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Physical Chemistry INSTRUCTION: Select the correct answer for each of the following sections. Mark only one answer for each item by shading the box corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 1 only. 1. Chemical equilibrium reactions are characterized by a. ΔG > 0 b. ΔG < 0 c. ΔG = 0 d. ΔG = ΔG o 2. Spontaneous reactions are characterized by a. ΔG > 0 b. ΔG < 0 c. ΔG o = 0 d. ΔG = 0 3. Capillary action is due to: a. Cohesion b. Viscosity c. Gravity d. Surface tension 4. An ideal gas has a compressibility factor of a. 1 b. 2 c. PV d. None of the given choices
5. The fraction of the total current carried by an ion is known as a. Ionic mobility b. Overvoltage c. Transference number d. Ionic conductance Prepared by JEPa‐a/for BSChem Graduate 2006
6. A measure of disorderliness in a system is given by a. Free energy b. Enthalpy c. Heat d. Entropy 7. There is no change in internal energy of an ideal gas during a. Adiabatic expansion b. Adiabatic compression c. Isothermal expansion d. None of the above
8. The efficiency of a heat engine is limited by a. First law of thermodynamics b. Second law of thermodynamics c. Third law of thermodynamics d. None of the above
9. Non‐ideal gas behavior is likely to be observed at a. Low pressure and low temperature b. High pressure and high temperature c. High pressure and low temperature d. Low pressure and high temperature
10. In an equilibrium reaction, Kp equals Kc when a. Reactants and products are all gases b. Temperature is constant c. Reactants and products have equal number of moles d. Reactants and products are all liquids
11. Natural chlorine is a mixture of isotopes. Determine its atomic mass if 75.53% of the naturally occurring element is chlorine‐35, which has a mass of 34.968. Chlorine‐37 has a mass of 36.958. a. 35.45 b. 35.00 c. 34.55 d. 36.47
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12. At 35oC, the vapor pressure of water is increased from 30 to 31 mm Hg against an external pressure of 10 atm. If the vapor pressure is to be maintained at 0.0395 atm for 100 g of water at 35oC and 10 atm, how much in g NaCl is to be added to the water? a. 58.55 b. 61.18 c. 52.88 d. 47.36 13. Given a solution of toluene in benzene at 20oC with the mole fraction of toluene equal to 0.20, the partial pressure of the solvent, benzene, is equal to 2.19 torr. The Henry constant for toluene is 10.95 torr. Calculate the activity of the solute. a. 0.800 b. 1.000 c. 0.500 d. 0.200 14. A certain sugar has a molar mass of 342 g/mol. At 0oC, the osmotic pressure of an aqueous solution of concentration of 1.5 g of sugar per 150 cm3 solvent is 0.649 atm. What is the osmotic pressure of the solution? a. 222 atm b. 0.32 atm c. 50 atm d. 0.65 atm 15. Given the reaction: KNO3 + energy U K + (aq ) + NO3− (aq ) , which of the following changes to the system would increase the concentration of K+ ions at equilibrium? a. The pressure of the system is decreased b. Additional solid KNO3 is added to the solution c. The temperature of the solution is increased d. The volume of the solution is added to the solution Prepared by JEPa‐a/for BSChem Graduate 2006
16. The specific heat capacity at constant volume of a lead‐silver alloy is equal to 0.0383 cal/deg‐g. The atomic masses of lead and silver are 207 and 107, respectively. Assuming that the alloy follows Dulong and Petit Law, find the mole ratio of lead to silver. a. ½ b. 2 c. 1 d. 4 17. Calculate the temperature change in oC of two moles of a diatomic gas contained in a piston given that q=65 J and w=210 J. a. – 2.5 b. – 4.5 c. – 5.5 d. – 3.5 18. A lead storage battery involves the two half‐reactions: PbSO4 ( s ) + 2e − U Pb + SO42− ; Eo (volts) = – 0.36
