nd the volume of CO2 gas produced from 100 g of CaCO3 if the CO2 is at a pressure of 746 torr and a temperature of 301 K. Assume the gas to be ideal. 1.10. According to Dalton’s law of partial pressures, the pressure of a mixture of ideal gases is the sum of the partial pressures of the gases. The partial pressure of a gas is defined to be the pressure that would be exerted if that gas were alone in the volume occupied by the gas mixturend the volume of CO2 gas produced from 100 g of CaCO3 if the CO2 is at a pressure of 746 torr and a temperature of 301 K. Assume the gas to be ideal. 1.10. According to Dalton’s law of partial pressures, the pressure of a mixture of ideal gases is the sum of the partial pressures of the gases. The partial pressure of a gas is defined to be the pressure that would be exerted if that gas were alone in the volume occupied by the gas mixturend the volume of CO2 gas produced from 100 g of CaCO3 if the CO2 is at a pressure of 746 torr and a temperature of 301 K. Assume the gas to be ideal. 1.10. According to Dalton’s law of partial pressures, the pressure of a mixture of ideal gases is the sum of the partial pressures of the gases. The partial pressure of a gas is defined to be the pressure that would be exerted if that gas were alone in the volume occupied by the gas mixture
Physical Chemistry Assignments for Midterm (Term 181) Summary by Dr Nguyen Quang Long (HCMUT, Faculty of Chemical Engineering) Chapter 1: Concepts & Properties of pure substances Summary from Physical Chemistry, Robert G Mortimer, 3rd ed., Chapter 1.9 Find the volume of CO2 gas produced from 100 g of CaCO3 if the CO2 is at a pressure of 746 torr and a temperature of 301 K Assume the gas to be ideal 1.10 According to Dalton’s law of partial pressures, the pressure of a mixture of ideal gases is the sum of the partial pressures of the gases The partial pressure of a gas is defined to be the pressure that would be exerted if that gas were alone in the volume occupied by the gas mixture a A sample of oxygen gas is collected over water at 25◦C at a total pressure of 748.5 torr, with a partial pressure of water vapor equal to 23.8 torr If the volume of the collected gas is equal to 454 mL, find the mass of the oxygen Assume the gas to be ideal b If the oxygen were produced by the decomposition of KClO3, find the mass of KClO3 1.11 The relative humidity is defined as the ratio of the partial pressure of water vapor to the pressure of water vapor at equilibrium with the liquid at the same temperature The equilibrium pressure of water vapor at 25◦ C is 23.756 torr If the relative humidity is 49%, estimate the amount of water vapor in moles contained in a room that is 8.0 m by 8.0 m and 3.0 m in height Calculate the mass of the water 1.17 a Find the fractional change in the volume of a sample of liquid water if its temperature is changed from 20◦C to 30◦C and its pressure is changed from bar to 26 bar b Estimate the percent change in volume of a sample of benzene if it is heated from 0◦C to 45◦C at atm c Estimate the percent change in volume of a sample of benzene if it is pressurized at 55◦C from atm to 50 atm 1.18 a Estimate the percent change in the volume of a sample of carbon tetrachloride if it is pressurized from atm to 10 atm at 25◦C b Estimate the percent change in the volume of a sample of carbon tetrachloride if its temperature is changed from 20◦Cto 40◦C Find the change in volume of 100 cm3 of liquid carbontetrachloride if its temperature