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7. 14 find the general solution to the following differential equations. a. b. section 7. 2 exercises solve the following equations using the method of undetermined coefficients. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. in each of the following problems, a. write the form for the particular solution for the meth... | openstax_calculus_volume_3_-_web | [
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7. 3 applications learning objectives 7. 3. 1 solve a second - order differential equation representing simple harmonic motion. 7. 3. 2 solve a second - order differential equation representing damped simple harmonic motion. 7. 3. 3 solve a second - order differential equation representing forced simple harmonic motion... | openstax_calculus_volume_3_-_web | [
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7. 3 • applications 769 figure 7. 2 a spring in its natural position ( a ), at equilibrium with a mass m attached ( b ), and in oscillatory motion ( c ). let denote the displacement of the mass from equilibrium. note that for spring - mass systems of this type, it is customary to adopt the convention that down is posit... | openstax_calculus_volume_3_-_web | [
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simple harmonic motion. the period of this motion ( the time it takes to complete one oscillation ) is and the frequency is ( figure 7. 3 ). ( 7. 5 ) ( 7. 6 ) 770 7 • second - order differential equations access for free at openstax. org figure 7. 3 a graph of vertical displacement versus time for simple harmonic motio... | openstax_calculus_volume_3_-_web | [
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7. 15 a 200 - g mass stretches a spring 5 cm. find the equation of motion of the mass if it is released from rest from a position 10 cm below the equilibrium position. what is the frequency of this motion? writing the general solution in the form has some advantages. it is easy to see the link between the differential ... | openstax_calculus_volume_3_-_web | [
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solution a. we have and note that both and are positive, so is in the first quadrant. thus, so we have the frequency is the amplitude is b. we have and note that is positive but is negative, so is in the fourth quadrant. thus, 7. 3 • applications 773 so we have the frequency is the amplitude is | openstax_calculus_volume_3_-_web | [
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7. 16 express the function in the form what is the frequency of motion? the amplitude? damped vibrations with the model just described, the motion of the mass continues indefinitely. clearly, this doesn ’ t happen in the real world. in the real world, there is almost always some friction in the system, which causes the... | openstax_calculus_volume_3_-_web | [
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##damped spring - mass system, with no change in direction ( a ) and only one change in direction ( b ). example 7. 19 overdamped spring - mass system a 16 - lb mass is attached to a 10 - ft spring. when the mass comes to rest in the equilibrium position, the spring measures 15 ft 4 in. the system is immersed in a medi... | openstax_calculus_volume_3_-_web | [
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7. 3 • applications 775 case 2 : in this case, we say the system is critically damped. the general solution has the form where is less than zero. the motion of a critically damped system is very similar to that of an overdamped system. it does not oscillate. however, with a critically damped system, if the damping is r... | openstax_calculus_volume_3_-_web | [
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7. 18 a 1 - lb weight stretches a spring 6 in., and the system is attached to a dashpot that imparts a damping force equal to half the instantaneous velocity of the mass. find the equation of motion if the mass is released from rest at a point 6 in. below equilibrium. case 3 : in this case, we say the system is underda... | openstax_calculus_volume_3_-_web | [
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7. 3 • applications 777 example 7. 22 chapter opener : modeling a motorcycle suspension system figure 7. 9 ( credit : modification of work by nseika, flickr ) for motocross riders, the suspension systems on their motorcycles are very important. the off - road courses on which they ride often include jumps, and losing c... | openstax_calculus_volume_3_-_web | [
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). a. set up the differential equation that models the behavior of the motorcycle suspension system. b. we are interested in what happens when the motorcycle lands after taking a jump. let time denote the time when the motorcycle first contacts the ground. if the motorcycle hits the ground with a velocity of 10 ft / se... | openstax_calculus_volume_3_-_web | [
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7. 3 • applications 779 figure 7. 11 graph of the equation of motion over a time of one second. student project landing vehicle nasa is planning a mission to mars. to save money, engineers have decided to adapt one of the moon landing vehicles for the new mission. however, they are concerned about how the different gra... | openstax_calculus_volume_3_-_web | [
