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scibench-atkins-p1.31
|
The composition of the atmosphere is approximately 80 per cent nitrogen and 20 per cent oxygen by mass. At what height above the surface of the Earth would the atmosphere become 90 per cent nitrogen and 10 per cent oxygen by mass? Assume that the temperature of the atmosphere is constant at $25^{\circ} \mathrm{C}$. What is the pressure of the atmosphere at that height?
Respond in this unit: $\mathrm{atm}$
|
0.0029
|
scibench-thermo-11.25
|
The half-cell potential for the reaction $\mathrm{O}_2(g)+4 \mathrm{H}^{+}(a q)+4 \mathrm{e}^{-} \rightarrow 2 \mathrm{H}_2 \mathrm{O}(l)$ is $+1.03 \mathrm{~V}$ at $298.15 \mathrm{~K}$ when $a_{\mathrm{O}_2}=1.00$. Determine $a_{\mathrm{H}^{+}}$
Respond in this unit: $10^{-4}$
|
4.16
|
scibench-thermo-9.9
|
The volatile liquids $A$ and $\mathrm{B}$, for which $P_A^*=165$ Torr and $P_B^*=85.1$ Torr are confined to a piston and cylinder assembly. Initially, only the liquid phase is present. As the pressure is reduced, the first vapor is observed at a total pressure of 110 . Torr. Calculate $x_{\mathrm{A}}$
Respond in this unit:
|
0.312
|
scibench-atkins-e1.12(a)
|
The densities of air at $-85^{\circ} \mathrm{C}, 0^{\circ} \mathrm{C}$, and $100^{\circ} \mathrm{C}$ are $1.877 \mathrm{~g} \mathrm{dm}^{-3}, 1.294 \mathrm{~g}$ $\mathrm{dm}^{-3}$, and $0.946 \mathrm{~g} \mathrm{dm}^{-3}$, respectively. From these data, and assuming that air obeys Charles's law, determine a value for the absolute zero of temperature in degrees Celsius.
Respond in this unit: $^{\circ} \mathrm{C}$
|
-273
|
scibench-thermo-10.6
|
Calculate the mean ionic activity of a $0.0350 \mathrm{~m} \mathrm{Na}_3 \mathrm{PO}_4$ solution for which the mean activity coefficient is 0.685 .
Respond in this unit:
|
0.0547
|
scibench-fund-7.08
|
When the force on an object depends on the position of the object, we cannot find the work done by it on the object by simply multiplying the force by the displacement. The reason is that there is no one value for the force-it changes. So, we must find the work in tiny little displacements and then add up all the work results. We effectively say, "Yes, the force varies over any given tiny little displacement, but the variation is so small we can approximate the force as being constant during the displacement." Sure, it is not precise, but if we make the displacements infinitesimal, then our error becomes infinitesimal and the result becomes precise. But, to add an infinite number of work contributions by hand would take us forever, longer than a semester. So, we add them up via an integration, which allows us to do all this in minutes (much less than a semester).
Force $\vec{F}=\left(3 x^2 \mathrm{~N}\right) \hat{\mathrm{i}}+(4 \mathrm{~N}) \hat{\mathrm{j}}$, with $x$ in meters, acts on a particle, changing only the kinetic energy of the particle. How much work is done on the particle as it moves from coordinates $(2 \mathrm{~m}, 3 \mathrm{~m})$ to $(3 \mathrm{~m}, 0 \mathrm{~m})$ ?
Respond in this unit: J
|
7.0
|
scibench-class-13.6
|
A string is set into motion by being struck at a point $L/4$ from one end by a triangular hammer. The initial velocity is greatest at $x = L/4$ and decreases linearly to zero at $x = 0$ and $x = L/2$. The region $L/2 \leq x \leq L$ is initially undisturbed. Determine the subsequent motion of the string. How many decibels down from the fundamental are the second harmonics?'
Respond in this unit: dB
|
4.4
|
scibench-matter-73.4(a)
|
The equilibrium pressure of $\mathrm{O}_2$ over solid silver and silver oxide, $\mathrm{Ag}_2 \mathrm{O}$, at $298 \mathrm{~K}$ is $11.85 \mathrm{~Pa}$. Calculate the standard Gibbs energy of formation of $\mathrm{Ag}_2 \mathrm{O}(\mathrm{s})$ at $298 \mathrm{~K}$.
Respond in this unit: $\mathrm{~kJ} \mathrm{~mol}^{-1}$
|
-11.2
|
scibench-class-9.22B.
|
A deuteron (nucleus of deuterium atom consisting of a proton and a neutron) with speed $14.9$ km / s collides elastically with a neutron at rest. Use the approximation that the deuteron is twice the mass of the neutron. If the deuteron is scattered through a LAB angle $\psi = 10^\circ$, the final speed of the deuteron is $v_d = 14.44$ km / s and the final speed of the neutron is $v_n = 5.18$ km / s. Another set of solutions for the final speed is $v_d = 5.12$ km / s for the deuteron and $v_n = 19.79$ km / s for the neutron. What is the maximum possible scattering angle of the deuteron?
Respond in this unit: $^\circ$
|
30
|
scibench-chemmc-1-11
|
$$
\text {Calculate the energy of a photon for a wavelength of } 100 \mathrm{pm} \text { (about one atomic diameter). }
$$
Respond in this unit: $10^{-15} \mathrm{~J}$
|
2
|
scibench-thermo-6.12
|
For the reaction $\mathrm{C}($ graphite $)+\mathrm{H}_2 \mathrm{O}(g) \rightleftharpoons$ $\mathrm{CO}(g)+\mathrm{H}_2(g), \Delta H_R^{\circ}=131.28 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at $298.15 \mathrm{~K}$. Use the values of $C_{P, m}^{\circ}$ at $298.15 \mathrm{~K}$ in the data tables to calculate $\Delta H_R^{\circ}$ at $125.0^{\circ} \mathrm{C}$.