is changed from 20◦C to 25◦C and its pressure is changed from atm to10 atm 1.23 Assuming that the coefficient of thermal expansion of gasoline s roughly equal to that of benzene, estimate the fraction of your gasoline expense that could be saved by purchasing gasoline in the morning instead of in the afternoon, assuming a temperature difference of 5◦C 1.25 The coefficient of thermal expansion of ethanol equals 1.12×10−3K−1 at 20◦C and atm The density at20◦C is equal to 0.7893 g cm−3 a Find the volume of mol of ethanol at 10◦C and atm b Find the volume of 1mol of ethanol at 30◦C and atm 1.33 * a By differentiation, find an expression for the coefficient of thermal expansion of a gas obeying the van der Waals equation of state b Find the value of the coefficient of thermal expansion of nitrogen gas at 298.15 K and Vm=24.4 L mol−1 1.36.* Write an expression for the isothermal compressibility of a nonideal gas obeying the Redlich– Kwong equation of state 1.37 The experimental value of the compression factor Z=PVm/RT for hydrogen gas at T=273.15 K and Vm= 0.1497 L/mol−1 is 1.1336 Find the values of Z predicted by the van der Waals, Dieterici, and Redlich–Kwong equations of state for these conditions Calculate the percent error for each 1.38 The parameters for the van der Waals equation of state for a mixture of gases can be approximated by use of the mixing rules: Where x1 and x2 are the mole fractions of the two substances and where a1,b1,a2, and b2 are the van der Waals parameters of the two substances The quantities a12 and b12 are defined by a Using these mixing rules and the van der Waals equation of state, find the pressure of a mixture of 0.79 mol of N2 and 0.21 mol of O2 at 298.15 K and at a mean molar volume (defined as V/ntotal) of 0.00350 m3mol−1 Compare your answer with the pressure of an ideal gas under the same conditions b Using the van der Waals equation of state, find the pressure of pure N2 at 298.15 K and at a molar volume of 0.00350 m3 mol−1 c Using the van der Waals equation of state, find the pressure of pure O2 at 298.15 K and at a molar volume of 0.00350 m3mol−1 1.43 The critical temperature of xenon is 289.73 K, and its critical pressure is 5.840 MPa (5.840×10 Pa) a Find the values of the van der Waals constants a and b for xenon b Find the value of the compression factor,Z, for xenon at a reduced temperature of 1.35 and a reduced pressure of 1.75 1.48 j Assume that the van der Waals equation of state can be used for a liquid Calculate the molar volume of liquid water at 100◦C and atm by the van der Waals equation of state (Get a numerical approximation to the solution of the cubic equation by a numerical method.) Compare your answer with the correct value, 18.798 cm3mol−1 Chapter 2: First Law of Thermodynamics Summary from Physical Chemistry, Robert G Mortimer, 3rd ed., Chapter 2.1 Calculate the work done on the surroundings if mol of neon (assumed ideal) is heated from 0◦C to 250◦C at a constant pressure of atm 2.2 Calculate the work done on the surroundings if 100 g of water freezes at ◦C and a constant pressure of atm The density of ice is 0.916 g cm-3 and that of liquid water is g cm −3 2.3 Calculate the work done on 100.0 g of benzene if it is pressurized reversibly from 1.00 atm to 50 atm at a constant temperature of 293.15 K 2.4 Calculate the work done on the surroundings if kg of water is heated from 25 ◦C to 100◦C at a constant pressure of atm 2.7.