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by the crew, so that it is descending at a rate of 2 m / sec when it touches down. find the equation of motion of the lander on the moon. 3. if the lander is traveling too fast when it touches down, it could fully compress the spring and “ bottom out. ” bottoming out could damage the landing craft and must be avoided a... | openstax_calculus_volume_3_-_web | [
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term behavior of the system is determined by so we call this part of the solution the steady - state solution. media this website ( http : / / www. openstax. org / l / 20 _ oscillations ) shows a simulation of forced vibrations. example 7. 23 forced vibrations a mass of 1 slug stretches a spring 2 ft and comes to rest ... | openstax_calculus_volume_3_-_web | [
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7. 20 a mass of 2 kg is attached to a spring with constant 32 n / m and comes to rest in the equilibrium position. beginning at time an external force equal to is applied to the system. find the equation of motion if there is no damping. what is the transient solution? what is the steady - state solution? student proje... | openstax_calculus_volume_3_-_web | [
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to its natural frequency, and the resulting resonance ultimately shook the bridge apart. media this website ( http : / / www. openstax. org / l / 20 _ tacomanarrow ) contains more information about the collapse of the tacoma narrows bridge. media during the short time the tacoma narrows bridge stood, it became quite a ... | openstax_calculus_volume_3_-_web | [
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the capacitor. furthermore, let l denote inductance in henrys ( h ), r denote resistance in ohms and c denote capacitance in farads ( f ). last, let denote electric potential in volts ( v ). kirchhoff ’ s voltage rule states that the sum of the voltage drops around any closed loop must be zero. so, we need to consider ... | openstax_calculus_volume_3_-_web | [
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7. 3 • applications 783 example 7. 24 the rlc series circuit find the charge on the capacitor in an rlc series circuit where h, f, and v. assume the initial charge on the capacitor is 0 c and the initial current is 9 a. what happens to the charge on the capacitor over time? solution we have the general solution to the ... | openstax_calculus_volume_3_-_web | [
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7. 21 find the charge on the capacitor in an rlc series circuit where h, f, and v. assume the initial charge on the capacitor is 0 c and the initial current is 4 a. section 7. 3 exercises 86. a mass weighing 4 lb stretches a spring 8 in. find the equation of motion if the spring is released from the equilibrium positio... | openstax_calculus_volume_3_-_web | [
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. find the position function of the block. b. find the period and frequency of the vibration. c. sketch a graph of d. at what time does the block first pass through the equilibrium position? 92. a 1 - kg mass is attached to a vertical spring with a spring constant of 21 n / m. the resistance in the spring - mass system... | openstax_calculus_volume_3_-_web | [
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7. 3 • applications 785 95. a 1 - kg mass stretches a spring 6. 25 cm. the resistance in the spring - mass system is equal to eight times the instantaneous velocity of the mass. a. find the equation of motion if the mass is released from a position 5 m below its equilibrium position with an upward velocity of 10 m / se... | openstax_calculus_volume_3_-_web | [
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##acitor is 7 c and the initial current is 0 a. 101. find the charge on the capacitor in an rlc series circuit where h, f, and v. assume the initial charge on the capacitor is 0. 001 c and the initial current is 0 a. 102. a series circuit consists of a device where h, f, and v. if the initial charge and current are bot... | openstax_calculus_volume_3_-_web | [
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7. 4 series solutions of differential equations learning objectives 7. 4. 1 use power series to solve first - order and second - order differential equations. in introduction to power series ( http : / / openstax. org / books / calculus - volume - 2 / pages / 6 - introduction ), we studied how functions can be represen... | openstax_calculus_volume_3_-_web | [
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. we want to find values for the coefficients such that ∞ ∞ we want the indices on our sums to match so that we can express them using a single summation. that is, we want to rewrite the first summation so that it starts with to re - index the first term, replace n with inside the sum, and change the lower summation li... | openstax_calculus_volume_3_-_web | [