PbO2 ( s ) + 4 H + + SO42− U PbSO4 + 2 H 2O ; Eo (volts) = 1.69 For a cell that duplicates the lead storage battery discharge reaction at unit concentrations, what is ΔG in kJ? a. – 792 b. – 396 c. + 792 d. + 396 19. What is the heat capacity at constant pressure of graphite assuming it obeys the Dulong and Petit’s Law? a. 6 cal/K‐mol b. 6 atm/mol‐L c. 6 L‐atm/mol d. 6 ergs/K
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20. A sealed isothermal container initially contains three moles of CO gas and four moles of O2 gas. The following reversible reaction took place: 2CO( g ) + O2 ( g ) U 2CO2 ( g ) At equilibrium, there were two moles of CO2 in the container. What was the total number of moles of gas present in the container at equilibrium? a. 6 b. 4 c. 5 d. 7 21. At 1035oC, two moles of ruthenium changes from the β to the α solid state. The ΔH for the transition is – 142 J/mol. The surrounding cooling bath is at STP. Find ΔS in J/K of the universe. a. 1.040 b. 0.642 c. 0.823 d. 0.217
22. Determine the barometric decrease in atmospheric pressure from sea level to an altitude of 1.8 x 106 cm. Assume air to be a uniform gas of molecular mass 29, and a uniform temperature of 0oC. a. 0.307 b. 0.998 c. 0.105 d. 304.1
23. Two moles of an ideal gas are expanded reversibly and isothermally at 0oC from 1 atm. Calculate the final volume occupied by the gas if the heat absorbed during the process is q = 750 cal. The external pressure over the system is 1 atm. a. 69.6 L b. 98.2 L c. 118.7 L d. 304.1 L Prepared by JEPa‐a/for BSChem Graduate 2006
24. A + B → C + D A+C → D + E A multi‐step reaction takes place by the above mechanism. Which of the species shown above is an intermediate in the reaction? a. A b. D c. B d. C 25. A bulb is filled with argon gas at the ambient pressure and is found to contain 7.98 g of argon at a temperature T. The bulb is then immersed in a bath whose temperature is 30oC hotter than the first one. The stopcock on the bulb is opened so that the argon gas pressure returns to the initial value. The bulb is now found to contain 5.33 g of argon. What is the value of the final temperature? The atomic mass of argon is 39.9. a. – 242oC b. – 90.9oC c. – 212oC d. – 182oC 26. Ammonia dissolves in water at 20oC to give a solution containing 0.040 mole fraction of ammonia. The total vapor pressure of the solution is 6.58 x 10–2 atm and the vapor pressure for water is 17.00 torr at the same temperature. Applying Henry’s and Raoult’s laws, calculate the Henry’s constant. a. 1200 b. 50.00 c. 842.5 d. 16.98
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27. A sample of an ideal gas at 29oC and 420 torr occupied a volume of 382 cm3. What was the number of moles of gas in this sample? a. 8.5 x 10–3 b. 4.9 x 102 c. 6.5 d. 8.9 x 10–2 28. The half‐life for a given decomposition reaction was halved as the initial concentration of a sole reactant was doubled. What is the order of the reaction? a. 2 b. 1 c. 3 d. 0 29. Given an atom of mass 10, following emission of a 2MeV gamma ray, calculate the recoil energy. a. 450 eV b. 198 eV c. 214 eV d. 222 eV 30. For the following reaction at 25oC: CuO( s) + H 2 ( g ) → Cu ( s ) + H 2O( g ) Values of the absolute entropies for the above substances are as follows: So (J/mol∙K): CuO = 43.5; H2 = 130.5; Cu = 33.5; H2O = 188.7 Calculate the ΔS o in J/mol∙K of the reaction assuming standard conditions. a. 48.2 b. 309.2 c. 135.2 d. 18.8 Prepared by JEPa‐a/for BSChem Graduate 2006