* a Obtain a formula for the work done in reversibly and isothermally compressing mol of a van der Waals gas from a volume V1 to a volume V2 b Using the formula from part a, find the work done in reversibly compressing mol of carbon dioxide from 10 L to L at 298.15 K Compare with the result obtained by assuming that the gas is ideal c Using the formula from part a, calculate the work done on the surroundings if mol of carbon dioxide expands isothermally but irreversibly from L to 10 L at an external pressure of atm Compare with the result obtained by assuming that the gas is ideal 2.10 Calculate the amount of heat required to bring mol of water from solid at 0◦C to gas at 100◦ C at a constant pressure of atm Calculate w for the process 2.12 The normal boiling temperature of ethanol is 78.5◦C, and its molar enthalpy change of vaporization at this temperature is 40.3 kJ mol−1 Find q and w if mol of ethanol are vaporized at 78.5◦C and a constant pressure of atm 2.13 a If a sample of mol of helium gas is isothermally and reversibly expanded at 298.15 K from a pressure of 2.5 atm to a pressure of atm, find w and q b If the sample of helium from part a is isothermally and irreversibly expanded from the same initial state to the same final state with Pext =1 atm, find w and q 2.14 Calculate q and w if mol of helium is heated reversibly from a volume of 20 L and a temperature of 300 K to a volume of 40 L and a temperature of 600 K The heating is done in such a way that the temperature remains proportional to the volume 2.15 The normal boiling temperature of ethanol is 78.5◦C, and its molar enthalpy change of vaporization at this temperature is 40.3 kJ mol−1 Find q and w if mol of ethanol are reversibly vaporized at 78.5◦C and a constant pressure of atm Neglect the volume of the liquid compared with that of the vapor 2.18 a Calculate q,w, and ∆U if mol of neon (assumed ideal) is heated at a constant pressure of atm from a temperature of 0◦C to a temperature of 250◦C b Calculate q,w, and ∆U if the same sample of neon is heated at a constant volume from the same initial state to 250◦C and is then expanded isothermally to the same final volume as in part a 2.19 Calculate q,w, and ∆U for melting 100 g of ice at 0◦C and a constant pressure of atm The density of ice is 0.916 g mL−1 2.20.Calculate q,w, and ∆U for vaporizing mol of liquid water at 100 ◦C to steam at 100◦C at a constant pressure of atm 2.21.* Consider the following three processes: (1) A sample of mol of helium gas is isothermally and reversibly expanded from a volume of 10 L and a temperature of 400 K to a volume of 40 L (2) The same sample is reversibly cooled at a constant volume of 10 L from 400 K to a temperature of 300 K, then expanded reversibly and isothermally to a volume of 40 L, and then heated reversibly from 300 K to 400 K at a constant volume of 40 L (3) The same sample is expanded irreversibly and isothermally at a temperature of 400 K from a volume of 10 L to a volume of 40 L with a constant external pressure of atm Calculate ∆U,q, and w for each process 2.22 kg of water is pressurized isothermally at 298.15 K from a pressure of atm to a pressure of 10 atm Calculate w for this process State any assumptions 2.24 A sample of mol of argon is heated from 25 ◦C to 100◦C, beginning at a pressure of atm (101,325 Pa) a Find q,w, and ∆U if the heating is done at constant volume b Find q,w, and ∆U if the heating is done at constant pressure 2.25 Find the final pressure if mol of nitrogen is expanded adiabatically and reversibly from