Respond in this unit: $\mathrm{~kJ} \mathrm{~mol}^{-1}$
|
132.9
|
scibench-atkins-e3.12(a)
|
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. The standard enthalpy of combustion of solid phenol $\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{OH}\right)$ is $-3054 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at $298 \mathrm{~K}_{\text {and }}$ its standard molar entropy is $144.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$. Calculate the standard Gibbs energy of formation of phenol at $298 \mathrm{~K}$.
Respond in this unit: $\mathrm{kJ} \mathrm{mol}^{-1}$
|
-50
|
scibench-fund-Question22.63
|
A spherical water drop $1.20 \mu \mathrm{m}$ in diameter is suspended in calm air due to a downward-directed atmospheric electric field of magnitude $E=462 \mathrm{~N} / \mathrm{C}$. What is the magnitude of the gravitational force on the drop?
Respond in this unit: $10^{-15} \mathrm{~N} $
|
8.87
|
scibench-class-9.42B.
|
A steel ball of velocity $5$ m/s strikes a smooth, heavy steel plate at an angle of $30^\circ$ from the normal. If the coefficient of restitution is 0.8, at what angle from the normal does the steel ball bounce off the plate?
Respond in this unit: $^\circ$
|
36
|
scibench-class-5.5
|
Calculate the maximum height change in the ocean tides caused by the Moon.
Respond in this unit: $\mathrm{m}$
|
0.54
|
scibench-atkins-p1.1
|
Recent communication with the inhabitants of Neptune has revealed that they have a Celsius-type temperature scale, but based on the melting point $(0^{\circ} \mathrm{N})$ and boiling point $(100^{\circ} \mathrm{N})$ of their most common substance, hydrogen. Further communications have revealed that the Neptunians know about perfect gas behaviour and they find that, in the limit of zero pressure, the value of $p V$ is $28 \mathrm{dm}^3$ atm at $0^{\circ} \mathrm{N}$ and $40 \mathrm{dm}^3$ atm at $100^{\circ} \mathrm{N}$. What is the value of the absolute zero of temperature on their temperature scale?
Respond in this unit: $^{\circ} \mathrm{N}$
|
-233
|
scibench-thermo-9.22
|
The densities of pure water and ethanol are 997 and $789 \mathrm{~kg} \mathrm{~m}^{-3}$, respectively. For $x_{\text {ethanol }}=0.35$, the partial molar volumes of ethanol and water are 55.2 and $17.8 \times 10^{-3} \mathrm{~L} \mathrm{~mol}^{-1}$, respectively. Calculate the change in volume relative to the pure components when $2.50 \mathrm{~L}$ of a solution with $x_{\text {ethanol }}=0.35$ is prepared.
Respond in this unit: $\mathrm{~L}$
|
-0.10
|
scibench-fund-Question23.13
|
The electric field in a certain region of Earth's atmosphere is directed vertically down. At an altitude of $300 \mathrm{~m}$ the field has magnitude $60.0 \mathrm{~N} / \mathrm{C}$; at an altitude of $200 \mathrm{~m}$, the magnitude is $100 \mathrm{~N} / \mathrm{C}$. Find the net amount of charge contained in a cube $100 \mathrm{~m}$ on edge, with horizontal faces at altitudes of 200 and $300 \mathrm{~m}$.
Respond in this unit: $\mu \mathrm{C}$
|
3.54
|
scibench-thermo-8.39
|
At $298.15 \mathrm{~K}, \Delta G_f^{\circ}(\mathrm{HCOOH}, g)=-351.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\Delta G_f^{\circ}(\mathrm{HCOOH}, l)=-361.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Calculate the vapor pressure of formic acid at this temperature.
Respond in this unit: $10^3 \mathrm{~Pa}$
|
1.51
|
scibench-fund-4.06
|
"Top gun" pilots have long worried about taking a turn too tightly. As a pilot's body undergoes centripetal acceleration, with the head toward the center of curvature, the blood pressure in the brain decreases, leading to loss of brain function.
There are several warning signs. When the centripetal acceleration is $2 g$ or $3 g$, the pilot feels heavy. At about $4 g$, the pilot's vision switches to black and white and narrows to "tunnel vision." If that acceleration is sustained or increased, vision ceases and, soon after, the pilot is unconscious - a condition known as $g$-LOC for " $g$-induced loss of consciousness."
What is the magnitude of the acceleration, in $g$ units, of a pilot whose aircraft enters a horizontal circular turn with a velocity of $\vec{v}_i=(400 \hat{\mathrm{i}}+500 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s}$ and $24.0 \mathrm{~s}$ later leaves the turn with a velocity of $\vec{v}_f=(-400 \hat{\mathrm{i}}-500 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s}$ ?
Respond in this unit: $\mathrm{m} / \mathrm{s}^2$
|
83.81
|
scibench-matter-10.1(a)
|
Suppose that the junction between two semiconductors can be represented by a barrier of height $2.0 \mathrm{eV}$ and length $100 \mathrm{pm}$. Calculate the transmission probability of an electron with energy $1.5 \mathrm{eV}$.