31. A refrigerator is maintained at –25oC in a room at ambient temperature of 35oC. The heat into the refrigerator is estimated as 104 J/min. Assuming that the unit is operating at 45% of its maximum thermodynamic efficiency, determine its power requirement in watts. a. 40.4 b. 89.8 c. 5380 d. 2299 32. At a certain temperature, 2 atm of CO are introduced into a vessel containing excess solid sulfur and a final equilibrium pressure of 1.18 atm is observed. Given the reaction, S ( s ) + 2CO( g ) U SO2 ( g ) + 2C ( s ) , find its Kp. a. 6.33 b. 2.28 c. 0.73 d. 0.87
33. Given the following Δ f G o in kJ/mol: C6H12O6(s) = –912; CO2(g) = –393; H2O (l) = –238; Calculate the standard free energy (Gibb’s energy) in kJ/mol for the oxidation of glucose, C6 H12O6 ( s ) + 6O2 ( g ) → 6CO2 ( g ) + 6 H 2O(l ) a. – 14370 b. 1842 c. – 4698 d. – 2874 34. The mass of an electron is 9.109 x 10–28 g. What is the molar mass of the electron? a. 4.39 x 1025 b. 6.61 x 1050 c. 5.48 x 10–4 d. 1.51 x 10–51
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35. How many α particles per second would be emitted form 4 x 10 gram of 210Po. The half‐life of 210Po is 138 days. a. 728 b. 543 c. 667 d. 401
36. The valve on a cylinder containing initially 15 L of an ideal gas at 25 atm, 25oC is opened to the atmosphere where the pressure is 760 torr. Assuming that the process is isothermal, how much work is KJ is done on the atmosphere by the action of expanding gas? a. 0.86 b. 3.64 c. 4.28 d. 5.85
37. At 30oC, Henry’s law constant for the solubility of oxygen gas in water is K O2 = 3.30 x 107 torr. Calculate the solubility of oxygen in grams at this temperature per 100 g of water. Assume air to be 20% O2 at room temperature. a. 3.1 x 10–7 b. 2.6 x 10–5 c. 4.6 x 10–6 d. 8.3 x 10–4 38. In an ideal solution of liquids A and B, the vapor pressure of a mixture of 0.60 mol of A and 2.4 mol of B is 0.42 atm at 70oC. 1.80 moles of A is added to the solution at 70oC and the vapor pressure of the solution rises to 0.55 atm. Calculate the vapor pressure if some of the vapor in equilibrium with the first solution were completely condensed. a. 0.51 atm b. 0.35 atm c. 0.20 atm d. 0.80 atm Prepared by JEPa‐a/for BSChem Graduate 2006
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39. 4.000 picogram (pg) of P decays by β emission to 0.500 pg in 75.9 days. Find the rate constant of the reaction in per day basis. a. 9.13 x 10–3 b. 2.74 x 10–2 c. 3.65 x 10–2 d. 4.18 x 10–3 40. At 1482 K and 12 atm, the equilibrium composition of sodium vapor contains 3.10 moles of Na monomer and 0.624 moles of Na dimer. Calculate the Kp for the dimerization of sodium at 1482 K. a. 2.01 x 10–2 b. 3.68 x 10–1 c. 2.47 d. 2.89 x 10–1
41. At 600oC, acetone decomposes producing CO and various hydrocarbons. The reaction is found to be first order in acetone concentration with a half‐life of 81.0 s. Given at 600oC, a one‐liter container into which acetone is injected at 0.48 atm, approximate how long would it take for the acetone pressure to drop to 0.45 atm? a. 39.8 s b. 7.5 s c. 81.0 s d. 15.0 s
42. During winter, the gauge pressure in an automobile tire when measured at 28oF was 30 pounds per square inch (psi). the same tire was used during summer. Assuming that the volume of the tire did not change, and no gas leaked out from the tire between winter and summer, what is the new pressure as measured on the gauge if the temperature rose to 115oF? a. 47.6 b. 37.9 c. 25.5 d. 35.3