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7. 4 • series solutions of differential equations 787 this recurrence relationship allows us to express each coefficient in terms of the coefficient two terms earlier. this yields one expression for even values of n and another expression for odd values of n. looking first at the equations involving even values of n, w... | openstax_calculus_volume_3_-_web | [
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∞ ∞ ∞ now, in the first summation, we see that when or the term evaluates to zero, so we can add these terms back into our sum to get ∞ ∞ similarly, in the third term, we see that when the expression evaluates to zero, so we can add that term back in as well. we have ∞ ∞ then, we need only shift the indices in our seco... | openstax_calculus_volume_3_-_web | [
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7. 22 find a power series solution for the following differential equations. a. b. we close this section with a brief introduction to bessel functions. complete treatment of bessel functions is well beyond the scope of this course, but we get a little taste of the topic here so we can see how series solutions to differ... | openstax_calculus_volume_3_-_web | [
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7. 4 • series solutions of differential equations 793 chapter review key terms boundary conditions the conditions that give the state of a system at different times, such as the position of a spring - mass system at two different times boundary - value problem a differential equation with associated boundary conditions... | openstax_calculus_volume_3_-_web | [
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with constant coefficients complementary equation general solution to a nonhomogeneous linear differential equation equation of simple harmonic motion solution for simple harmonic motion alternative form of solution for shm forced harmonic motion charge in a rlc series circuit 794 7 • chapter review access for free at ... | openstax_calculus_volume_3_-_web | [
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7. 1 second - order linear equations • second - order differential equations can be classified as linear or nonlinear, homogeneous or nonhomogeneous. • to find a general solution for a homogeneous second - order differential equation, we must find two linearly independent solutions. if and are linearly independent solu... | openstax_calculus_volume_3_-_web | [
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7. 2 nonhomogeneous linear equations • to solve a nonhomogeneous linear second - order differential equation, first find the general solution to the complementary equation, then find a particular solution to the nonhomogeneous equation. • let be any particular solution to the nonhomogeneous linear differential equation... | openstax_calculus_volume_3_-_web | [
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7. 3 applications • second - order constant - coefficient differential equations can be used to model spring - mass systems. • an examination of the forces on a spring - mass system results in a differential equation of the form where represents the mass, is the coefficient of the damping force, is the spring constant,... | openstax_calculus_volume_3_-_web | [
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7. 4 series solutions of differential equations • power series representations of functions can sometimes be used to find solutions to differential equations. • differentiate the power series term by term and substitute into the differential equation to find relationships between the power series coefficients. review e... | openstax_calculus_volume_3_-_web | [
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138. find the general solution to this equation ( hint : call ). 139. assuming the system starts from rest, show that the particular solution can be written as 140. [ t ] using your solutions derived earlier, plot the solution to the system over the interval find, analytically, the period of the fast and slow amplitude... | openstax_calculus_volume_3_-_web | [
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. 69. 70. 71. 72. 73. 74. 75. 76. integrals involving u2 −a2, a > 0 77. 78. 79. 80. 81. 82. 83. 84a. 84b. 802 a • table of integrals access for free at openstax. org integrals involving a2 −u2, a > 0 85. 86. 87. 88. 89. 90. 91. 92. 93a. 93b. integrals involving 2au −u2, a > 0 94. 95. 96. 97. integrals involving a + bu,... | openstax_calculus_volume_3_-_web | [
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and origin. 151. symmetric with respect to x - axis only. 153. symmetry with respect to x - axis only. 155. line 157. 159. hyperbola ; polar form or 161. 163. 822 answer key access for free at openstax. org 165. 167. answer key 823 y - axis symmetry 169. y - axis symmetry 171. 824 answer key access for free at openstax... | openstax_calculus_volume_3_-_web | [
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##0 answer key access for free at openstax. org 297. 299. 301. answer key 831 303. 305. 307. hyperbola 309. ellipse 311. ellipse 313. at the point 2. 25 feet above the vertex. 832 answer key access for free at openstax. org 315. 0. 5625 feet 317. length is 96 feet and height is approximately 26. 53 feet. 319. 321. revi... | openstax_calculus_volume_3_-_web | [
