | mcq | jee-main-2017-offline | 4,254 |
Xt4C2Fl0OwalJsTp | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | The combustion of benzene(l) gives CO<sub>2</sub>(g) and H<sub>2</sub>O(l). Given that heat of combustion of benzene at constant volume is –3263.9 kJ mol<sup>–1</sup> at 25<sup>o</sup>C; heat of combustion (in kJ mol<sup>–1</sup>) of benzene at constant pressure will be :<br/>
(R = 8.314 JK<sup>–1</sup> mol<sup>–1</sup... | [{"identifier": "A", "content": "\u20133267.6"}, {"identifier": "B", "content": "4152.6"}, {"identifier": "C", "content": "\u2013452.46"}, {"identifier": "D", "content": "3260"}] | ["A"] | null | Formula of Heat of combination is
<br><br>$$\Delta H = \Delta u\,\, + \,\,\Delta ng\,\,RT$$
<br><br>Where, $$\Delta H$$ $$=$$ Heat of combination at constant pressure
<br><br>$$\Delta u\, = $$ Heat at constant volume
<br><br>$$\Delta {n_g}$$ change in number of moles for gaseous molecule.
<br><br>R = gas constant
<... | mcq | jee-main-2018-offline | 4,255 |
4IHDNNQSZPLQjgvdk7u1S | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | For which of the following reactions, $$\Delta $$H is equal to $$\Delta $$U? | [{"identifier": "A", "content": "N<sub>2</sub>(g) + 3H<sub>2</sub>(g) $$ \\to $$ 2NH<sub>3</sub>(g)"}, {"identifier": "B", "content": "2HI(g) $$ \\to $$ H<sub>2</sub>(g) + I<sub>2</sub>(g)"}, {"identifier": "C", "content": "2NO<sub>2</sub>(g) $$ \\to $$ N<sub>2</sub>O<sub>4</sub>(g)"}, {"identifier": "D", "content": "2... | ["B"] | null | $$\Delta $$H = $$\Delta $$$$\mu $$ + $$\Delta $$ng RT
<br><br>$$\therefore\,\,\,$$ $$\Delta $$H = $$\Delta $$$$\mu $$
<br><br>When, $$\Delta $$ng RT = 0
<br><br>$$ \Rightarrow $$ $$\Delta $$ng = 0
<br><br>For this reaction,
<br><br>2HI(g) $$ \to $$ H<sub>2</sub> (g) + I<sub>2</sub> (g)
<br><br>$$\Delta $$ng = (1 + 1) ... | mcq | jee-main-2018-online-15th-april-morning-slot | 4,256 |
6orHD6VOmxopDeO891jVu | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | Given
<br/><br/>(i) C (graphite) + O<sub>2</sub>(g) $$ \to $$ CO<sub>2</sub>(g); $$\Delta $$rH$$^\Theta $$ = x kJ mol<sup>$$-$$1</sup>
<br/><br/>(ii) C(graphite) + $${1 \over 2}$$O<sub>2</sub>(g) $$ \to $$ CO(g); $$\Delta $$rH$$^\Theta $$ = y kJ mol<sup>$$-$$1</sup>
<br/><br/>(iii) CO(g) + $${1 \over 2}$$ O<sub>2</... | [{"identifier": "A", "content": "z = x + y "}, {"identifier": "B", "content": "x = y + z "}, {"identifier": "C", "content": "x = y \u2013 z "}, {"identifier": "D", "content": "y = 2z \u2013 x"}] | ["B"] | null | In reaction (i), the product is CO<sub>2</sub>
<br><br>If we add reaction (ii) and (iii) we get,
<br> C + O<sub>2</sub> $$ \to $$ CO<sub>2</sub>
<br>here also product is CO<sub>2</sub> from same reactant C and O<sub>2</sub>.
<br><br>So according to hess law, we can say
<br... | mcq | jee-main-2019-online-12th-january-evening-slot | 4,257 |
uNXhBdsR5e8WMjmcMen8X | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | For silver, C<sub>p</sub>(J K<sup>–1</sup> mol<sup>–1</sup>) = 23 +0.01 T. If the temperature (T) of 3 moles of silver is raised from 300
K to 1000 K at 1 atm pressure, the value of $$\Delta H$$ will be close to : | [{"identifier": "A", "content": "62 KJ"}, {"identifier": "B", "content": "16 KJ"}, {"identifier": "C", "content": "13 KJ"}, {"identifier": "D", "content": "21 KJ"}] | ["A"] | null | Give that,
<br><br>n = 3
<br><br>T<sub>1</sub> = 300
<br><br>T<sub>2</sub> = 1000
<br><br>C<sub>p</sub> = 23 + 0.01T
<br><br>We know,
<br><br>$$\Delta $$H = $$\int\limits_{{T_1}}^{{T_2}} {n{C_p}dT} $$
<br><br>= $$\int\limits_{300}^{1000} {3\left( {23 + {T \over {100}}} \right)dT} $$
<br><br>= $$3\left[ {23T + {{{T^2}} ... | mcq | jee-main-2019-online-8th-april-morning-slot | 4,258 |
rXXFZN7gz7QMbQrDjk3rsa0w2w9jx0xcvqr | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | The difference between $$\Delta $$H and $$\Delta $$U ($$\Delta $$H – $$\Delta $$U), when the combustion of one mole of heptane(l) is carried
out at a temperature T, is equal to : | [{"identifier": "A", "content": "\u2013 4 RT"}, {"identifier": "B", "content": "3 RT"}, {"identifier": "C", "content": "\u2013 3 RT"}, {"identifier": "D", "content": "4 RT"}] | ["A"] | null | We know,
<br><br>$$\Delta $$H - $$\Delta $$U = $$\Delta $$n<sub>g</sub>RT
<br><br>C<sub>7</sub>H<sub>16</sub>($$l$$) + 11O<sub>2</sub>(g) $$ \to $$ 7CO<sub>2</sub>(g) + 8H2O($$l$$)
<br><br>Here $$\Delta $$n<sub>g</sub> = 7 - 11 = - 4
<br><br>$$ \therefore $$ $$\Delta $$H - $$\Delta $$U = - 4RT | mcq | jee-main-2019-online-10th-april-evening-slot | 4,259 |
ty3980b18OTQObHTXBjgy2xukewg8gvc | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | The internal energy change (in J) When 90 g of
water undergoes complete evaporation at
100<sup>o</sup>C is ____________.
<br/><br/>(Given : $$\Delta $$H<sub>vap</sub> for water at 373 K = 41 kJ/mol,
<br/>R = 8.314 JK<sup>–1</sup> mol<sup>–1</sup>) | [] | null | 189494TO189495 | H<sub>2</sub>O(l) ⇌ H<sub>2</sub>O(g)
<br><br>90 gm of H<sub>2</sub>O = $${{90} \over {18}}$$ moles of H<sub>2</sub>O = 5 moles of H<sub>2</sub>O
<br><br>$$\Delta $$H<sub>vap</sub> = $$\Delta $$U + $$\Delta $$n<sub>g</sub>RT
<br><br>$$ \Rightarrow $$ $$\Delta $$U = $$\Delta $$H<sub>vap</sub> - $$\Delta $$n<sub>g</sub>R... | integer | jee-main-2020-online-2nd-september-morning-slot | 4,261 |
uUBameTGHZjPdkQgNjjgy2xukfp1w2mk | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | Lattice enthalpy and enthalpy of solution of NaCl are 788 kJ mol<sup>–1</sup>, and 4 kJ mol<sup>–1</sup>, respectively.