Respond in this unit:
|
0.8
|
scibench-quan-10.1
|
Calculate the magnitude of the spin angular momentum of a proton. Give a numerical answer.
Respond in this unit: $10^{-35} \mathrm{~J} \mathrm{~s}$
|
9.13
|
scibench-fund-Question21.59
|
What is the total charge in coulombs of $75.0 \mathrm{~kg}$ of electrons?
Respond in this unit: $10^{13} \mathrm{C}$
|
-1.32
|
scibench-thermo-12.8
|
Imagine tossing a coin 50 times. What are the probabilities of observing heads 25 times (i.e., 25 successful experiments)?
Respond in this unit:
|
0.11
|
scibench-class-2.2
|
If the coefficient of static friction between the block and plane in the previous example is $\mu_s=0.4$, at what angle $\theta$ will the block start sliding if it is initially at rest?
Respond in this unit: $^{\circ}$
|
22
|
scibench-thermo-1.6
|
One liter of fully oxygenated blood can carry 0.18 liters of $\mathrm{O}_2$ measured at $T=298 \mathrm{~K}$ and $P=1.00 \mathrm{~atm}$. Calculate the number of moles of $\mathrm{O}_2$ carried per liter of blood. Hemoglobin, the oxygen transport protein in blood has four oxygen binding sites. How many hemoglobin molecules are required to transport the $\mathrm{O}_2$ in $1.0 \mathrm{~L}$ of fully oxygenated blood?
Respond in this unit: $10^{21}$
|
1.11
|
scibench-fund-Question22.5
|
A charged particle produces an electric field with a magnitude of $2.0 \mathrm{~N} / \mathrm{C}$ at a point that is $50 \mathrm{~cm}$ away from the particle. What is the magnitude of the particle's charge?
Respond in this unit: $\mathrm{pC}$
|
56
|
scibench-atkins-e2.1(a)(a)
|
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Calculate the work needed for a $65 \mathrm{~kg}$ person to climb through $4.0 \mathrm{~m}$ on the surface of the Earth.
Respond in this unit: $\mathrm{J}$
|
2600
|
scibench-quan-14.5
|
For $\mathrm{NaCl}, R_e=2.36 Å$. The ionization energy of $\mathrm{Na}$ is $5.14 \mathrm{eV}$, and the electron affinity of $\mathrm{Cl}$ is $3.61 \mathrm{eV}$. Use the simple model of $\mathrm{NaCl}$ as a pair of spherical ions in contact to estimate $D_e$. [One debye (D) is $3.33564 \times 10^{-30} \mathrm{C} \mathrm{m}$.]
Respond in this unit: $\mathrm{eV}$
|
4.56
|
scibench-chemmc-5-13
|
In the infrared spectrum of $\mathrm{H}^{127} \mathrm{I}$, there is an intense line at $2309 \mathrm{~cm}^{-1}$. Calculate the force constant of $\mathrm{H}^{127} \mathrm{I}$.
Respond in this unit: $ \mathrm{~N} \cdot \mathrm{m}^{-1}$
|
313
|
scibench-atkins-e2.31(a)(a)
|
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. For a van der Waals gas, $\pi_T=a / V_{\mathrm{m}}^2$. Calculate $\Delta U_{\mathrm{m}}$ for the isothermal expansion of nitrogen gas from an initial volume of $1.00 \mathrm{dm}^3$ to $24.8 \mathrm{dm}^3$ at $298 \mathrm{~K}$.
Respond in this unit: $\mathrm{J} \mathrm{mol}^{-1}$
|
131
|
scibench-atkins-e2.7(a)
|
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. A strip of magnesium of mass $15 \mathrm{~g}$ is placed in a beaker of dilute hydrochloric acid. Calculate the work done by the system as a result of the reaction. The atmospheric pressure is 1.0 atm and the temperature $25^{\circ} \mathrm{C}$.
Respond in this unit: $\text{kJ}$
|
-1.5
|
scibench-atkins-20.2
|
Caesium (m.p. $29^{\circ} \mathrm{C}$, b.p. $686^{\circ} \mathrm{C}$ ) was introduced into a container and heated to $500^{\circ} \mathrm{C}$. When a hole of diameter $0.50 \mathrm{~mm}$ was opened in the container for $100 \mathrm{~s}$, a mass loss of $385 \mathrm{mg}$ was measured. Calculate the vapour pressure of liquid caesium at $500 \mathrm{~K}$.
Respond in this unit: $\mathrm{kPa}$
|
8.7
|
scibench-atkins-e1.1(a)(b)
|
What pressure would $131 \mathrm{g}$ of xenon gas in a vessel of volume $1.0 \mathrm{dm}^3$ exert at $25^{\circ} \mathrm{C}$ if it behaved as a van der Waals gas?
Respond in this unit: $\mathrm{atm}$
|
22
|
scibench-thermo-13.22
|
The vibrational frequency of $I_2$ is $208 \mathrm{~cm}^{-1}$. At what temperature will the population in the first excited state be half that of the ground state?
Respond in this unit: $\mathrm{~K}$
|
432
|
scibench-thermo-18.37
|
The activation energy for a reaction is $50 . \mathrm{J} \mathrm{mol}^{-1}$. Determine the effect on the rate constant for this reaction with a change in temperature from $273 \mathrm{~K}$ to $298 \mathrm{~K}$.
Respond in this unit:
|
0.15
|
scibench-thermo-9.7
|
The osmotic pressure of an unknown substance is measured at $298 \mathrm{~K}$. Determine the molecular weight if the concentration of this substance is $31.2 \mathrm{~kg} \mathrm{~m}^{-3}$ and the osmotic pressure is $5.30 \times 10^4 \mathrm{~Pa}$. The density of the solution is $997 \mathrm{~kg} \mathrm{~m}^{-3}$.