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43. Estimate the zero‐point entropy of NO in cal/mol‐K. a. 0 b. 2.76 c. 1.38 d. 4.18
44. Determine the heat transferred when 627 J of work is done on a system consisting of 2 moles of an ideal gas at constant temperature. a. 0 b. – 627 J c. 627 J d. 1254 J
45. When [C] and [D] are doubled, the initial rate of the reaction C + D → E increases by a factor of eight. Which of the following rate laws is consistent with this observation? a. Rate = k[C][D] b. Rate = k[C]2[D]2 c. Rate = k[D]2 d. Rate = k[C]2[D]
46. After 66 minutes, a sample of 1944 K is found to have decayed to 12.5% of the original amount present. What is the half life of 44 19 K ? a. 22 min b. 66 min c. 44 min d. 88 min 47. What is the pressure of a column of air at a height of 10 km and a temperature of 2oC? Assume that the pressure at zero height is 760 mm Hg and the molar mass of air is 29. a. 449 b. 340 c. 219 d. 759
Prepared by JEPa‐a/for BSChem Graduate 2006
48. Which of the of the following statements is TRUE about the electromotive force of a system when all concentrations are unity? a. E < Eo b. E = Eo c. E = 0 d. E > Eo 49. A hypothetical gas’ empirical formula is B C B. Predict the structure of the gas if the ratio of heat capacities CP / CV is 1.32. a. Non‐linear b. Trigonal c. Linear d. Cannot be determined 50. A mixture of the vapors of two liquids X and Y which form ideal solutions is contained in a cylinder with a piston at constant temperature T. The mixture contains 60% X, with vapor pressures PXo and PYo given as 1.2 and 0.4 atm, respectively. The mixture is then slowly compressed. Calculate the total pressure at which the liquid first condenses. a. 0.475 atm b. 1.200 atm c. 0.800 atm d. 0.666 atm
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SITUATIONAL PROBLEMS:
Situation #01 – The activation energy for the thermal decomposition of gaseous acetaldehyde is 190.37 kJ/mol and the molecular diameter, σ, of a molecule of acetaldehyde is 5 x 10–8 cm. This decomposition is a second order reaction. 51. Determine the number of molecules colliding per milliliter per second at 800 K and 760 torr. a. 2.10 x 1031 b. 4.75 x 1015 c. 9.17 x 1021 d. 2.88 x 1028
52. Calculate the second order rate constant, k, in L/mol‐sec. a. 6.9 x 102 b. 7.7 x 10– 2 c. 8.3 x 104 d. 6.0 x 10– 23 53. Determine the pre‐exponential factor A at 800 K. a. 1.10 x 1013 b. 2.07 x 1011 c. 1.86 x 1015 d. 2.24 x 1017 Situation #02 – The standard enthalpy of the hydrogenation of propene is –214 kJ/mol. The standard enthalpy of the oxidation of propane to carbon dioxide and water is –2222 kJ/mol. The standard heat of formation of water is –286 kJ/mol. 54. Find the standard enthalpy in kJ/mol of the combustion reaction of propane at 25oC. a. –2076 b. –2068 c. –2060 d. –2084 Prepared by JEPa‐a/for BSChem Graduate 2006
55. Find the standard energy in kJ of the combustion reaction of propene at 25oC assuming all reactants and products behave as ideal gases. a. –2068 b. –2075 c. –2069 d. –2094
56. Find W in kJ of the combustion reaction of propene at 25oC. a. 2.0 b. 1.0 c. 4.0 d. 0 Situation #03 – A kilogram of acetylene was compressed from 10–2 L to 10–3 L at a constant temperature of 150oC. Calculate the minimum work that must be expended in the compression process assuming the gas to be