<br/>The hydration enthalpy of NaCl is : | [{"identifier": "A", "content": "\u2013780 kJ mol<sup>\u20131</sup>"}, {"identifier": "B", "content": "\u2013784 kJ mol<sup>\u20131</sup>"}, {"identifier": "C", "content": "780 kJ mol<sup>\u20131</sup>"}, {"identifier": "D", "content": "784 kJ mol<sup>\u20131</sup>"}] | ["B"] | null | $$\Delta $$H<sub>sol</sub> = Lattice enthalpy + $$\Delta $$H<sub>hyd</sub>
<br><br>$$ \Rightarrow $$ 4 = 788 + $$\Delta $$H<sub>hyd</sub>
<br><br>$$ \Rightarrow $$ $$\Delta $$H<sub>hyd</sub> = –784 kJ mol<sup>–1</sup> | mcq | jee-main-2020-online-5th-september-evening-slot | 4,262 |
eXcTwCrf4G9XSwsCSmjgy2xukfc82l0k | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | The process that is NOT endothermic in nature
is : | [{"identifier": "A", "content": "Ar(g) + e<sup>-</sup> $$ \\to $$ Ar<sup>-</sup>(g)"}, {"identifier": "B", "content": "H(g) + e<sup>-</sup> $$ \\to $$ H<sup>-</sup>(g)"}, {"identifier": "C", "content": "Na(g) $$ \\to $$ Na<sup>+</sup>(g) + e<sup>-</sup>"}, {"identifier": "D", "content": "O<sup>-</sup>(g) + e<sup>-</sup... | ["B"] | null | H(g) + e<sup>-</sup> $$ \to $$ H<sup>-</sup>(g) is exothermic
<br><br>rest of all endothermic process. | mcq | jee-main-2020-online-4th-september-evening-slot | 4,263 |
fEIDA08mB1iW9zxyLf7k9k2k5icl3zo | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | If enthalpy of atomisation for Br<sub>2(1)</sub> is x kJ/mol
and bond enthalpy for Br<sub>2</sub> is y kJ/mol, the
relation between them : | [{"identifier": "A", "content": "does not exist"}, {"identifier": "B", "content": "is x < y"}, {"identifier": "C", "content": "is x > y"}, {"identifier": "D", "content": "is x = y"}] | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264997/exam_images/xnctexndos5letrbgfdr.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 9th January Morning Slot Chemistry - Thermodynamics Question 104 English Explanation">
<br><br>$$ ... | mcq | jee-main-2020-online-9th-january-morning-slot | 4,265 |
yzpBP1pwH97hc22ATX7k9k2k5eqoeeu | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | The standard heat of formation $$\left( {{\Delta _f}H_{298}^0} \right)$$ of ethane (in kj/mol), if the heat of combustion of
ethane, hydrogen and graphite are - 1560, -393.5 and -286 Kj/mol, respectively is : | [] | null | -192.5 | 2C(graphite)+ 3H(g) $$ \to $$ C<sub>2</sub>H<sub>6</sub>(g)
<br><br>$${\Delta _f}H$$(C<sub>2</sub>H<sub>6</sub>) = 2$$\Delta H$$<sub>comb</sub>(C<sub>graphite</sub>) + 3$$\Delta H$$<sub>comb</sub>(H<sub>2</sub>)<br><br> - $$\Delta H$$<sub>comb</sub>(C<sub>2</sub>H<sub>6</sub>)
<br><br>= – (286$$ \times $$2) - (393.5$$ ... | integer | jee-main-2020-online-7th-january-evening-slot | 4,266 |
BIkxzCDshgJcEHOyO81klue5n23 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | An exothermic reaction X $$ \to $$ Y has an activation energy 30 kJ mol<sup>$$-$$1</sup>. If energy change $$\Delta$$E during the reaction is $$-$$20 kJ, then the activation energy for the reverse reaction in kJ is ___________. (Integer answer) | [] | null | 50 | X $$ \to $$ Y
<br><br>$$\Delta $$E = (E<sub>a</sub>)<sub>f</sub>
– (E<sub>a</sub>)<sub>b</sub>
<br><br>$$ \Rightarrow $$ – 20 = 30 – (E<sub>a</sub>)<sub>b</sub>
<br><br>$$ \Rightarrow $$ (E<sub>a</sub>)<sub>b</sub> = 50 kJ | integer | jee-main-2021-online-26th-february-morning-slot | 4,268 |
lypZaEMUgK7SBYxVbL1kluswvdn | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | The average S-F bond energy in kJ mol<sup>$$-$$1</sup> of SF<sub>6</sub> is _____________. (Rounded off to the nearest integer)<br/><br/>[Given : The values of standard enthalpy of formation of SF<sub>6</sub>(g), S(g) and F(g) are - 1100, 275 and 80 kJ mol<sup>$$-$$1</sup> respectively.] | [] | null | 309 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l7rqujrj/0f6b0ef6-761a-46cc-a9ca-a65eb48d3da2/4a0b61f0-2ebd-11ed-bc10-01eb53e9c79f/file-1l7rqujrk.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l7rqujrj/0f6b0ef6-761a-46cc-a9ca-a65eb48d3da2/4a0b61f0-2ebd-11ed-bc10-01eb53e9c79f/fi... | integer | jee-main-2021-online-26th-february-evening-slot | 4,269 |
J9D2dt0iXwgf8friUG1kmj8wg9f | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | The standard enthalpies of formation of Al<sub>2</sub>O<sub>3</sub> and CaO are $$-$$1675 kJ mol<sup>-1</sup> and $$-$$635 kJ mol<sup>$$-$$1</sup> respectively.<br/><br/>For the reaction<br/><br/>3CaO + 2Al $$ \to $$ 3Ca + Al<sub>2</sub>O<sub>3</sub> the standard reaction enthalpy $$\Delta$$<sub>r</sub>H<sup>0</sup> = ... | [] | null | 230 | $$3CaO + 2Al\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_{}} 3Ca + A{l_2}{O_3}$$<br><br>$$\Delta H_{reaction}^o = 3\Delta {H^o}_f(Ca,s) + \Delta {H^o}_f(A{l_2}{O_3},s) - 3\Delta {H^o}_f(CaO,s) - 2\Delta {H^o}_f(Al,S)$$<br><br>$$ = 0 + ( - 1675) - 3( - 635) - 0$$<br><br>$$ = - 1675 + 1905$$<br><br>$$ = 230$$ KJ | integer | jee-main-2021-online-17th-march-morning-shift | 4,270 |
6E1rff9oqbp6wzaF1R1kmlntbdb | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | For the reaction C<sub>2</sub>H<sub>6</sub> $$ \to $$ C<sub>2</sub>H<sub>4</sub> + H<sub>2</sub><br/><br/>the reaction enthalpy $$\Delta$$<sub>r</sub>H = __________ kJ mol<sup>$$-$$1</sup>. (Round off to the Nearest Integer).<br/><br/>[ Given : Bond enthalpies in kJ mol<sup>$$-$$1</sup> : C-C : 347, C = C : 611; C-H : ... | [] | null | 128 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266412/exam_images/xqnr8ycf8rxtzbvwmps8.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 18th March Morning Shift Chemistry - Thermodynamics Question 84 English Explanation"><br><br>$$\De... | integer | jee-main-2021-online-18th-march-morning-shift | 4,271 |