Respond in this unit: $10^3 \mathrm{~g} \mathrm{~mol}^{-1}$
|
1.45
|
scibench-atkins-e3.14(a)
|
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the maximum non-expansion work per mole that may be obtained from a fuel cell in which the chemical reaction is the combustion of methane at $298 \mathrm{~K}$.
Respond in this unit: $\mathrm{kJ} \mathrm{mol}^{-1}$
|
817.90
|
scibench-atkins-e1.14(a)(b)
|
Express the van der Waals parameters $b=0.0226 \mathrm{dm}^3 \mathrm{~mol}^{-1}$ in SI base units.
Respond in this unit: $\mathrm{~m}^3 \mathrm{~mol}^{-1}$
|
0.0000226
|
scibench-atkins-e3.16(a)
|
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Suppose that $3.0 \mathrm{mmol} \mathrm{N}_2$ (g) occupies $36 \mathrm{~cm}^3$ at $300 \mathrm{~K}$ and expands to $60 \mathrm{~cm}^3$. Calculate $\Delta G$ for the process.
Respond in this unit: $\text{J}$
|
-3.8
|
scibench-atkins-e1.18(a)(c)
|
A vessel of volume $22.4 \mathrm{dm}^3$ contains $2.0 \mathrm{~mol} \mathrm{H}_2$ and $1.0 \mathrm{~mol} \mathrm{~N}_2$ at $273.15 \mathrm{~K}$. Calculate their total pressure.
Respond in this unit: $\mathrm{atm}$
|
3.0
|
scibench-fund-Question22.3
|
The nucleus of a plutonium-239 atom contains 94 protons. Assume that the nucleus is a sphere with radius $6.64 \mathrm{fm}$ and with the charge of the protons uniformly spread through the sphere. At the surface of the nucleus, what are the magnitude of the electric field produced by the protons?
Respond in this unit: $10^{21} \mathrm{~N} / \mathrm{C}$
|
3.07
|
scibench-thermo-2.13
|
A system consisting of $82.5 \mathrm{~g}$ of liquid water at $300 . \mathrm{K}$ is heated using an immersion heater at a constant pressure of 1.00 bar. If a current of $1.75 \mathrm{~A}$ passes through the $25.0 \mathrm{ohm}$ resistor for 100 .s, what is the final temperature of the water?
Respond in this unit: $\mathrm{~K}$
|
322
|
scibench-quan-2.13
|
When an electron in a certain excited energy level in a one-dimensional box of length $2.00 Å$ makes a transition to the ground state, a photon of wavelength $8.79 \mathrm{~nm}$ is emitted. Find the quantum number of the initial state.
|
4
|
scibench-atkins-e3.15(a)(b)
|
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the Carnot efficiency of a modern steam turbine that operates with steam at $300^{\circ} \mathrm{C}$ and discharges at $80^{\circ} \mathrm{C}$.
Respond in this unit:
|
0.38
|
scibench-chemmc-1-15
|
A helium-neon laser (used in supermarket scanners) emits light at $632.8 \mathrm{~nm}$. Calculate the frequency of this light.
Respond in this unit: $10^{14} \mathrm{~Hz}$
|
4.738
|
scibench-fund-Question21.3
|
What must be the distance between point charge $q_1=$ $26.0 \mu \mathrm{C}$ and point charge $q_2=-47.0 \mu \mathrm{C}$ for the electrostatic force between them to have a magnitude of $5.70 \mathrm{~N}$ ?
Respond in this unit: m
|
1.39
|
scibench-thermo-14.6
|
Imagine gaseous $\mathrm{Ar}$ at $298 \mathrm{~K}$ confined to move in a two-dimensional plane of area $1.00 \mathrm{~cm}^2$. What is the value of the translational partition function?
Respond in this unit: $10^{17}$
|
3.9
|
scibench-thermo-14.5
|
At what temperature are there Avogadro's number of translational states available for $\mathrm{O}_2$ confined to a volume of 1000. $\mathrm{cm}^3$ ?
Respond in this unit: $\mathrm{~K}$
|
0.068
|
scibench-class-Problem8.12
|
Consider a comet moving in a parabolic orbit in the plane of Earth's orbit. If the distance of closest approach of the comet to the $\operatorname{Sun}$ is $\beta r_E$, where $r_E$ is the radius of Earth's (assumed) circular orbit and where $\beta<1$, show that the time the comet spends within the orbit of Earth is given by
$$
\sqrt{2(1-\beta)} \cdot(1+2 \beta) / 3 \pi \times 1 \text { year }
$$
If the comet approaches the Sun to the distance of the perihelion of Mercury, how many days is it within Earth's orbit?
Respond in this unit: $ \text { days }$
|
76
|
scibench-atkins-e3.17(a)
|
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. The change in the Gibbs energy of a certain constant-pressure process was found to fit the expression $\Delta G / \text{J}=-85.40+36.5(T / \text{K})$. Calculate the value of $\Delta S$ for the process.