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three vectors form the adjacent edges of a parallelepiped. they are not coplanar. 2. 42 n 2. 43 possible set of parametric equations : related set of symmetric equations : 2. 44 2. 45 2. 46 these lines are skew because their direction vectors are not parallel and there is no point that lies on both lines. 2. 47 or 2. 4... | openstax_calculus_volume_3_-_web | [
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2. 61 spherical coordinates with the origin located at the center of the earth, the z - axis aligned with the north pole, and the x - axis aligned with the prime meridian section 2. 1 exercises 1. a. b. 3. a. b. 5. a. b. 7. a. b. 9. a. b. answer key 839 11. 13. 15. a. b. c. answers will vary ; d. 17. 19. 21. a. b. answ... | openstax_calculus_volume_3_-_web | [
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a. ( each component is expressed in centimeters per second ) ; ( expressed in centimeters per second ) ; ( each component expressed in centimeters per second squared ) ; b. answer key 841 section 2. 3 exercises 123. 6 125. 0 127. 129. 131. a. rad ; b. is not acute. 133. a. rad ; b. is acute. 135. 137. 139. rad 141. ort... | openstax_calculus_volume_3_-_web | [
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lines are skew. 263. the lines are equal. 265. a. ℝb. for instance, the line passing through with direction vector 844 answer key access for free at openstax. org c. for instance, the line passing through and point that belongs to is a line that intersects ; 267. a. b. 269. a. b. 271. a. b. and c. 273. a. b. c. 275. 27... | openstax_calculus_volume_3_-_web | [
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331. parabola 333. ellipse answer key 847 335. ellipse 337. a. ellipsoid ; b. the third equation ; c. 339. a. b. cylinder centered at with rulings parallel to the y - axis 341. a. b. hyperboloid of one sheet centered at with the z - axis as its axis of symmetry 343. a. b. elliptic cone centered at with the z - axis as ... | openstax_calculus_volume_3_-_web | [
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by the set of points 417. 419. 421. a. c. 852 answer key access for free at openstax. org review exercises 423. true 425. false 427. a. b. c. can ’ t cross a vector with a scalar ; d. 429. 431. 433. 435. 437. 439. trace : is a circle, trace : is a hyperbola ( or a pair of lines if trace : is a hyperbola ( or a pair of ... | openstax_calculus_volume_3_-_web | [
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3. 17 section 3. 1 exercises 1. 3. 5. a. b. c. yes, the limit as t approaches is equal to d. 7. a. b. c. yes 9. 11. 13. the limit does not exist because the limit of as t approaches infinity does not exist. 15. where k is an integer 17. where n is an integer 19. answer key 855 21. all t such that ∞ 23. a variation of t... | openstax_calculus_volume_3_-_web | [
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zero. 141. and 143. 145. 147. 149. 151. the curvature is decreasing over this interval. 153. section 3. 4 exercises 155. 157. 159. 161. speed = 163. 165. 167. 169. 171. 173. 44. 185 sec answer key 861 175. sec 177. 88. 37 sec 179. the range is approximately 886. 29 m. 181. m / sec 183. 185. 187. 189. 191. 193. 195. 197... | openstax_calculus_volume_3_-_web | [
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4. 40 is a minimum. section 4. 1 exercises 1. 3. this is the volume when the radius is and the height is 5. all points in the 7. 9. all real ordered pairs in the of the form 11. 13. the set ℝ 15. a hyperbola 17. a line ; line through the origin 19. three lines 21. 23. 25. 27. 29. the level curves are parabolas of the f... | openstax_calculus_volume_3_-_web | [
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301. 303. a. b. 305. a. b. 307. a. b. c. 309. section 4. 7 exercises 311. 313. 315. maximum at 317. relative minimum at 319. the second derivative test fails. since for all x and y different from zero, and when either x or y equals zero ( or both ), then the absolute minimum occurs at 321. is a saddle point. 323. is a ... | openstax_calculus_volume_3_-_web | [
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critical point review exercises 395. true, by clairaut ’ s theorem 397. false 399. answers may vary 401. does not exist 403. continuous at all points on the except where 405. 407. 409. 411. 413. 415. 874 answer key access for free at openstax. org 417. maximum : minimum : 419. cm3 chapter 5 checkpoint 5. 1 5. 2 a. 26 b... | openstax_calculus_volume_3_-_web | [
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5. 48 section 5. 1 exercises 1. 27. 3. 0. 5. 21. 3. 7. a. 28 b. 1. 75 ft. 9. a. b. here and 11. 13. 40. 15. 17. 19. 21. 0. 23. 25. 27. 29. 31. 33. 35. 37. 49. a. b. c. d. 53. a. for b. c. answer key 877 55. a. b. 59. f ; here where and are the midpoints of the subintervals of the partitions of and respectively. section... | openstax_calculus_volume_3_-_web | [