1krt6xg0q | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | If the standard molar enthalpy change for combustion of graphite powder is $$-$$2.48 $$\times$$ 10<sup>2</sup> kJ mol<sup>$$-$$1</sup>, the amount of heat generated on combustion of 1 g of graphite powder is ___________ kJ. (Nearest integer) | [] | null | 21 | 1 mol graphite = 12 gm C<br><br>For 1 g of graphite = $${{248} \over {12}}$$ = 20.67 kJ/gm heat evolved. | integer | jee-main-2021-online-22th-july-evening-shift | 4,272 |
1krz2vf85 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | For water at 100$$^\circ$$ C and 1 bar,<br/><br/>$$\Delta$$<sub>vap</sub> H $$-$$ $$\Delta$$<sub>vap</sub> U = _____________ $$\times$$ 10<sup>2</sup> J mol<sup>$$-$$1</sup>. (Round off to the Nearest Integer)<br/><br/>[Use : R = 8.31 J mol<sup>$$-$$1</sup> K<sup>$$-$$1</sup>]<br/><br/>[Assume volume of H<sub>2</sub>O(... | [] | null | 31 | H<sub>2</sub>O<sub>(l)</sub> $$\rightleftharpoons$$ H<sub>2</sub>O<sub>(v)</sub><br><br>$$\Delta$$H = $$\Delta$$U + $$\Delta$$n<sub>g</sub>RT<br><br>For 1 mole waters;<br><br>$$\Delta$$n<sub>g</sub> = 1<br><br>$$\therefore$$ $$\Delta$$n<sub>g</sub>RT = 1 mol $$\times$$ 8.31 J/mol-k $$\times$$ 373 K<br><br>= 3099.63 J $... | integer | jee-main-2021-online-27th-july-morning-shift | 4,274 |
1ks1j4qch | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | When 400 mL of 0.2 M H<sub>2</sub>SO<sub>4</sub> solution is mixed with 600 mL of 0.1 M NaOH solution, the increase in temperature of the final solution is __________ $$\times$$ 10<sup>$$-$$2</sup> K. (Round off to the nearest integer).<br/><br/>[Use : H<sup>+</sup> (aq) + OH<sup>$$-$$</sup> (aq) $$\to$$ H<sub>2</sub>O... | [] | null | 82 | $${n_{{H^ + }}} = {{400 \times 0.2} \over {1000}} \times 2 = 0.16$$<br><br>$${n_{O{H^ - }}} = {{600 \times 0.1} \over {1000}} = 0.06$$ (L.R.)<br><br>Now, heat liberated from reaction = heat gained by solutions<br><br>or, 0.06 $$\times$$ 57.1 $$\times$$ 10<sup>3</sup><br><br>= (1000 $$\times$$ 1.0) $$\times$$ 4.18 $$\ti... | integer | jee-main-2021-online-27th-july-evening-shift | 4,275 |
1ktcs3u07 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | For water $$\Delta$$<sub>vap</sub> H = 41 kJ mol<sup>$$-$$1</sup> at 373 K and 1 bar pressure. Assuming that water vapour is an ideal gas that occupies a much larger volume than liquid water, the internal energy change during evaporation of water is ___________ kJ mol<sup>$$-$$1</sup><br/><br/>[Use : R = 8.3 J mol<sup>... | [] | null | 38 | H<sub>2</sub>O(l) $$\to$$ H<sub>2</sub>O(g) : $$\Delta$$H = 41 $${{kJ} \over {mol}}$$<br><br>$$\Rightarrow$$ From the relation : $$\Delta$$H = $$\Delta$$U + $$\Delta$$n<sub>g</sub>RT<br><br>$$\Rightarrow$$ 41$${{kJ} \over {mol}}$$ = $$\Delta$$U + (1) $$\times$$ $${{8.3} \over {1000}}$$ $$\times$$ 373<br><br>$$\Delta$$ ... | integer | jee-main-2021-online-26th-august-evening-shift | 4,277 |
1kteedvt8 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | 200 mL of 0.2 M HCl is mixed with 300 mL of 0.1 M NaOH. The molar heat of neutralization of this reaction is $$-$$57.1 kJ. The increase in temperature in $$^\circ$$C of the system on mixing is x $$\times$$ 10<sup>$$-$$2</sup>. The value of x is ___________. (Nearest integer)<br/><br/>[Given : Specific heat of water = 4... | [] | null | 82 | $$\Rightarrow$$ Millimoles of HCl = 200 $$\times$$ 0.2 = 40<br><br>$$\Rightarrow$$ Millimoles of NaOH = 300 $$\times$$ 0.1 = 30<br><br>$$\Rightarrow$$ Heat released = $$\left( {{{30} \over {1000}} \times 57.1 \times 1000} \right)$$ = 1713 J<br><br>$$\Rightarrow$$ Mass of solution = 500 ml $$\times$$ 1 gm/ml = 500 gm<br... | integer | jee-main-2021-online-27th-august-morning-shift | 4,278 |
1l549y2xc | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>17.0 g of NH<sub>3</sub> completely vapourises at $$-$$33.42$$^\circ$$C and 1 bar pressure and the enthalpy change in the process is 23.4 kJ mol<sup>$$-$$1</sup>. The enthalpy change for the vapourisation of 85 g of NH<sub>3</sub> under the same conditions is _________ kJ.</p> | [] | null | 117 | Number of moles of $\mathrm{NH}_{3}=5$
<br/><br/>
So, required $\Delta \mathrm{H}=5 \times 23.4$
<br/><br/>
$$
=117 \mathrm{~kJ}
$$ | integer | jee-main-2022-online-29th-june-morning-shift | 4,279 |
1l55numhx | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>For combustion of one mole of magnesium in an open container at 300 K and 1 bar pressure, $$\Delta$$<sub>C</sub>H<sup>$$\Theta $$</sup> = $$-$$601.70 kJ mol<sup>$$-$$1</sup>, the magnitude of change in internal energy for the reaction is __________ kJ. (Nearest integer)</p>
<p>(Given : R = 8.3 J K<sup>$$-$$1</sup> m... | [] | null | 600 | $\mathrm{Mg}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{MgO}(\mathrm{s})$
<br/><br/>
$$
\begin{aligned}
&\Delta \mathrm{H}=\Delta \mathrm{U}+\Delta \mathrm{ngRT} \\\\
&\Delta \mathrm{ng}=-\frac{1}{2} \\\\
&-601.70=\Delta \mathrm{U}-\frac{1}{2}(8.3)(300) \times 10^{-3} \\\\
&\Delta \math... | integer | jee-main-2022-online-28th-june-evening-shift | 4,280 |
1l58ee6jd | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>For complete combustion of methanol</p>
<p>CH<sub>3</sub>OH(I) + $${3 \over 2}$$O<sub>2</sub>(g) $$\to$$ CO<sub>2</sub>(g) + 2H<sub>2</sub>O(I)</p>
<p>the amount of heat produced as measured by bomb calorimeter is 726 kJ mol<sup>$$-$$1</sup> at 27$$^\circ$$C. The enthalpy of combustion for the reaction is $$-$$x kJ ... | [] | null | 727 | $\mathrm{CH}_{3} \mathrm{OH}(\mathrm{l})+\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})$
<br/><br/>
$$
\begin{aligned}
&\Delta \mathrm{H}=\Delta \mathrm{U}+\Delta \mathrm{n}_{\mathrm{g}} \mathrm{RT} \\\\
&=-726 \mathrm{~kJ}+\left(\frac{-1}{2}\rig... | integer | jee-main-2022-online-26th-june-morning-shift | 4,281 |