Respond in this unit: $\mathrm{J} \mathrm{K}^{-1}$
|
-36.5
|
scibench-thermo-6.37
|
$\mathrm{N}_2 \mathrm{O}_3$ dissociates according to the equilibrium $\mathrm{N}_2 \mathrm{O}_3(\mathrm{~g}) \rightleftharpoons \mathrm{NO}_2(\mathrm{~g})+\mathrm{NO}(\mathrm{g})$. At $298 \mathrm{~K}$ and one bar pressure, the degree of dissociation defined as the ratio of moles of $\mathrm{NO}_2(g)$ or $\mathrm{NO}(g)$ to the moles of the reactant assuming no dissociation occurs is $3.5 \times 10^{-3}$. Calculate $\Delta G_R^{\circ}$ for this reaction.
Respond in this unit: $\mathrm{~kJ} \mathrm{~mol}^{-1}$
|
28
|
scibench-atkins-e1.16(a)
|
In an industrial process, nitrogen is heated to $500 \mathrm{~K}$ at a constant volume of $1.000 \mathrm{~m}^3$. The gas enters the container at $300 \mathrm{~K}$ and $100 \mathrm{~atm}$. The mass of the gas is $92.4 \mathrm{~kg}$. Use the van der Waals equation to determine the approximate pressure of the gas at its working temperature of $500 \mathrm{~K}$. For nitrogen, $a=1.352 \mathrm{dm}^6 \mathrm{~atm} \mathrm{~mol}^{-2}, b=0.0387 \mathrm{dm}^3 \mathrm{~mol}^{-1}$.
Respond in this unit: $\text{atm}$
|
140
|
scibench-thermo-6.13
|
At $298.15 \mathrm{~K}, \Delta G_f^{\circ}(\mathrm{C}$, graphite $)=0$, and $\Delta G_f^{\circ}(\mathrm{C}$, diamond $)=2.90 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Therefore, graphite is the more stable solid phase at this temperature at $P=P^{\circ}=1$ bar. Given that the densities of graphite and diamond are 2.25 and $3.52 \mathrm{~kg} / \mathrm{L}$, respectively, at what pressure will graphite and diamond be in equilibrium at $298.15 \mathrm{~K}$ ?
Respond in this unit: $10^4 \mathrm{bar}$
|
1.51
|
scibench-thermo-7.4
|
One mole of Ar initially at 310 . K undergoes an adiabatic expansion against a pressure $P_{\text {external }}=0$ from a volume of $8.5 \mathrm{~L}$ to a volume of $82.0 \mathrm{~L}$. Calculate the final temperature using the ideal gas
Respond in this unit: $\mathrm{~K}$
|
310
|
scibench-quan-16.1
|
Find the number of CSFs in a full CI calculation of $\mathrm{CH}_2 \mathrm{SiHF}$ using a 6-31G** basis set.
Respond in this unit: $10^{28} $
|
1.86
|
scibench-atkins-1.4
|
Estimate the molar volume of $\mathrm{CO}_2$ at $500 \mathrm{~K}$ and 100 atm by treating it as a van der Waals gas.
Respond in this unit: $\mathrm{dm}^3\mathrm{~mol}^{-1}$
|
0.366
|
scibench-fund-Question21.63
|
Two point charges of $30 \mathrm{nC}$ and $-40 \mathrm{nC}$ are held fixed on an $x$ axis, at the origin and at $x=72 \mathrm{~cm}$, respectively. A particle with a charge of $42 \mu \mathrm{C}$ is released from rest at $x=28 \mathrm{~cm}$. If the initial acceleration of the particle has a magnitude of $100 \mathrm{~km} / \mathrm{s}^2$, what is the particle's mass?
Respond in this unit: $10^{-6} \mathrm{~kg}$
|
2.2
|
scibench-matter-38.3
|
The carbon-carbon bond length in diamond is $154.45 \mathrm{pm}$. If diamond were considered to be a close-packed structure of hard spheres with radii equal to half the bond length, what would be its expected density? The diamond lattice is face-centred cubic and its actual density is $3.516 \mathrm{~g} \mathrm{~cm}^{-3}$.
Respond in this unit: $\mathrm{~g} \mathrm{~cm}^{-3}$
|
7.654
|
scibench-fund-Question23.47
|
An unknown charge sits on a conducting solid sphere of radius $10 \mathrm{~cm}$. If the electric field $15 \mathrm{~cm}$ from the center of the sphere has the magnitude $3.0 \times 10^3 \mathrm{~N} / \mathrm{C}$ and is directed radially inward, what is the net charge on the sphere?
Respond in this unit: $\mathrm{nC}$
|
-7.5
|
scibench-thermo-2.10
|
A muscle fiber contracts by $3.5 \mathrm{~cm}$ and in doing so lifts a weight. Calculate the work performed by the fiber. Assume the muscle fiber obeys Hooke's law $F=-k x$ with a force constant $k$ of $750 . \mathrm{N} \mathrm{m}^{-1}$.
Respond in this unit: $\mathrm{~J}$
|
0.46
|
scibench-class-10.12
|
Show that the small angular deviation of $\epsilon$ of a plumb line from the true vertical (i.e., toward the center of Earth) at a point on Earth's surface at a latitude $\lambda$ is $\epsilon = \frac{R\omega^2sin\lambda cos\lambda}{g_0 - R\omega^2 cos^2\lambda}$ where R is the radius of Earth. What is the value (in seconds of arc) of the maximum deviation? Note that the entire denominator in the answer is actually the effective $g$, and $g_0$ denotes the pure gravitational component.
Respond in this unit: min
|
6
|
scibench-thermo-15.4
|
For an ensemble consisting of a mole of particles having two energy levels separated by $1000 . \mathrm{cm}^{-1}$, at what temperature will the internal energy equal $3.00 \mathrm{~kJ}$ ?