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figure. answer key 885 359. a. and the functions and are continuous and differentiable, and the partial derivatives and are continuous on b. and c. is the sqaure of vertices in the see the following figure. 361. a. and the functions and are continuous and differentiable, and the partial derivatives and are continuous o... | openstax_calculus_volume_3_-_web | [
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7. 22 a. ∞ b. section 7. 1 exercises 1. linear, homogenous 3. nonlinear 5. linear, homogeneous 11. 13. answer key 901 15. 17. 19. 21. 23. 25. 27. 29. 31. 33. 35. 37. 39. 41. no solutions exist. 43. 45. 47. 49. a. b. 51. a. b. 902 answer key access for free at openstax. org section 7. 2 exercises 55. 57. 59. 61. 63. 65.... | openstax_calculus_volume_3_-_web | [
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587 graph of a function of two variables 310 gravitational force 628 green ’ s theorem 636, 722 grid curves 682 h harmonic function 648 heat equation 339 heat flow 698 helix 239, 240 higher - order partial derivatives 337 homogeneous functions 372 homogeneous linear equation 746 hooke ’ s law 770 hurricanes 582 hyperbo... | openstax_calculus_volume_3_-_web | [
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chemistry 2e senior contributing authors paul flowers, university of north carolina at pembroke klaus theopold, university of delaware richard langley, stephen f. austin state university william r. robinson, phd openstax rice university 6100 main street ms - 375 houston, texas 77005 to learn more about openstax, visit ... | openstax_chemistry2e-web | [
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##x tutor logo, connexions name, connexions logo, rice university name, and rice university logo are not subject to the license and may not be reproduced without the prior and express written consent of rice university. hardcover book isbn - 13 978 - 1 - 947172 - 62 - 3 b & w paperback book isbn - 13 978 - 1 - 59399 - ... | openstax_chemistry2e-web | [
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economics foundation charles koch foundation leon lowenstein foundation, inc. the maxfield foundation burt and deedee mcmurtry michelson 20mm foundation national science foundation the open society foundations jumee yhu and david e. park iii brian d. patterson usa - international foundation the bill and stephanie sick ... | openstax_chemistry2e-web | [
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4. 1 writing and balancing chemical equations 160 4. 2 classifying chemical reactions 166 4. 3 reaction stoichiometry 180 4. 4 reaction yields 185 4. 5 quantitative chemical analysis 190 key terms 198 key equations 199 summary 199 exercises 200 chapter 5 thermochemistry 211 introduction 211 5. 1 energy basics 212 5. 2 ... | openstax_chemistry2e-web | [
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chapter 10 liquids and solids 475 introduction 475 10. 1 intermolecular forces 476 10. 2 properties of liquids 487 10. 3 phase transitions 493 10. 4 phase diagrams 503 10. 5 the solid state of matter 510 10. 6 lattice structures in crystalline solids 516 key terms 534 key equations 535 summary 535 exercises 536 chapter... | openstax_chemistry2e-web | [
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of other reaction classes 749 introduction 749 15. 1 precipitation and dissolution 749 15. 2 lewis acids and bases 763 15. 3 coupled equilibria 767 key terms 772 key equations 772 summary 772 exercises 773 chapter 16 thermodynamics 783 introduction 783 16. 1 spontaneity 783 16. 2 entropy 787 16. 3 the second and third ... | openstax_chemistry2e-web | [
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935 19. 1 occurrence, preparation, and properties of transition metals and their compounds 935 19. 2 coordination chemistry of transition metals 948 19. 3 spectroscopic and magnetic properties of coordination compounds 962 key terms 971 summary 972 exercises 973 chapter 20 organic chemistry 977 introduction 977 20. 1 h... | openstax_chemistry2e-web | [
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21. 6 biological effects of radiation 1059 key terms 1067 key equations 1068 summary 1069 exercises 1070 appendix a the periodic table 1077 appendix b essential mathematics 1079 appendix c units and conversion factors 1087 appendix d fundamental physical constants 1091 access for free at openstax. org appendix e water ... | openstax_chemistry2e-web | [
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##tax and its content contributors. because our books are openly licensed, you are free to use the entire book or pick and choose the sections that are most relevant to the needs of your course. feel free to remix the content by assigning your students certain chapters and sections in your syllabus, in the order that y... | openstax_chemistry2e-web | [
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maintaining the same organization as the first edition. substantial improvements have been made in the figures, illustrations, and example exercises that support the text narrative. coverage and scope our chemistry 2e textbook adheres to the scope and sequence of most general chemistry courses nationwide. we strive to ... | openstax_chemistry2e-web | [