1l6e1z2l5 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>The enthalpy of combustion of propane, graphite and dihydrogen at $$298 \mathrm{~K}$$ are $$-2220.0 \mathrm{~kJ} \mathrm{~mol}^{-1},-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ and $$-285.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ respectively. The magnitude of enthalpy of formation of propane $$\left(\mathrm{C}_{3} \mathrm{H}... | [] | null | 104 | Enthalpy of combustion of propane, graphite and $$\mathrm{H}_{2}$$ at $$298 \mathrm{~K}$$ are
<br/><br/>
$$\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 3 \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{I}), \Delta \mathrm{H}_{1}=-2220 \mathrm{~kJ} \mathrm{~mol}^{... | integer | jee-main-2022-online-25th-july-morning-shift | 4,284 |
1l6f7qjv9 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>While performing a thermodynamics experiment, a student made the following observations.</p>
<p>HCl + NaOH $$\to$$ NaCl + H<sub>2</sub>O $$\Delta$$H = $$-$$57.3 kJ mol<sup>$$-$$1</sup></p>
<p>CH<sub>3</sub>COOH + NaOH $$\to$$ CH<sub>3</sub>COONa + H<sub>2</sub>O $$\Delta$$H = $$-$$55.3 kJ mol<sup>$$-$$1</sup></p>
<p... | [] | null | 2 | (I) $$\mathrm{HCl}+\mathrm{NaOH} \rightarrow \mathrm{NaCl}+\mathrm{H}_{2} \mathrm{O}$$
<br/><br/>
$$
\Delta \mathrm{H}_{1}=-57.3 \,\mathrm{KJ} \mathrm{mol}^{-1}
$$
<br/><br/>
(II) $$\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{NaOH} \rightarrow \mathrm{CH}_{3} \mathrm{COONa}+\mathrm{H}_{2} \mathrm{O}$$
<br/><br/>
$$
\Delta \m... | integer | jee-main-2022-online-25th-july-evening-shift | 4,285 |
1l6gsb4xo | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>$$2.4 \mathrm{~g}$$ coal is burnt in a bomb calorimeter in excess of oxygen at $$298 \mathrm{~K}$$ and $$1 \mathrm{~atm}$$ pressure. The temperature of the calorimeter rises from $$298 \mathrm{~K}$$ to $$300 \mathrm{~K}$$. The enthalpy change during the combustion of coal is $$-x \mathrm{~kJ} \mathrm{~mol}^{-1}$$. T... | [] | null | 200 | $$\mathrm{Q}($$ Heat evolved $$)=-\frac{\mathrm{C}_{\text {system }} \Delta \mathrm{T}}{\mathrm{n}}$$
<br/><br/>
$$\mathrm{n}_{\text {coal }}=\frac{2.4}{12}$$
<br/><br/>
$$\mathrm{Q}=\frac{-20(300-298)}{0.2}$$
<br/><br/>
$$Q=-200 \mathrm{~kJ} / \mathrm{mol}$$
<br/><br/>
$$x=200$$
| integer | jee-main-2022-online-26th-july-morning-shift | 4,286 |
1l6i67wh8 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>For the reaction</p>
<p>$$\mathrm{H}_{2} \mathrm{F}_{2}(\mathrm{~g}) \rightarrow \mathrm{H}_{2}(\mathrm{~g})+\mathrm{F}_{2}(\mathrm{~g})$$</p>
<p>$$\Delta U=-59.6 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ at $$27^{\circ} \mathrm{C}$$.</p>
<p>The enthalpy change for the above reaction is ($$-$$) __________ $$\mathrm{kJ} \,\m... | [] | null | 57 | $\mathrm{H}_{2} \mathrm{~F}_{2}(\mathrm{~g}) \longrightarrow \mathrm{H}_{2}(\mathrm{~g})+\mathrm{F}_{2}(\mathrm{~g})$
<br/><br/>
$\Delta \mathrm{U}=-59.6 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at $27^{\circ} \mathrm{C}$
<br/><br/>
$$
\begin{aligned}
\Delta \mathrm{H} &=\Delta \mathrm{U}+\Delta \mathrm{n}_{g} \mathrm{RT} \\
&... | integer | jee-main-2022-online-26th-july-evening-shift | 4,287 |
1l6p8ogqi | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>When 600 mL of 0.2 M HNO<sub>3</sub> is mixed with $$400 \mathrm{~mL}$$ of 0.1 M NaOH solution in a flask, the rise in temperature of the flask is ___________ $$\times 10^{-2}{ }\,^{\circ} \mathrm{C}$$.</p>
<p>(Enthalpy of neutralisation $$=57 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ and Specific heat of water $$=4.2 \,\ma... | [] | null | 54 | HNO<sub>3</sub><br>
600 mL × 0.2 M = 120 m mol <br><br>
NaOH<br>
400 mL × 0.1 M = 40 m mol <br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l7vzh473/2c505161-f77d-4a29-9463-89bd7ef6b91f/294280f0-3112-11ed-9c98-ad39d53b642b/file-1l7vzh474.png?format=png" data-orsrc="https://app-content.cdn.exam... | integer | jee-main-2022-online-29th-july-morning-shift | 4,288 |
1ldo3wq0n | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>$$0.3 \mathrm{~g}$$ of ethane undergoes combustion at $$27^{\circ} \mathrm{C}$$ in a bomb calorimeter. The temperature of calorimeter system (including the water) is found to rise by $$0.5^{\circ} \mathrm{C}$$. The heat evolved during combustion of ethane at constant pressure is ____________ $$\mathrm{kJ} ~\mathrm{m... | [] | null | 1006 | $\mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})+\frac{7}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\ell)$
<br/><br/>$\begin{aligned} & \text { No. of moles of ethane }=\frac{0.3}{30}=0.01 \\\\ & \text { Heat evolved in Bomb calorimeter }=20 \times 0.5 \\\\ & =10 \mathrm{~kJ... | integer | jee-main-2023-online-1st-february-evening-shift | 4,289 |
1ldolm7ow | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>At $$25^{\circ} \mathrm{C}$$, the enthalpy of the following processes are given :</p>
<p><style type="text/css">
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:... | [] | null | 499 | $\frac{\text { (i) }+\text { (iii) }}{2}-$ (ii) gives desired reaction
<br/><br/>$$
\begin{aligned}
& \Delta \mathrm{H}_{\mathrm{r}}=\frac{436+78}{2}-(-242) \\\\
& =\frac{436+78}{2}+242=499
\end{aligned}
$$ | integer | jee-main-2023-online-1st-february-morning-shift | 4,291 |
1ldppzlwp | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>The enthalpy change for the conversion of $$\frac{1}{2} \mathrm{Cl}_{2}(\mathrm{~g})$$ to $$\mathrm{Cl}^{-}$$(aq) is ($$-$$) ___________
$$\mathrm{kJ} \mathrm{mol}^{-1}$$ (Nearest integer)</p>
<p>Given : $$\Delta_{\mathrm{dis}} \mathrm{H}_{\mathrm{Cl}_{2(\mathrm{~g})}^{\theta}}^{\ominus}=240 \mathrm{~kJ} \mathrm{~m... | [] | null | 610 | $$
\begin{aligned}