Respond in this unit: $\mathrm{~K}$
|
1310
|
scibench-atkins-e2.5(a)(b)
|
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. A sample of $4.50 \mathrm{~g}$ of methane occupies $12.7 \mathrm{dm}^3$ at $310 \mathrm{~K}$. Calculate the work that would be done if the same expansion occurred reversibly.
Respond in this unit: $\mathrm{J}$
|
-167
|
scibench-class-10.20
|
Calculate the effective gravitational field vector $g$ at Earth's surface at the poles. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result $g = 9.780356[1 + 0.0052885sin^2\lambda - 0.0000059 sin^2 (2\lambda )]$ $m/s^2$ where $\lambda$ is the latitude?
Respond in this unit: $m/s^2$
|
9.832
|
scibench-fund-3.01
|
In an orienteering class, you have the goal of moving as far (straight-line distance) from base camp as possible by making three straight-line moves. You may use the following displacements in any order: (a) $\vec{a}, 2.0 \mathrm{~km}$ due east (directly toward the east); (b) $\vec{b}, 2.0 \mathrm{~km} 30^{\circ}$ north of east (at an angle of $30^{\circ}$ toward the north from due east); (c) $\vec{c}, 1.0 \mathrm{~km}$ due west. Alternatively, you may substitute either $-\vec{b}$ for $\vec{b}$ or $-\vec{c}$ for $\vec{c}$. What is the greatest distance you can be from base camp at the end of the third displacement? (We are not concerned about the direction.)
Respond in this unit: m
|
4.8
|
scibench-class-9.22A.
|
A deuteron (nucleus of deuterium atom consisting of a proton and a neutron) with speed $14.9$ km / s collides elastically with a neutron at rest. Use the approximation that the deuteron is twice the mass of the neutron. If the deuteron is scattered through a LAB angle $\psi = 10^\circ$, what is the final speed of the neutron?
Respond in this unit: km / s
|
5.18
|
scibench-class-Problem2.20
|
A gun fires a projectile of mass $10 \mathrm{~kg}$ of the type to which the curves of Figure 2-3 apply. The muzzle velocity is $140 \mathrm{~m} / \mathrm{s}$. Through what angle must the barrel be elevated to hit a target on the same horizontal plane as the gun and $1000 \mathrm{~m}$ away? Compare the results with those for the case of no retardation.
Respond in this unit: $^{\circ}$
|
17.4
|
scibench-thermo-14.16
|
Calculate the rotational partition function for $\mathrm{SO}_2$ at $298 \mathrm{~K}$ where $B_A=2.03 \mathrm{~cm}^{-1}, B_B=0.344 \mathrm{~cm}^{-1}$, and $B_C=0.293 \mathrm{~cm}^{-1}$
Respond in this unit:
|
5840
|
scibench-class-8.5
|
Calculate the time needed for a spacecraft to make a Hohmann transfer from Earth to Mars
Respond in this unit: $10^7 \mathrm{~s}$
|
2.24
|
scibench-fund-Question22.83
|
An electric dipole with dipole moment
$$
\vec{p}=(3.00 \hat{\mathrm{i}}+4.00 \hat{\mathrm{j}})\left(1.24 \times 10^{-30} \mathrm{C} \cdot \mathrm{m}\right)
$$
is in an electric field $\vec{E}=(4000 \mathrm{~N} / \mathrm{C}) \hat{\mathrm{i}}$. What is the potential energy of the electric dipole?
Respond in this unit: $10^{-26} \mathrm{~J} $
|
-1.49
|
scibench-thermo-18.39
|
Consider the gas phase thermal decomposition of 1.0 atm of $\left(\mathrm{CH}_3\right)_3 \mathrm{COOC}\left(\mathrm{CH}_3\right)_3(\mathrm{~g})$ to acetone $\left(\mathrm{CH}_3\right)_2 \mathrm{CO}(\mathrm{g})$ and ethane $\left(\mathrm{C}_2 \mathrm{H}_6\right)(\mathrm{g})$, which occurs with a rate constant of $0.0019 \mathrm{~s}^{-1}$. After initiation of the reaction, at what time would you expect the pressure to be $1.8 \mathrm{~atm}$ ?
Respond in this unit: $\mathrm{~s}$
|
269
|
scibench-quan-4.42
|
Use the normalized Numerov-method harmonic-oscillator wave functions found by going from -5 to 5 in steps of 0.1 to estimate the probability of being in the classically forbidden region for the $v=0$ state.
Respond in this unit:
|
0.16
|
scibench-quan-17.9
|
Calculate the energy needed to compress three carbon-carbon single bonds and stretch three carbon-carbon double bonds to the benzene bond length $1.397 Å$. Assume a harmonicoscillator potential-energy function for bond stretching and compression. Typical carboncarbon single- and double-bond lengths are 1.53 and $1.335 Å$; typical stretching force constants for carbon-carbon single and double bonds are 500 and $950 \mathrm{~N} / \mathrm{m}$.
Respond in this unit: $\mathrm{kcal} / \mathrm{mol}$
|
27
|
scibench-fund-Question21.31
|
Earth's atmosphere is constantly bombarded by cosmic ray protons that originate somewhere in space. If the protons all passed through the atmosphere, each square meter of Earth's surface would intercept protons at the average rate of 1500 protons per second. What would be the electric current intercepted by the total surface area of the planet?
Respond in this unit: $\mathrm{~mA}$
|
122
|
scibench-fund-Question22.57
|
An electric dipole consisting of charges of magnitude $1.50 \mathrm{nC}$ separated by $6.20 \mu \mathrm{m}$ is in an electric field of strength 1100 $\mathrm{N} / \mathrm{C}$. What is the magnitude of the electric dipole moment?