a volume of 20 L to a volume of 40 L, beginning at a pressure of 2.5 atm Assume nitrogen to be ideal with CV, m = 5R/2 2.26 A sample of mol of neon gas is expanded from a volume of L and a temperature of 400 K to a volume of L a Find the final temperature if the expansion is adiabatic and reversible Assume that the gas is ideal and that CV=3nR/2=constant b Find ∆U,q, and w for the expansion of part a c Find ∆U, q, w, and the final temperature if the expansion is adiabatic but at a constant external pressure of atm, starting from the same state as in part a and ending at the same volume as in part a d.Find ∆U, q, and w if the expansion is reversible and isothermal, starting at the same state as in part a and ending at the same volume as in part a State any assumptions and approximations 2.27 Find the final temperature and the final volume if mol of nitrogen is expanded adiabatically and reversibly from STP to a pressure of 0.6 atm Assume nitrogen to be ideal with CV, m=5R/2 2.28 mol of carbon dioxide is expanded adiabatically and reversibly from 298.15 K and a molar volume of L mol−1 to a volume of 20 L mol −1 a Find the final temperature, assuming the gas to be ideal withCV, m=5R/2 = constant b Find the final temperature, assuming the gas to be described by the van der Waals equation with CV, m=5R/2 = constant 2.29 A sample of 20 g of acetylene, C2H2, is expanded reversibly and adiabatically from a temperature of 500 K and a volume of 25 L to a volume of 50 L Use the value of CV, m obtained from the value in Table A.8 for 500 K with the assumption that acetylene is an ideal gas a Find the percent difference between this value of CV, m that you obtain and 5R/2 b Find the final temperature c Find the values of ∆U, q, and w for the process 2.30 a A sample of mol of argon gas is adiabatically and reversibly expanded from a temperature of 453.15K and a volume of 15.0 L to a final temperature of 400.0 K Find the final volume, ∆U, w, and q for the process Assume argon to be ideal and assume that CV, m= 3/2R b Consider an irreversible adiabatic expansion with the same initial state and the same final volume, carried out with P(transferred)=1 atm Find the final temperature, ∆U, w, and q for this process 2.31 a Find the final temperature, ∆U, q, and w for the reversible adiabatic expansion of O2 gas from 373.15 K and a molar volume of 10 L to a molar volume of 20 L Assume the gas to be ideal with CV, m= 5R/2 b Repeat the calculation of part a for argon instead of oxygen Assume that CV, m=3R/2 c Explain in physical terms why your answers for parts a and b are as they are 2.32 a mol of O2 gas is compressed isothermally and reversibly from a pressure of atm and a temperature of 100 ◦ C to a pressure of atm Find ∆U,q,w, and ∆H for this process State any assumptions or approximations Assume that the gas is ideal b The same sample is compressed adiabatically and reversibly from a pressure of atm and a temperature of 100.0◦ C to a pressure of atm Find ∆U,q, and w for this process State any assumptions or approximations Assume that CV, m=5RT /2 and that the gas is ideal 2.35 A sample of mol of water vapor originally at 500 K and a volume of 10 L is expanded reversibly and adiabatically to a volume of 20.0 L Assume that the water vapor obeys the van der Waals equation of state and that its heat capacity at constant volume is described by Eq (2.4-25) withα=22.2JK−1 mol−1 and β=10.3×10 −3 JK−2 mol−1 a Find the final temperature b Find the value of w and ∆U