& \frac{1}{2} \mathrm{Cl}_2(\mathrm{~g}) \longrightarrow \mathrm{Cl}_{\text {(aq) }}^{-} \quad \Delta \mathrm{H}=? \\\\
& \begin{aligned}
\Delta \mathrm{H} & =\frac{1}{2} \Delta_{\mathrm{diss}} \mathrm{H}_{\mathrm{Cl}_2}^{\circ}+\Delta_{\mathrm{eg}} \Delta \mathrm{H}_{\mathrm{Cl}(\mathrm{g})}^{\circ}... | integer | jee-main-2023-online-31st-january-morning-shift | 4,292 |
1lgq5dsyf | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>$$\mathrm{A}_{2}+\mathrm{B}_{2} \rightarrow 2 \mathrm{AB} . \Delta H_{f}^{0}=-200 \mathrm{~kJ} \mathrm{~mol}^{-1}$$</p>
<p>$$\mathrm{AB}, \mathrm{A}_{2}$$ and $$\mathrm{B}_{2}$$ are diatomic molecules. If the bond enthalpies of $$\mathrm{A}_{2}, \mathrm{~B}_{2}$$ and $$\mathrm{AB}$$ are in the ratio $$1: 0.5: 1$$, t... | [] | null | 400 | To find the bond enthalpy of $$\mathrm{A}_{2}$$, we can use the given information about the reaction and the bond enthalpies' ratio. The reaction is:
<br/><br/>
$$\mathrm{A}_{2}+\mathrm{B}_{2} \rightarrow 2 \mathrm{AB}$$
<br/><br/>
The enthalpy change for the reaction, $$\Delta H_{f}^{0}$$, is given as:
<br/><br/>
$$\D... | integer | jee-main-2023-online-13th-april-morning-shift | 4,294 |
1lgv134aw | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>Solid fuel used in rocket is a mixture of $$\mathrm{Fe}_{2} \mathrm{O}_{3}$$ and $$\mathrm{Al}$$ (in ratio 1 : 2). The heat evolved $$(\mathrm{kJ})$$ per gram of the mixture is ____________. (Nearest integer)</p>
<p>Given: $$\Delta \mathrm{H}_{\mathrm{f}}^{\theta}\left(\mathrm{Al}_{2} \mathrm{O}_{3}\right)=-1700 \ma... | [] | null | 4 | <p>First, let's consider the reaction :
<br/><br/>$$2\mathrm{Al}(s) + \mathrm{Fe}_2\mathrm{O}_3(s) \rightarrow \mathrm{Al}_2\mathrm{O}_3(s) + 2\mathrm{Fe}(s)$$</p>
<p>The heat change for this reaction $$\Delta H^0$$ can be calculated from the heats of formation of the reactants and the products :
<br/><br/>$$\Delta... | integer | jee-main-2023-online-11th-april-morning-shift | 4,295 |
1lgvvcw7q | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>The number of endothermic process/es from the following is ______________.</p>
<p>A. $$\mathrm{I}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{I}(\mathrm{g})$$</p>
<p>B. $$\mathrm{HCl}(\mathrm{g}) \rightarrow \mathrm{H}(\mathrm{g})+\mathrm{Cl}(\mathrm{g})$$</p>
<p>C. $$\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \ma... | [] | null | 4 | <p>An endothermic process is one that absorbs heat from the surroundings. Here are the types of the given reactions:</p>
<p>A. $\mathrm{I}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{I}(\mathrm{g})$</p>
<p>This process involves the dissociation of iodine molecules into individual iodine atoms. This requires energy to break ... | integer | jee-main-2023-online-10th-april-evening-shift | 4,296 |
1lgygw4e4 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>Given</p>
<p><style type="text/css">
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
.tg th{border-color:black;border-style:solid;border-width:1px;font-... | [{"identifier": "A", "content": "$$\\frac{x-2y}{2}$$"}, {"identifier": "B", "content": "$$\\frac{x+2y}{2}$$"}, {"identifier": "C", "content": "$$2y-x$$"}, {"identifier": "D", "content": "$$\\frac{2x-y}{2}$$"}] | ["A"] | null | <p>The standard enthalpy change for the reaction</p>
<p>$$\mathrm{C(graphite)+\frac{1}{2}O_2(g)\to CO(g)}$$</p>
<p>can be calculated using Hess's Law, which states that the total enthalpy change for a reaction is the same whether it occurs in one step or in many steps. </p>
<p>If we modify the given reactions to re... | mcq | jee-main-2023-online-10th-april-morning-shift | 4,297 |
1lh32ufqd | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>Consider the following data</p>
<p>Heat of combustion of $$\mathrm{H}_{2}(\mathrm{g})\quad\quad=-241.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$$</p>
<p>Heat of combustion of $$\mathrm{C}(\mathrm{s})\quad\quad=-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$$</p>
<p>Heat of combustion of $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\m... | [] | null | 278 | The reaction for the formation of $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})$$ is given by:
<br/><br/>
$$2\mathrm{C}(\mathrm{s}) + 6\mathrm{H}_{2}(\mathrm{g}) + \frac{1}{2}\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l}) + 3\mathrm{H}_{2}\mathrm{O}(\mathrm{l})$$
... | integer | jee-main-2023-online-6th-april-evening-shift | 4,298 |
1lsg8rlk4 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>Two reactions are given below:</p>
<p>$$\begin{aligned}
& 2 \mathrm{Fe}_{(\mathrm{s})}+\frac{3}{2} \mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{Fe}_2 \mathrm{O}_{3(\mathrm{~s})}, \Delta \mathrm{H}^{\circ}=-822 \mathrm{~kJ} / \mathrm{mol} \\
& \mathrm{C}_{(\mathrm{s})}+\frac{1}{2} \mathrm{O}_{2(\mathrm{~g}... | [] | null | 492 | <p>$$2 \mathrm{Fe}_{(\mathrm{s})}+\frac{3}{2} \mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{Fe}_2 \mathrm{O}_{3(\mathrm{~s})}, \Delta \mathrm{H}^{\circ}=-822 \mathrm{~kJ} / \mathrm{mol}$$ ........ (1)</p>
<p>$$\mathrm{C}_{(\mathrm{s})}+\frac{1}{2} \mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{CO}_{(\mathrm{g})}, \D... | integer | jee-main-2024-online-30th-january-evening-shift | 4,300 |
luz2umyx | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>When equal volume of $$1 \mathrm{~M} \mathrm{~HCl}$$ and $$1 \mathrm{~M} \mathrm{~H}_2 \mathrm{SO}_4$$ are separately neutralised by excess volume of $$1 \mathrm{M}$$ $$\mathrm{NaOH}$$ solution. $$x$$ and $$y \mathrm{~kJ}$$ of heat is liberated respectively. The value of $$y / x$$ is __________.</p> | [] | null | 2 | <p>To solve this problem, we need to understand the concept of neutralization reactions and the heat evolved during these reactions.