Respond in this unit: $10^{-15} \mathrm{C} \cdot \mathrm{m}$
|
9.30
|
scibench-fund-Question22.73
|
The electric field in an $x y$ plane produced by a positively charged particle is $7.2(4.0 \hat{\mathrm{i}}+3.0 \hat{\mathrm{j}}) \mathrm{N} / \mathrm{C}$ at the point $(3.0,3.0) \mathrm{cm}$ and $100 \hat{\mathrm{i}} \mathrm{N} / \mathrm{C}$ at the point $(2.0,0) \mathrm{cm}$. What is the $x$ coordinate of the particle?
Respond in this unit: $\mathrm{~cm}$
|
-1.0
|
scibench-thermo-18.4
|
Carbon-14 is a radioactive nucleus with a half-life of 5760 years. Living matter exchanges carbon with its surroundings (for example, through $\mathrm{CO}_2$ ) so that a constant level of ${ }^{14} \mathrm{C}$ is maintained, corresponding to 15.3 decay events per minute. Once living matter has died, carbon contained in the matter is not exchanged with the surroundings, and the amount of ${ }^{14} \mathrm{C}$ that remains in the dead material decreases with time due to radioactive decay. Consider a piece of fossilized wood that demonstrates $2.4{ }^{14} \mathrm{C}$ decay events per minute. How old is the wood?
Respond in this unit: $10^{11} \mathrm{~s}$
|
4.86
|
scibench-thermo-5.5
|
One mole of $\mathrm{H}_2 \mathrm{O}(l)$ is compressed from a state described by $P=1.00$ bar and $T=350$. K to a state described by $P=590$. bar and $T=750$. K. In addition, $\beta=2.07 \times 10^{-4} \mathrm{~K}^{-1}$ and the density can be assumed to be constant at the value $997 \mathrm{~kg} \mathrm{~m}^{-3}$. Calculate $\Delta S$ for this transformation, assuming that $\kappa=0$.
Respond in this unit: $\mathrm{~K}^{-1}$
|
57.2
|
scibench-thermo-13.5
|
The vibrational frequency of $I_2$ is $208 \mathrm{~cm}^{-1}$. What is the probability of $I_2$ populating the $n=2$ vibrational level if the molecular temperature is $298 \mathrm{~K}$ ?
Respond in this unit:
|
0.086
|
scibench-atkins-e2.32(a)
|
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. The volume of a certain liquid varies with temperature as
$$
V=V^{\prime}\left\{0.75+3.9 \times 10^{-4}(T / \mathrm{K})+1.48 \times 10^{-6}(T / \mathrm{K})^2\right\}
$$
where $V^{\prime}$ is its volume at $300 \mathrm{~K}$. Calculate its expansion coefficient, $\alpha$, at $320 \mathrm{~K}$.
Respond in this unit: $\mathrm{~K}^{-1}$
|
0.00131
|
scibench-matter-66.5(a)
|
Calculate the change in Gibbs energy of $35 \mathrm{~g}$ of ethanol (mass density $0.789 \mathrm{~g} \mathrm{~cm}^{-3}$ ) when the pressure is increased isothermally from 1 atm to 3000 atm.
Respond in this unit: $\mathrm{~kJ}$
|
12
|
scibench-fund-Question22.49
|
A $10.0 \mathrm{~g}$ block with a charge of $+8.00 \times 10^{-5} \mathrm{C}$ is placed in an electric field $\vec{E}=(3000 \hat{\mathrm{i}}-600 \hat{\mathrm{j}}) \mathrm{N} / \mathrm{C}$. What is the magnitude of the electrostatic force on the block?
Respond in this unit: $\mathrm{~N}$
|
0.245
|
scibench-matter-37.4
|
Calculate the typical wavelength of neutrons after reaching thermal equilibrium with their surroundings at $373 \mathrm{~K}$. For simplicity, assume that the particles are travelling in one dimension.
Respond in this unit: $\mathrm{pm}$
|
226
|
scibench-matter-36.3(a)
|
At $300 \mathrm{~K}$ and $20 \mathrm{~atm}$, the compression factor of a gas is 0.86 . Calculate the volume occupied by $8.2 \mathrm{mmol}$ of the gas under these conditions.
Respond in this unit: $\mathrm{~cm}^3$
|
8.7
|
scibench-fund-Question22.43
|
An electron is released from rest in a uniform electric field of magnitude $2.00 \times 10^4 \mathrm{~N} / \mathrm{C}$. Calculate the acceleration of the electron. (Ignore gravitation.)
Respond in this unit: $10^{15} \mathrm{~m} / \mathrm{s}^2$
|
3.51
|
scibench-thermo-3.5
|
A mass of $34.05 \mathrm{~g}$ of $\mathrm{H}_2 \mathrm{O}(s)$ at $273 \mathrm{~K}$ is dropped into $185 \mathrm{~g}$ of $\mathrm{H}_2 \mathrm{O}(l)$ at $310 . \mathrm{K}$ in an insulated container at 1 bar of pressure. Calculate the temperature of the system once equilibrium has been reached. Assume that $C_{P, m}$ for $\mathrm{H}_2 \mathrm{O}(l)$ is constant at its values for $298 \mathrm{~K}$ throughout the temperature range of interest.