c Compare your values with those obtained if water vapor is assumed to be an ideal gas and its heatcapacity at constant pressure is constant and equal to its value at 500 K 2.36 a A sample of mol of H2 gas is reversibly and isothermally expanded from a volume of 20 L to a volume of 50 L at a temperature of 300 K Find q,w, and ∆U for this process b.The same sample of H2 gas is reversibly and adiabatically (without any transfer of heat) expanded from a volume of 20 L and a temperature of 300 K to a final volume of 50 L Find the final temperature Find q,w, and ∆U for this process 2.37 A sample of mol of N2 gas is expanded from an initial pressure of atm and an initial temperature of 450 K to a pressure of 0.4 atm a Find the final temperature if the expansion is adiabatic and reversible Assume thatCV= 5nR/2, so that γ=7/5=1.400 b Find ∆U,q, and w for the expansion of part a c Find ∆U,q,w, and the final temperature if the expansion is adiabatic but at a constant external pressure of 0.400 atm, starting from the same state as in part a and ending at the same volume as in part a d Find ∆U,q, and w if the expansion is reversible and isothermal, ending at the same pressure as in part a 2.40 a The Joule–Thomson coefficient of nitrogen gas at 50 atm and 0◦C equals 044 K atm −1 Estimate the final temperature if nitrogen gas is expanded through a porous plug from a pressure of 60.0 atm to a pressure of 1.00 atm at 0◦C b Estimate the value of (∂Hm/∂P)T for nitrogen gas at 50 atm and 0◦C State any assumptions 2.41 A sample of 3.00 mol of argon is heated from 25.00◦C to 100.00◦C, beginning at a pressure of atm (101,325 Pa) a Find q,w,∆U, and ∆H if the heating is done at constant volume b Find q,w,∆U, and ∆H if the heating is done at constant pressure 2.42 a Calculate ∆H and ∆U for heating mol of argon from 100 K to 300 K at a constant pressure of 1.00 atm State any assumptions b Calculate ∆H and ∆U for heating mol of argon from 100 K to 300 K at a constant volume of 30.6 L c Explain the differences between the results of parts a and b 2.43 a Find q, w, ∆U, and ∆H for heating mol of neon gas from 273.15 K to 373.15 K at a constant pressure of atm State any approximations and assumptions b Find q,w,∆U, and ∆H for heating mol of neon gas from 273.15 K to 373.15 K at a constant volume of 22.4 L State any approximations and assumptions 2.44 Supercooled steam is condensed irreversibly but at a constant pressure of atm and a constant temperature of 96.5 ◦C Find the molar enthalpy change State any assumptions and approximations 2.45 The enthalpy change of fusion of mercury is 2331 J mol−1 Find ∆H for converting 100.0 g of solid mercury at−75.0◦C to liquid mercury at 25.0◦C at a constant pressure of 1.000 atm Assume that the heat capacities are constant and equal to their values in Table A.6 of the appendix 2.46 Find ∆H if 100.0 g of supercooled liquid mercury at −50.0 ◦ C freezes irreversibly at constant temperature and a constant pressure of 1.000 atm The enthalpy change of fusion at the normal melting temperature is 2331 J mol −1 Assume that the heat capacities are constant and equal to their values in Table A.6 of the appendix 2.47 Find the value of q and the value of ∆H if mol of solid water (ice) at−10◦C is turned into liquid water at 80◦C, with the process at a constant pressure of atm Assume that the heat capacities are constant and equal to their values in Table A.6 of the appendix Summary from Thermodynamics - An engineering approach, Yunus A Çengel, 