<p>When an acid and a base react, they undergo a neutralization reaction to produce water and a salt. The heat released in this process is known as the enthalpy of neutralization.</p>
<... | integer | jee-main-2024-online-9th-april-morning-shift | 4,301 |
luz2umwz | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>The heat of solution of anhydrous $$\mathrm{CuSO}_4$$ and $$\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}$$ are $$-70 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ and $$+12 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ respectively.</p>
<p>The heat of hydration of $$\mathrm{CuSO}_4$$ to $$\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}$... | [] | null | 82 | <p>(I) $$\mathrm{CuSO}_4+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{CuSO}_4$$
Solution $$\Delta \mathrm{H}=-70 \mathrm{~kJ}$$</p>
<p>(II) $$\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{CuSO}_4$$ Solution $$\mathrm{\Delta H=12 \mathrm{~kJ}}$$</p>
<p>(I) - (II)</p>
... | integer | jee-main-2024-online-9th-april-morning-shift | 4,302 |
lv0vys57 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>The enthalpy of formation of ethane $$(\mathrm{C}_2 \mathrm{H}_6)$$ from ethylene by addition of hydrogen where the bond-energies of $$\mathrm{C}-\mathrm{H}, \mathrm{C}-\mathrm{C}, \mathrm{C}=\mathrm{C}, \mathrm{H}-\mathrm{H}$$ are $$414 \mathrm{~kJ}, 347 \mathrm{~kJ}, 615 \mathrm{~kJ}$$ and $$435 \mathrm{~kJ}$$ res... | [] | null | 125 | <p>$$\begin{aligned}
& \mathrm{C}_2 \mathrm{H}_4+\mathrm{H}_2 \longrightarrow \mathrm{C}_2 \mathrm{H}_6 \\
& \begin{aligned}
\Delta \mathrm{H} & =(615)+(435)-(347)-2(414) \\
& =615+435-347-828 \\
& =-125 \mathrm{~kJ}
\end{aligned}
\end{aligned}$$</p> | integer | jee-main-2024-online-4th-april-morning-shift | 4,303 |
lv7v4hc8 | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R)</p>
<p>Assertion (A) : Enthalpy of neutralisation of strong monobasic acid with strong monoacidic base is always $$-57 \mathrm{~kJ} \mathrm{~mol}^{-1}$$</p>
<p>Reason (R) : Enthalpy of neutralisation is the amoun... | [{"identifier": "A", "content": "(A) is true but (R) is false"}, {"identifier": "B", "content": "Both (A) and (R) are true and (R) is the correct explanation of (A)"}, {"identifier": "C", "content": "Both (A) and (R) are true but (R) is not the correct explanation of (A)"}, {"identifier": "D", "content": "(A) is false ... | ["B"] | null | <p>Enthalpy of neutralisation of strong acids and bases is $$-57 \mathrm{~kJ} / \mathrm{mol}$$. which is fixed for reaction of 1 mole of $$\mathrm{H}^{+}$$ with 1 mole of $$\mathrm{OH}^{-}$$ to form 1 mole of water.</p> | mcq | jee-main-2024-online-5th-april-morning-shift | 4,304 |
lv9s2sjb | chemistry | thermodynamics | reactions-related-to-enthalpies-and-hess's-law | <p>Combustion of 1 mole of benzene is expressed at</p>
<p>$$\mathrm{C}_6 \mathrm{H}_6(\mathrm{l})+\frac{15}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 6 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \text {. }$$</p>
<p>The standard enthalpy of combustion of $$2 \mathrm{~mol}$$ of benzene is $$-^{\prime... | [] | null | 6535 | <p>To determine the standard enthalpy of combustion of 2 moles of benzene, we need to use the standard enthalpy of formation values provided and apply Hess's Law. Here is a step-by-step explanation:</p>
<h3>Given Data:</h3>
<ol>
<li><strong>Standard enthalpy of formation of benzene ($C_6H_6(l)$):</strong></li>
</ol>
... | integer | jee-main-2024-online-5th-april-evening-shift | 4,305 |
NrUdplY76GSyd3Yg | chemistry | thermodynamics | second-law-of-thermodynamics | Identify the correct statement regarding a spontaneous process : | [{"identifier": "A", "content": "For a spontaneous process in an isolated system, the change in entropy is positive"}, {"identifier": "B", "content": "Endothermic processes are never spontaneous"}, {"identifier": "C", "content": "Exothermic processes are always spontaneous "}, {"identifier": "D", "content": "Lowering o... | ["A"] | null | Spontaneity of reaction depends on tendency to acquire minimum energy state and maximum randomness. For a spontaneous process in an isolated system the change in entropy is positive. | mcq | aieee-2007 | 4,306 |
J3nQebb8KPSS3bvn4VTDj | chemistry | thermodynamics | second-law-of-thermodynamics | Two blocks of the same metal having same mass and at temperature T<sub>1</sub> and T<sub>2</sub>, respectively, are brought in contact with each other and allowed to attain thermal equilibrium at constant pressure. The change in entropy, $$\Delta $$S, for this process is : | [{"identifier": "A", "content": "2C<sub>p</sub> In $$\\left[ {{{{{\\left( {{T_1} + {T_2}} \\right)}^{{1 \\over 2}}}} \\over {{T_1}{T_2}}}} \\right]$$"}, {"identifier": "B", "content": "2C<sub>p</sub> In $$\\left[ {{{\\left( {{T_1} + {T_2}} \\right)} \\over {2{T_1}{T_2}}}} \\right]$$"}, {"identifier": "C", "content": "C... | ["C"] | null | When two blocks comes in contact with each other and attain thermal equilibrium then
<br><br>final temperature of the blocks,
<br><br>T<sub>f</sub> = $${{{T_1} + {T_2}} \over 2}$$
<br><br>$$\Delta $$S = $$\Delta $$S<sub>1</sub> + $$\Delta $$S<sub>2</sub>
<br><br>= C<sub>p</sub> $$\ln \left( {{{{T_f}} \over {{T_1}}}} \r... | mcq | jee-main-2019-online-11th-january-morning-slot | 4,309 |
d3f4lJ3VjKthAZZtmx7k9k2k5llm4zr | chemistry | thermodynamics | second-law-of-thermodynamics | The true statement amongst the following is : | [{"identifier": "A", "content": "S is a function of temperature but $$\\Delta $$S is not\na function of temperature."}, {"identifier": "B", "content": "Both S and $$\\Delta $$S are not functions of\ntemperature."}, {"identifier": "C", "content": "Both $$\\Delta $$S and S are functions of temperature."}, {"identifier": ... | ["C"] | null | $$\Delta S = \int {{{d{q_{rev}}} \over T}} $$
<br><br>S = Kln(w)
<br><br>Both entropy and change in entropy are
function of temperature. | mcq | jee-main-2020-online-9th-january-evening-slot | 4,310 |
1lgrlronp | chemistry | thermodynamics | second-law-of-thermodynamics | <p>One mole of an ideal gas at $$350 \mathrm{~K}$$ is in a $$2.0 \mathrm{~L}$$ vessel of thermally conducting walls, which are in contact with the surroundings. It undergoes isothermal reversible expansion from 2.0 L to $$3.0 \mathrm{~L}$$ against a constant pressure of $$4 \mathrm{~atm}$$. The change in entropy of the... | [] | null | 3 | <p>For an isothermal, reversible process, the change in entropy (ΔS) of the system can be calculated using the formula:</p>
<p>$ \Delta S = nR \ln\left(\frac{V_2}{V_1}\right) $</p>
<p>where (n) is the number of moles, (R) is the gas constant, and (V_2) and (V_1) are the final and initial volumes, respectively.</p>
<p>S... | integer | jee-main-2023-online-12th-april-morning-shift | 4,311 |
kt4Qsk8Vq7TCfuAU | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | The two lines $$x=ay+b,z=cy+d$$ and $$x = a'y + b',z = c'y + d'$$ will be perpendicular, if and only if : | [{"identifier": "A", "content": "$$aa' + cc' + 1 = 0$$ "}, {"identifier": "B", "content": "$$aa' + bb'cc' + 1 = 0$$ "}, {"identifier": "C", "content": "$$aa' + bb'cc' = 0$$ "}, {"identifier": "D", "content": "$$\\left( {a + a'} \\right)\\left( {b + b'} \\right) + \\left( {c + c'} \\right) = 0$$ "}] | ["A"] | null | $${{x - b} \over a} = {y \over 1} = {{z - d} \over c};$$
<br/><br/>$${{x - b'} \over {a'}}$$
$$ = {y \over 1} = {{z - d'} \over c'}$$
<br><br>For perpenedicularity of lines $$aa' + 1 + cc' = 0$$ | mcq | aieee-2003 | 4,312 |
UTyglZ3FzG2VUgaZ | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | A line makes the same angle $$\theta $$, with each of the $$x$$ and $$z$$ axis.
<br/><br/>If the angle $$\beta \,$$, which it makes with y-axis, is such that $$\,{\sin ^2}\beta = 3{\sin ^2}\theta ,$$ then $${\cos ^2}\theta $$ equals : | [{"identifier": "A", "content": "$${2 \\over 5}$$ "}, {"identifier": "B", "content": "$${1 \\over 5}$$"}, {"identifier": "C", "content": "$${3 \\over 5}$$"}, {"identifier": "D", "content": "$${2 \\over 3}$$"}] | ["C"] | null | <b>Concept :</b> If a line makes the angle $$\alpha ,\beta ,\gamma $$ with x, y, z axis respectively then
$$${\cos ^2}\alpha + {\cos ^2}\beta + {\cos ^2}\gamma = 1$$$
<br><br>In this question given that the line makes angle θ with x and z-axis and β with y−axis.