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with a focus on accessibility. we have emphasized and improved that approach in the second edition. to accommodate users of specific assistive technologies, all alternative text was reviewed and revised for comprehensiveness and clarity. many illustrations were revised to improve the color contrast, which is important ... | openstax_chemistry2e-web | [
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they ’ ve learned through practice problems. 4 preface access for free at openstax. org additional resources student and instructor resources we ’ ve compiled additional resources for both students and instructors, including getting started guides, an instructor solutions manual, and powerpoint slides. instructor resou... | openstax_chemistry2e-web | [
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1989. dr. flowers teaches courses in general and analytical chemistry, and conducts experimental research involving the development of new devices and methods for microscale chemical analysis. klaus theopold, university of delaware dr. klaus theopold ( born in berlin, germany ) received his vordiplom from the universit... | openstax_chemistry2e-web | [
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##iken, jackson state university vicki moravec, trine university jason powell, ferrum college thomas sorensen, university of wisconsin – milwaukee allison soult, university of kentucky reviewers casey akin, college station independent school district lara al - hariri, university of massachusetts – amherst sahar atwa, u... | openstax_chemistry2e-web | [
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antonio nirmala shankar, rutgers university jonathan smith, temple university bryan spiegelberg, rider university ron sternfels, roane state community college cynthia strong, cornell college kris varazo, francis marion university victor vilchiz, virginia state university alex waterson, vanderbilt university juchaoyan, ... | openstax_chemistry2e-web | [
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1. 6 mathematical treatment of measurement results your alarm goes off and, after hitting “ snooze ” once or twice, you pry yourself out of bed. you make a cup of coffee to help you get going, and then you shower, get dressed, eat breakfast, and check your phone for messages. on your way to school, you stop to fill you... | openstax_chemistry2e-web | [
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1. 1 chemistry in context learning objectives by the end of this section, you will be able to : • outline the historical development of chemistry • provide examples of the importance of chemistry in everyday life • describe the scientific method • differentiate among hypotheses, theories, and laws • provide examples il... | openstax_chemistry2e-web | [
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, and soaps were prepared by combining these alkalis with fats. alcohol was produced by fermentation and purified by distillation. attempts to understand the behavior of matter extend back for more than 2500 years. as early as the sixth century bc, greek philosophers discussed a system in which water was the basis of a... | openstax_chemistry2e-web | [
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, cortisone came into use to treat arthritis and other disorders and injuries, but it took a 36 - step process to synthesize. chemist percy lavon julian turned to a more plentiful source : soybeans. previously, julian had developed a lab to isolate soy protein, which was used in firefighting among other applications. h... | openstax_chemistry2e-web | [
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wine making help provide sustenance in the form of food and drink to the world ’ s population. medicine, pharmacology, biotechnology, and botany identify and produce substances that help keep us healthy. environmental science, geology, oceanography, and atmospheric science incorporate many chemical ideas to help us bet... | openstax_chemistry2e-web | [
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1. 1 • chemistry in context 11 observations that acts as a guide for gathering and checking information. a hypothesis is tested by experimentation, calculation, and / or comparison with the experiments of others and then refined as needed. some hypotheses are attempts to explain the behavior that is summarized in laws.... | openstax_chemistry2e-web | [
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comes from greek and means “ small. ” the microscopic domain of chemistry is often visited in the imagination. some aspects of the microscopic domain are visible through standard optical microscopes, for example, many biological cells. more sophisticated instruments are capable of imaging even smaller entities such as ... | openstax_chemistry2e-web | [