5th ed., Chapter 10 Chapter 4: Basic thermodynamics cycle Summary from Thermodynamics - An engineering approach, Yunus A Çengel, 5th ed., Chapter & 10 10-9C Consider a simple ideal Rankine cycle with fixed turbine inlet temperature and condenser pressure What is the effect of increasing the boiler pressure on 10-4 A steady-flow Carnot cycle uses water as the working fluid Water changes from saturated liquid to saturated vapor as heat is transferred to it from a source at 250 ° C Heat rejec tion takes place at a pressure of 20 kPa Show the cycle on a T-s diagram relative to the saturation lines, and determine (a) the thermal efficiency, (b) the amount of heat rejected, in kJ/kg, and (c) the net work output Pump work input: Turbine work output: Heat supplied: 10-SC Consider a simple ideal Rankine cyc le with fixed turbine inlet conditions What is the effect of lowering the condenser pressure on Heat rejected: Cycle efficiency: Pump work input: Turbine work output: Heat supplied: Heat rejected: Cycle efficiency: Moisture content at turbine exit: (a) (c) (a) (c) (a) (c) (a) (c) (a) (c) (a) (c) increases, (b) decreases, remains the same increases, (b) decreases, remains the same increases, (b) decreases, remains the same increases, (b) decreases, remains the same increases, (b) decreases, remains the same increases, (b) decreases, remains the same Moisture content at turbine exit: 17 (a) (c) (a) (c) (a) (c) (a) (c) (a) (c) (a) (c) increases, (b) decreases, remains the same increases, (b) decreases, remains the same increases, (b) decreases, remains the same increases, (b) decreases, remains the same increases, (b) decreases, remains the same increases, (b) decreases, remains the same 18 19 20 21 22 23 Answer key of odd-numbered questions From Physical Chemistry, Robert G Mortimer, 3rd ed., Chapter to Chapter K Answers to Numerical Exercises and Odd-Numbered Numerical Problems 1.3 a g 32.3 ft s−2 b R 22, 591 lb ft2 s−2 (◦ R)−1 mol−1 poundals (◦ R)−1 mol−1 c g 32.3 ft s−2 Chapter Exercises 1.1 a R b V c P 82.058 cm3 atm K−1 mol−1 97.86 L 4.157 × 105 Pa 4.157 bar 4.103 atm 3118 torr 1.5 a parsec 3.084 × 1013 km b parsec 3.259 light-years c distance to sun 4.848 × 10−6 parsec 1.4 b κT 1.000 atm−1 c α 3.4112 × 10−3 K−1 1.5 V (100.0◦ C) 1.7 roughly 50 piano tuners in Chicago 2.00154 L 1.6 a Vm (1.000 bar) b Vm (100.0 bar) 22,591 ft 1.9 V 0.02514 m3 73.53 cm3 mol−1 72.63 cm3 mol−1 25.14 L 1.11 n(H2 O) 120.2 mol H2 O m(H2 O) 2.165 kg H2 O 1.7 b P 101250 Pa 0.9993 atm P(ideal) 101322 Pa 0.99998 atm c P 2.429 × 106 Pa 23.97 atm P(ideal) 2.479 × 106 Pa 24.47 atm 1.15 (∂P/∂V)T,n (∂P/∂T )V,n (∂P/∂n)T,V −4.526 × 106 Pa m−3 371.2 Pa K−1 1.014 × 105 Pa mol−1 1.9 b TBoyle 505 K d Vm 1.06 × 10−4 m3 mol−1 If Z 1, P 211 atm 1.17 a ∆V /V ≈ 0.93 × 10−3 b ∆V /V ≈ 0.05567 c ∆V /V ≈ 0.00480 1.13 a 1.56 Pa K1/2 m6 mol−2 b 2.68 × 10−5 m3 mol−1 1.19 ∆V 1.23 ∆V /V Chapter Problems 0.52 cm3 0.006 1.25 a V (10◦ C) b V (30◦ C) 1.1 c 1.802617 × 1012 furlongs fortnight−1 57.72 cm3 59.02 cm3 1309 24 1310 K Answers to Numerical Exercises and Odd-Numbered Numerical Problems 1.29 b κT 4.120 × 10−6 Pa−1 For an ideal gas, κT 4.034 × 10−6 Pa−1 1.31 b P 1.97 × 107 Pa 1.33 b α 3.363 × 10−3 K−1 194 atm 1.37 Van der Waals: Z 1.1434 (0.86% error) Dieterici: Z 1.1255 (0.71% error) Redlich–Kwong: Z 1.1153 (1.6% error) 1.39 a κT b κT 9.843 × 9.945 × 10−6 Pa−1 1.41 a P b P 28.8 bar 28.8 bar 1.43 a a b b Z 0.4192 Pa m6 mol−2 5.192 × 10−5 m3 mol−1 0.7305 10−6 Pa−1 1.45 a N(N2 ) 1.9 × 1022 