<br><br>$$\therefore\: cos^2\theta+cos^2\beta+cos^2\th... | mcq | aieee-2004 | 4,313 |
YwetrlhmGeDvUihA | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | If a line makes an angle of $$\pi /4$$ with the positive directions of each of $$x$$-axis and $$y$$-axis, then the angle that the line makes with the positive direction of the $$z$$-axis is : | [{"identifier": "A", "content": "$${\\pi \\over 4}$$"}, {"identifier": "B", "content": "$${\\pi \\over 2}$$ "}, {"identifier": "C", "content": "$${\\pi \\over 6}$$"}, {"identifier": "D", "content": "$${\\pi \\over 3}$$"}] | ["B"] | null | Let the angle of line makes with the positive direction of $$z$$-axis is $$\alpha $$ direction cosines of line with the $$+ve$$ directions of $$x$$-axis, $$y$$-axis, and $$z$$-axis is $$l,$$ $$m,$$ $$n$$ respectively.
<br><br>$$\therefore$$ $$l = \cos {\pi \over 4},m = \cos {\pi \over 4},\,\,n = cos\,\alpha $$
<br>... | mcq | aieee-2007 | 4,314 |
6XCk3G13gwVOzXa9 | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | Let $$L$$ be the line of intersection of the planes $$2x+3y+z=1$$ and $$x+3y+2z=2.$$ If $$L$$ makes an angle $$\alpha $$ with the positive $$x$$-axis, then cos $$\alpha $$ equals | [{"identifier": "A", "content": "$$1$$ "}, {"identifier": "B", "content": "$${1 \\over {\\sqrt 2 }}$$ "}, {"identifier": "C", "content": "$${1 \\over {\\sqrt 3 }}$$"}, {"identifier": "D", "content": "$${1 \\over 2}$$ "}] | ["C"] | null | Let the direction cosines of line $$L$$ be $$l,m,n,$$
<br><br>then $$2l+3m+n=0$$ $$\,\,\,\,\,\,\,....\left( i \right)$$
<br><br>and $$l + 3m + 2n = 0\,\,\,\,\,\,\,\,\,\,....\left( {ii} \right)$$
<br><br>on solving equation $$(i)$$ and $$(ii),$$ we get
<br><br>$${l \over {6 - 3}} = {m \over {1 - 4}} = {n \over {6 - 3... | mcq | aieee-2007 | 4,315 |
liW5CBWFat8KJOch | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | The projections of a vector on the three coordinate axis are $$6,-3,2$$ respectively. The direction cosines of the vector are : | [{"identifier": "A", "content": "$${6 \\over 5},{{ - 3} \\over 5},{2 \\over 5}$$ "}, {"identifier": "B", "content": "$${6 \\over 7 },{{ - 3} \\over 7},{2 \\over 7}$$"}, {"identifier": "C", "content": "$${- 6 \\over 7 },{{ - 3} \\over 7},{2 \\over 7}$$ "}, {"identifier": "D", "content": "$$6, -3, 2$$ "}] | ["B"] | null | Let $$P\left( {{x_1},{y_1},{z_1}} \right)$$ and $$Q\left( {{x_2},{y_2},{z_2}} \right)$$ be the initial and final points of the vector whose projections on the three coordinates axes are $${6, - 3,2}$$ then
<br><br>$${x_2} - {x_1}, = 6;\,\,{y_2} - {y_1} = - 3;\,\,{z_2} - {z_1} = 2$$
<br><br>So that directions ratios o... | mcq | aieee-2009 | 4,316 |
4yK9enk8xtYf7Hy4fE6wX | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | ABC is a triangle in a plane with vertices
<br/><br> A(2, 3, 5), B(−1, 3, 2) and C($$\lambda $$, 5, $$\mu $$).
<br/><br/>If the median through A is equally inclined to the coordinate axes, then the value of ($$\lambda $$<sup>3</sup> + $$\mu $$<sup>3</sup> + 5) is : </br> | [{"identifier": "A", "content": "1130"}, {"identifier": "B", "content": "1348"}, {"identifier": "C", "content": "676"}, {"identifier": "D", "content": "1077"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267089/exam_images/rmtgi7eihcbphpv9sdfi.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2016 (Online) 10th April Morning Slot Mathematics - 3D Geometry Question 270 English Explanation">
<br><br>DR'... | mcq | jee-main-2016-online-10th-april-morning-slot | 4,319 |
jUxJqw5CxzEzFWDDqXW8u | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | An angle between the lines whose direction cosines are gien by the equations,
<br/>$$l$$ + 3m + 5n = 0 and 5$$l$$m $$-$$ 2mn + 6n$$l$$ = 0, is : | [{"identifier": "A", "content": "$${\\cos ^{ - 1}}\\left( {{1 \\over 3}} \\right)$$"}, {"identifier": "B", "content": "$${\\cos ^{ - 1}}\\left( {{1 \\over 4}} \\right)$$"}, {"identifier": "C", "content": "$${\\cos ^{ - 1}}\\left( {{1 \\over 6}} \\right)$$"}, {"identifier": "D", "content": "$${\\cos ^{ - 1}}\\left( {{1 ... | ["C"] | null | Given
<br><br>l + 3m + 5n = 0
<br><br>and 5$$l$$m $$-$$ 2mn + 6n$$l$$ = 0
<br><br>From eq. (1) we have
<br><br>$$l$$ = $$-$$ 3m $$-$$ 5n
<br><br>Put the value of $$l$$ in eq. (2), we get ;
<br><br>5 ($$-$$3m $$-$$5n) m $$-$$ 2mn + 6n ($$-$$ 3m $$-$$ 5n) = 0
<br><br>$$ \Rightarrow $$ 15m<sup>2</sup> + 45mn + 3... | mcq | jee-main-2018-online-15th-april-evening-slot | 4,320 |
3FhkSd7tirtXKNl5jLwyP | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | If a point R(4, y, z) lies on the line segment joining
the points P(2, –3, 4) and Q(8, 0, 10), then the
distance of R from the origin is : | [{"identifier": "A", "content": "$$2 \\sqrt {14}$$"}, {"identifier": "B", "content": "$$ \\sqrt {53}$$"}, {"identifier": "C", "content": "$$2 \\sqrt {21}$$"}, {"identifier": "D", "content": "6"}] | ["A"] | null | Equation of PQ is
<br><br> $${{x - 2} \over {8 - 2}} = {{y + 3} \over {0 - \left( { - 3} \right)}} = {{z - 4} \over {10 - 4}}$$
<br><br>$$ \Rightarrow $$ $${{x - 2} \over 6} = {{y + 3} \over 3} = {{z - 4} \over 6}$$
<br><br>Point R (4, y, z) lies on this
<br><br>$$ \therefore $$ $${{4 - 2} \over 6} = {{y + 3} \over 3} ... | mcq | jee-main-2019-online-8th-april-evening-slot | 4,321 |
5BKZvRMs9hDCERctl67k9k2k5iu7qri | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | The projection of the line segment joining the
points (1, –1, 3) and (2, –4, 11) on the line
joining the points (–1, 2, 3) and (3, –2, 10)
is ____________. | [] | null | 8 | Let A (1, – 1, 3), B(2, – 4, 11), C (–1, 2, 3) & D (3, –2, 10)
<br><br>$$ \therefore $$ $$\overrightarrow {AB} = \widehat i - 3\widehat j + 8\widehat k$$
<br><br>$$ \Rightarrow $$ $$\overrightarrow {CD} = 4\widehat i - 4\widehat j + 7\widehat k$$
<br><br>Projection of $$\overrightarrow {AB} $$ on $$\overrightarro... | integer | jee-main-2020-online-9th-january-morning-slot | 4,322 |