57. IDEAL. a. b. c. d.
1.09 x 103 J 3.12 x 105 J 1.11 x 105 J 3.08 x 103 J
58. van der Waals. The values of van der Waals’ constants a and b are 4.47 L2 atm‐mol–2 and 0.0571 L/mol, respectively. a. –4.98 x 109 J b. –1.55 x 107 J c. –8.15 x 109 J d. –0.95 x 107 J
59. If acetylene satisfies the van der Waals equation, what would be its critical pressure in atm? a. 282 b. 197 c. 50.8 d. 1371
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Situation #04 – A moving boundary experiment was performed initially at 25oC with 0.100 M KCl on the bottom and 0.0700 M NaCl on top. The transport numbers of K+ and Na+ ions in these solutions are 0.490 and 0.388, respectively. The boundary moved downward. The cross‐sectional area of the tube was 0.100 cm2. The charge passed through was 96.5 coulombs. 60. How many equivalents were transported? a. 1.00 x 10–3 b. 1.43 x 10–3 c. 0.25 x 10–3 d. 0.68 x 10–3 61. How far (in centimeters) did the boundary move? a. 65.4 b. 79.2 c. 49.0 d. 57.6 62. While the current was flowing, what was the concentration in mol/L of NaCl just above the boundary? a. 7.92 x 10–2 b. 2.18 x 10–1 c. 8.14 x 10–4 d. 6.24 x 10–5 Situation #05 – Four moles of an ideal nitrogen gas was expanded from 10 L to 25 L. The initial temperature was 35oC. Assume Cv = 2.5 R. Calculate the maximum work obtained by: 63. the isothermal expansion in J. a. 92.7 b. 9385.4 c. 7039.6 d. 2243.0 Prepared by JEPa‐a/for BSChem Graduate 2006
64. the adiabatic expansion in kJ where the final temperature was –243oC. a. –16.7 b. –9.2 c. –5.8 d. –23.1 65. Find the enthalpy change in J if the final temperature was –243oC. a. –24,210 b. –59,164 c. –8,090 d. –32,358 Situation #06 – At 1 atm, 120 g of benzene is vaporized at its boiling point of 80.2oC. The heat of vaporization is 94.4 cal/g. 66. Calculate W in units of joule. a. –4522 b. –293.6 c. +293.6 d. +4522 67. Calculate q in joules. a. 39497 b. 7480 c. 15627 d. 395 68. Calculate ΔU in joules. a. 34975 b. 44019 c. 0 d. 15921
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Situation #07 – Two equimolar solutions A and B with equal volume of solutions are mixed together and the reaction A + B → C occurs. After 60 minutes, A is 75% reacted. How much of A will NOT react after two hours if:
69. the reaction is zero order in both A and B? a. 50% b. 0% c. 25% d. 75%
70. if the reaction is first order in both A and B? a. 62.8% b. 25.0% c. 35.7% d. 14.3%
71. the reaction is first order in A and zero order in B? a. 21.7% b. 6.26% c. 32.2% d. 52.08% Situation #08 – Two grams of liquid water at 100oC is initially at 1.00 atm pressure and is confined to a volume in which no vapor is present. A valve is then opened and the water evaporates into an evacuated space of such volume that the final pressure is 0.10 atm. The entire apparatus is in a heat reservoir at 100oC. The ΔE for the vaporization of water is 2259 J/g at 100oC. Assuming that the vapor is an ideal gas and that the volume of the liquid is negligible as compared to the volume of the vapor, calculate: 72. q in joules for the water. a. 4173 b. 4863 c. 2617 d. 1914 Prepared by JEPa‐a/for BSChem Graduate 2006
73. ΔS for water in J/K. a. 50.40 b. 28.16 c. 14.24 d. 45.20 74. ΔS for the universe in J/K. a. 34.01 b. 3.05 c. 15.68 d. 25.43 Situation #09 – Three moles of an ideal monoatomic gas initially at 1 atm and 300K are put through the following cycle, all stages of which are reversible: (I) isothermal compression to 2 atm (II) isobaric temperature increase to 400K (III) return to the initial state by the path, P = a + bT, where a and b are constants. 75. Calculate ΔU in joules for the second step. a. 3741 b. 1247 c. 8107 d. 6236 76. Calculate ΔS in J/K for the first step. a. –8.6 b. –17.3 c. –5.8 d. –14.2
77. Which of the following statements is TRUE about ΔU and ΔS for the cycle described? a. Both ΔU and ΔS are zero. b. ΔU is positive and ΔS is zero. c. ΔU is zero and ΔS is positive. d. ΔU is positive and ΔS is negative. Situation #10 – Given the data below where Ve is the volume adsorbed at equilibrium and V is the volume adsorbed at time t. The adsorption rate follows first‐order kinetics. t (sec) 1380 3000 4260 7320 3 0.179 0.121 0.043 Ve – V (cm ) 0.284 78. Determine the rate constant K in per second. a. 3.20 x 10–4 b. 1.80 x 10–2 c. 1.60 x 10–3 d. 2.30 x 10–5 79. Determine the volume adsorbed at 3500 sec if Ve is equal to 0.451 cm3. a. 0.281 b. 0.302 c. 0.325 d. 0.290 80. Determine Ve – V if t is 800 seconds. a. 0.354 b. 0.418 c. 0.166 d. 0.201
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