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molecules, is within the microscopic arena. the formula h2o, which can describe water at either the macroscopic or microscopic levels, is an example of the symbolic domain. the abbreviations ( g ) for gas, ( s ) for solid, and ( l ) for liquid are also symbolic. figure 1. 5 ( a ) moisture in the air, icebergs, and the ... | openstax_chemistry2e-web | [
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1. 2 phases and classification of matter learning objectives by the end of this section, you will be able to : • describe the basic properties of each physical state of matter : solid, liquid, and gas • distinguish between mass and weight • apply the law of conservation of matter • classify matter as an element, compou... | openstax_chemistry2e-web | [
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and specialized analytical instruments used to detect trace amounts of metals. 14 1 • essential ideas access for free at openstax. org figure 1. 7 a plasma torch can be used to cut metal. ( credit : “ hypertherm ” / wikimedia commons ) link to learning in a tiny cell in a plasma television, the plasma emits ultraviolet... | openstax_chemistry2e-web | [
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an astronaut ’ s mass does not change just because she goes to the moon. but her weight on the moon is only one - sixth her earth - bound weight because the moon ’ s gravity is only one - sixth that of the earth ’ s. she may feel “ weightless ” during her trip when she experiences negligible external forces ( gravitati... | openstax_chemistry2e-web | [
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1. 2 • phases and classification of matter 15 figure 1. 8 ( a ) the mass of beer precursor materials is the same as the mass of beer produced : sugar has become alcohol and carbon dioxide. ( b ) the mass of the lead, lead oxide, and sulfuric acid consumed by the production of electricity is exactly equal to the mass of... | openstax_chemistry2e-web | [
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either elements or other compounds, or both. mercury ( ii ) oxide, an orange, crystalline solid, can be broken down by heat into the elements mercury and oxygen ( figure 1. 9 ). when heated in the absence of air, the compound sucrose is broken down into the element carbon and the compound water. ( the initial stage of ... | openstax_chemistry2e-web | [
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, which are colorless gases when uncombined. free sodium, an element that is a soft, shiny, metallic solid, and free chlorine, an element that is a yellow - green gas, combine to form sodium chloride ( table salt ), a compound that is a white, crystalline solid. a mixture is composed of two or more types of matter that... | openstax_chemistry2e-web | [
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figure 1. 10 ( a ) oil and vinegar salad dressing is a heterogeneous mixture because its composition is not uniform throughout. ( b ) a commercial sports drink is a homogeneous mixture because its composition is uniform throughout. ( credit a “ left ” : modification of work by john mayer ; credit a “ right ” : modifica... | openstax_chemistry2e-web | [
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1. 2 • phases and classification of matter 17 although there are just over 100 elements, tens of millions of chemical compounds result from different combinations of these elements. each compound has a specific composition and possesses definite chemical and physical properties that distinguish it from all other compou... | openstax_chemistry2e-web | [
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0. 47 table 1. 1 18 1 • essential ideas access for free at openstax. org atoms and molecules an atom is the smallest particle of an element that has the properties of that element and can enter into a chemical combination. consider the element gold, for example. imagine cutting a gold nugget in half, then cutting one o... | openstax_chemistry2e-web | [
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can see with our unaided eye is a single thread of a spider web : these strands are about 1 / 10, 000 of a centimeter ( 0. 0001 cm ) in diameter. although the cross - section of one strand is almost impossible to see without a microscope, it is huge on an atomic scale. a single carbon atom in the web has a diameter of ... | openstax_chemistry2e-web | [
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1. 2 • phases and classification of matter 19 figure 1. 13 these images provide an increasingly closer view : ( a ) a cotton boll, ( b ) a single cotton fiber viewed under an optical microscope ( magnified 40 times ), ( c ) an image of a cotton fiber obtained with an electron microscope ( much higher magnification than... | openstax_chemistry2e-web | [
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consist of two or more identical atoms, as in the molecules found in the elements hydrogen, oxygen, and sulfur, or it may consist of two or more different atoms, as in the molecules found in water. each water molecule is a unit that contains two hydrogen atoms and one oxygen atom. each glucose molecule is a unit that c... | openstax_chemistry2e-web | [
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