rAho8VIbIc91mUekGJ1kls51pef | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | Let $$\alpha$$ be the angle between the lines whose direction cosines satisfy the equations l + m $$-$$ n = 0 and l<sup>2</sup> + m<sup>2</sup> $$-$$ n<sup>2</sup> = 0. Then the value of sin<sup>4</sup>$$\alpha$$ + cos<sup>4</sup>$$\alpha$$ is : | [{"identifier": "A", "content": "$${{3 \\over 8}}$$"}, {"identifier": "B", "content": "$${{3 \\over 4}}$$"}, {"identifier": "C", "content": "$${{1 \\over 2}}$$"}, {"identifier": "D", "content": "$${{5 \\over 8}}$$"}] | ["D"] | null | $${l^2} + {m^2} + {n^2} = 1$$<br><br>$$ \therefore $$ $$2{n^2} = 1 $$ ($$ \because $$ l<sup>2</sup> + m<sup>2</sup> $$-$$ n<sup>2</sup> = 0)
<br><br>$$\Rightarrow n = \pm {1 \over {\sqrt 2 }}$$<br><br>$$ \therefore $$ $${l^2} + {m^2} = {1 \over 2}$$ & $$l + m = {1 \over {\sqrt 2 }}$$<br><br>$$ \Rightarrow {1 \over... | mcq | jee-main-2021-online-25th-february-morning-slot | 4,323 |
1ktfvxn17 | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m $$-$$ n = 0 and mn + nl + lm = 0, is : | [{"identifier": "A", "content": "$${\\pi \\over 2}$$"}, {"identifier": "B", "content": "$$\\pi - {\\cos ^{ - 1}}\\left( {{4 \\over 9}} \\right)$$"}, {"identifier": "C", "content": "$${\\cos ^{ - 1}}\\left( {{8 \\over 9}} \\right)$$"}, {"identifier": "D", "content": "$${\\pi \\over 3}$$"}] | ["A"] | null | n = 2 (l + m)<br><br>lm + n(l + m) = 0<br><br>lm + 2(l + m)<sup>2</sup> = 0<br><br>2l<sup>2</sup> + 2m<sup>2</sup> + 5ml = 0<br><br>$$2{\left( {{l \over m}} \right)^2} + 2 + 5\left( {{l \over m}} \right) = 0$$<br><br>2t<sup>2</sup> + 5t + 2 = 0<br><br>(t + 2)(2t + 1) = 0<br><br>$$ \Rightarrow t = - 2; - {1 \over 2}$$<... | mcq | jee-main-2021-online-27th-august-evening-shift | 4,324 |
1l57oj6hy | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | <p>If two straight lines whose direction cosines are given by the relations $$l + m - n = 0$$, $$3{l^2} + {m^2} + cnl = 0$$ are parallel, then the positive value of c is :</p> | [{"identifier": "A", "content": "6"}, {"identifier": "B", "content": "4"}, {"identifier": "C", "content": "3"}, {"identifier": "D", "content": "2"}] | ["A"] | null | <p>Given that the direction cosines satisfy $l + m - n = 0$, we find that $n = l + m$.</p>
<p>The other equation is $3l^2 + m^2 + cnl = 0$, and substituting $n = l + m$ gives $3l^2 + m^2 + cl(l + m) = 0$.</p>
<p>This simplifies to $(3 + c)l^2 + clm + m^2 = 0$.</p>
<p>As the lines are parallel, they share the same direc... | mcq | jee-main-2022-online-27th-june-morning-shift | 4,325 |
1l6m6hocr | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | <p>Let $$\mathrm{P}(-2,-1,1)$$ and $$\mathrm{Q}\left(\frac{56}{17}, \frac{43}{17}, \frac{111}{17}\right)$$ be the vertices of the rhombus PRQS. If the direction ratios of the diagonal RS are $$\alpha,-1, \beta$$, where both $$\alpha$$ and $$\beta$$ are integers of minimum absolute values, then $$\alpha^{2}+\beta^{2}$$ ... | [] | null | 450 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l7rb45xm/29b2975e-d397-4ba9-941a-4cc0bd7b15f1/c362a6a0-2e7f-11ed-8702-156c00ced081/file-1l7rb45xn.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l7rb45xm/29b2975e-d397-4ba9-941a-4cc0bd7b15f1/c362a6a0-2e7f-11ed-8702-156c00ced081... | integer | jee-main-2022-online-28th-july-morning-shift | 4,326 |
lsam59tf | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | Consider a $\triangle A B C$ where $A(1,3,2), B(-2,8,0)$ and $C(3,6,7)$. If the angle bisector of $\angle B A C$ meets
the line $B C$ at $D$, then the length of the projection of the vector $\overrightarrow{A D}$ on the vector $\overrightarrow{A C}$ is : | [{"identifier": "A", "content": "$\\frac{37}{2 \\sqrt{38}}$"}, {"identifier": "B", "content": "$\\sqrt{19}$"}, {"identifier": "C", "content": "$\\frac{39}{2 \\sqrt{38}}$"}, {"identifier": "D", "content": "$\\frac{\\sqrt{38}}{2}$"}] | ["A"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsqeg6dq/195e875b-1d41-47ba-b7a7-6f56da027c9a/8f22c6e0-cdc0-11ee-9f50-677e7e372eae/file-6y3zli1lsqeg6dr.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsqeg6dq/195e875b-1d41-47ba-b7a7-6f56da027c9a/8f22c6e0-cdc0-11ee-9f... | mcq | jee-main-2024-online-1st-february-evening-shift | 4,327 |
jaoe38c1lseyroz7 | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | <p>Let $$O$$ be the origin and the position vectors of $$A$$ and $$B$$ be $$2 \hat{i}+2 \hat{j}+\hat{k}$$ and $$2 \hat{i}+4 \hat{j}+4 \hat{k}$$ respectively. If the internal bisector of $$\angle \mathrm{AOB}$$ meets the line $$\mathrm{AB}$$ at $$\mathrm{C}$$, then the length of $$O C$$ is</p> | [{"identifier": "A", "content": "$$\\frac{3}{2} \\sqrt{34}$$\n"}, {"identifier": "B", "content": "$$\\frac{2}{3} \\sqrt{31}$$\n"}, {"identifier": "C", "content": "$$\\frac{2}{3} \\sqrt{34}$$\n"}, {"identifier": "D", "content": "$$\\frac{3}{2} \\sqrt{31}$$"}] | ["C"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lt2yowkb/31073c70-5b0c-4f0f-80c0-62ea5ac61070/2035eab0-d4a9-11ee-bdd1-01c80c3e2d9a/file-1lt2yowkc.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lt2yowkb/31073c70-5b0c-4f0f-80c0-62ea5ac61070/2035eab0-d4a9-11ee-bdd1-01c80c3e2d9a... | mcq | jee-main-2024-online-29th-january-morning-shift | 4,328 |
jaoe38c1lsfkjy12 | maths | 3d-geometry | direction-cosines-and-direction-ratios-of-a-line | <p>Let $$\mathrm{P}(3,2,3), \mathrm{Q}(4,6,2)$$ and $$\mathrm{R}(7,3,2)$$ be the vertices of $$\triangle \mathrm{PQR}$$. Then, the angle $$\angle \mathrm{QPR}$$ is</p> | [{"identifier": "A", "content": "$$\\cos ^{-1}\\left(\\frac{7}{18}\\right)$$\n"}, {"identifier": "B", "content": "$$\\frac{\\pi}{6}$$\n"}, {"identifier": "C", "content": "$$\\cos ^{-1}\\left(\\frac{1}{18}\\right)$$\n"}, {"identifier": "D", "content": "$$\\frac{\\pi}{3}$$"}] | ["D"] | null | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsr8wgd3/6b24122f-fe39-4086-be4a-889687b965f8/a5aaee70-ce37-11ee-9412-cd4f9c6f2c40/file-6y3zli1lsr8wgd4.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsr8wgd3/6b24122f-fe39-4086-be4a-889687b965f8/a5aaee70-ce37-11ee... | mcq | jee-main-2024-online-29th-january-evening-shift | 4,329 |
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