Respond in this unit: $\mathrm{~K}$
|
292
|
scibench-atkins-p2.11(b)
|
Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. An average human produces about $10 \mathrm{MJ}$ of heat each day through metabolic activity. Human bodies are actually open systems, and the main mechanism of heat loss is through the evaporation of water. What mass of water should be evaporated each day to maintain constant temperature?
Respond in this unit: $\text{kg}$
|
4.09
|
scibench-chemmc-D-7
|
Evaluate the series
$$
S=\sum_{n=0}^{\infty} \frac{1}{3^n}
$$
Respond in this unit:
|
1.5
|
scibench-quan-11.22
|
How many states belong to the carbon configurations $1 s^2 2 s^2 2 p^2$?
Respond in this unit:
|
15
|
scibench-matter-55.4(a)
|
A chemical reaction takes place in a container of cross-sectional area $50 \mathrm{~cm}^2$. As a result of the reaction, a piston is pushed out through $15 \mathrm{~cm}$ against an external pressure of $1.0 \mathrm{~atm}$. Calculate the work done by the system.
Respond in this unit: $\mathrm{~J}$
|
-75
|
scibench-thermo-1.5
|
A gas sample is known to be a mixture of ethane and butane. A bulb having a $230.0 \mathrm{~cm}^3$ capacity is filled with the gas to a pressure of $97.5 \times 10^3 \mathrm{~Pa}$ at $23.1^{\circ} \mathrm{C}$. If the mass of the gas in the bulb is $0.3554 \mathrm{~g}$, what is the mole percent of butane in the mixture?
Respond in this unit: %
|
32
|
scibench-thermo-2.4
|
A hiker caught in a thunderstorm loses heat when her clothing becomes wet. She is packing emergency rations that if completely metabolized will release $35 \mathrm{~kJ}$ of heat per gram of rations consumed. How much rations must the hiker consume to avoid a reduction in body temperature of $2.5 \mathrm{~K}$ as a result of heat loss? Assume the heat capacity of the body equals that of water and that the hiker weighs $51 \mathrm{~kg}$.
Respond in this unit: $\mathrm{~g}$
|
15
|
scibench-atkins-e3.18(a)
|
Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the change in Gibbs energy of $35 \mathrm{~g}$ of ethanol (mass density $0.789 \mathrm{~g} \mathrm{~cm}^{-3}$ ) when the pressure is increased isothermally from $1 \mathrm{~atm}$ to $3000 \mathrm{~atm}$.
Respond in this unit: $\text{kJ}$
|
12
|
scibench-matter-66.1
|
Calculate $\Delta_{\mathrm{r}} G^{\ominus}(375 \mathrm{~K})$ for the reaction $2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{CO}_2(\mathrm{~g})$ from the values of $\Delta_{\mathrm{r}} G^{\ominus}(298 \mathrm{~K})$ : and $\Delta_{\mathrm{r}} H^{\ominus}(298 \mathrm{~K})$, and the GibbsHelmholtz equation.
Respond in this unit: $\mathrm{~kJ} \mathrm{~mol}^{-1}$
|
-501
|
scibench-class-Problem1.40
|
The height of a hill in meters is given by $z=2 x y-3 x^2-4 y^2-18 x+28 y+12$, where $x$ is the distance east and $y$ is the distance north of the origin. What is the $x$ distance of the top of the hill?
Respond in this unit: m
|
-2
|
scibench-quan-7.56
|
Calculate the uncertainty $\Delta L_z$ for the hydrogen-atom stationary state: $2 p_z$.
Respond in this unit:
|
0
|
scibench-atkins-e2.2(a)
|
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. A chemical reaction takes place in a container of cross-sectional area $100 \mathrm{~cm}^2$. As a result of the reaction, a piston is pushed out through $10 \mathrm{~cm}$ against an external pressure of $1.0 \mathrm{~atm}$. Calculate the work done by the system.
Respond in this unit: $\mathrm{J}$
|
-100
|
scibench-fund-Question21.69
|
In the radioactive decay of Eq. 21-13, $\mathrm{a}^{238} \mathrm{U}$ nucleus transforms to ${ }^{234} \mathrm{Th}$ and an ejected ${ }^4 \mathrm{He}$. (These are nuclei, not atoms, and thus electrons are not involved.) When the separation between ${ }^{234} \mathrm{Th}$ and ${ }^4 \mathrm{He}$ is $9.0 \times 10^{-15} \mathrm{~m}$, what are the magnitudes of the electrostatic force between them?
Respond in this unit: $10^2 \mathrm{~N}$
|
5.1
|
scibench-atkins-e2.23(a)(a)
|
Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Given the reactions (1) and (2) below, determine $\Delta_{\mathrm{r}} H^{\ominus}$ for reaction (3).
(1) $\mathrm{H}_2(\mathrm{g})+\mathrm{Cl}_2(\mathrm{g}) \rightarrow 2 \mathrm{HCl}(\mathrm{g})$, $\Delta_{\mathrm{r}} H^{\ominus}=-184.62 \mathrm{~kJ} \mathrm{~mol}^{-1}$
(2) $2 \mathrm{H}_2(\mathrm{g})+\mathrm{O}_2(\mathrm{g}) \rightarrow 2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$, $\Delta_{\mathrm{r}} H^\ominus=-483.64 \mathrm{~kJ} \mathrm{~mol}^{-1}$
(3) $4 \mathrm{HCl}(\mathrm{g})+\mathrm{O}_2(\mathrm{g}) \rightarrow 2 \mathrm{Cl}_2(\mathrm{g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$
Respond in this unit: $\mathrm{KJ} \mathrm{mol}^{-1}$
|
-114.40
|
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