molecules b N(N2 , in classroom, from Julius Caesar) ≈ × 106 1.47 b V (25◦ C) 1.00294 cm3 d 3.9601◦ C from the first set of parameters, 3.6066◦ C from the second set of parameters e α 2.069 × 10−4 1.49 a TRUE b FALSE c FALSE d FALSE e TRUE f FALSE g TRUE h TRUE i FALSE j TRUE Chapter Exercises 2.1 a wrev b wrev 2.2 a w b w −8934 J −9065 J −507 J −859 J 2.4 a wsurr 507 J b ∆P −3.06 atm 2.5 q 1.602 Btu 2.6 a ∆m 2.801 × 10−14 kg 2.8 w −8106 J q 8106 J 2.11 a ∆U 83 J w −1824 J q 1907 J b ∆T −6.66 K 2.12 a w q b q w c ∆U −5690 J 6708 J 8151 J −7138 J 1013 J 2.13 V 7.98 L 2.14 T2 ∆U w 2.18 a P2 b P 473.3 K 2184 J 2184 J 1.231 × 105 Pa 1.231 × 105 Pa 2.19 w −5066 J ∆U −5066 J T2 418.8 K T2 (rev) 315.0 K 25 1.215 atm 1311 K Answers to Numerical Exercises and Odd-Numbered Numerical Problems ∆U(rev) −11536 J w(rev) −11536 J Chapter Problems 2.1 wsurr 2.21 a CP,m (He) 20.786 J K Mol−1 CP,m (Ne) 20.786 J K mol−1 CP,m (Ar) 20.786 J K mol−1 5R/2 20.786 J K mol−1 b CP,m (N2 ) 29.124 J K mol−1 CP,m (O2 ) 29.376 J K mol−1 CP,m (CO) 29.142 J K mol−1 7R/2 29.101 J K mol−1 2.3 w 4.79 J 2.7 b w 1765 J c wsurr 507 J 2.9 I −8.3145 × 104 Pa 2.22 CP,m (298.15 K) 37.1 J K−1 mol−1 CP,m (500 K) 45.1 J K−1 mol−1 CP,m (1000 K) 52.1 J K−1 mol−1 5R/2 20.786 J K mol−1 2.11 ∆T 2.13 a q b q 2.24 CP,m 25.10 J K−1 mol−1 3R 24.944 J K−1 mol−1 0.6% difference 2.29 Tf 7263 K 3.771 K 2.32 ∆H ≈ −199 kJ mol−1 From ∆f H values, ∆H ◦ −w −w 4543 J 2975 J 2.19 q 33.35 kJ w 0.92 J ∆U 33.35 kJ 2.28 Tf 5229 K 2.31 ∆Tcal 0.117 K 2.17 E 9.0 × 109 J mol−1 v 4.2 × 105 m s−1 2.27 a ∆U 935 J b ∆H 1559 J q 3086 J w −2151 J 54.530 kJ mol−1 −0.8206 atm 2.15 q 120.9 kJ w −8.771 kJ 2.26 At 298.15 K, CP,m 29.37 J K−1 mol−1 At 500 K, CP,m 31.42 J K−1 mol−1 At 1000 K, CP,m 34.0 J K−1 mol−1 At 2000 K, CP,m 38.3 J K−1 mol−1 2.30 ∆U ◦ 2079 J 2.21 (1) q (2) q (3) q −w −w −w 2.23 a µJ b T2 −1.43 × 104 K m−3 mol 282 K 9221 J, ∆U 6916 J 3040 J 2.25 P2 0.947 atm 2.27 a T2 b V2 −174.264 kJ mol−1 26 25.7 K 0.0705 m−3 1312 K Answers to Numerical Exercises and Odd-Numbered Numerical Problems b q ∆U 1247 J w ∆H 2079 J 2.29 a percent difference −41.9% b T2 425.7 K c q ∆U w −5103 J 2.45 ∆H 2.31 a T2 282.8 K q w ∆U −1878 J b T2 235.1 K q w ∆U −1722 J 2.33 298.15 K Ar H −0.01 He O 5.41 C 0.25 500 K 0 2.27 0.087 2.35 a T2 403.2 K b ∆U 2599 J w 2599 J c T2 403.6 K 2.37 a T2 346.4 K b w ∆U −4310 J c q ∆U w −2770 J T2 383.4 K d ∆U q −w 6860 J 2.41 a w q b ∆U q w ∆U 2806 J 2806 J 4677 J −1871 J 2.43 a q ∆H 2079 J w −831.45 J ∆U 1248 J 1000 K 2000 K 0 0.62 0.024 0.19 0.80 5745 J 2.47 q ∆H 24.80 kJ 2.49 a ∆H ◦ ∆U ◦ b ∆H ◦ ∆U ◦ c ∆H ◦ ∆U ◦ 1236.79 kJ mol−1 1234.31 kJ mol−1 −565.99 kJ mol−1 −563.53 kJ mol−1 −1366.84 kJ mol−1 −1364.37 kJ mol−1 2.51 a ∆H ◦ 348K b ∆H ◦ 348K c ∆H ◦ 348K −1233.38 kJ mol−1 −566.66 kJ mol−1 −1368.19 kJ mol−1 2.53 a ∆H ◦ −3119.71 kJ mol−1 b ∆H ◦ −2875.76 kJ mol−1 c ∆H −2855.68 kJ mol−1 z 2.55 a ∆f H ◦ (C12 H22 O11 ) −2224.5 kJ mol−1 ∆U ◦ −5640.9 kJ mol−1 b ∆f H ◦ (C18 H36 O2 ) −947.7 kJ mol−1 The enthalpy change per gram is −39.65 kJ g−1 The enthalpy change per gram of sucrose −16.48 kJ g−1 2.57 a ∆H ◦ b ∆U ◦ c ∆U ◦ −890.309 kJ mol−1 −885.351 kJ mol−1 −885.347 kJ mol−1 2.59 a ∆U ◦ ≈ −2796 kJ mol−1 ∆H ◦ ≈ −2794 kJ mol−1 ◦ b ∆H298K −2855.68 kJ mol−1 ◦ ∆H373K −2852.74 kJ mol−1 ◦ c ∆U ≈ −606 kJ mol−1 ∆H ◦ ≈ −608 kJ mol−1 27 1313 K Answers to Numerical Exercises and Odd-Numbered Numerical Problems b ηhp 16.4 4.1 × 10−9 dollars J−1 c 3.6 × 10−8 dollars J−1 2.61 a ∆H ◦ ≈ 76 kJ mol−1 From enthalpy changes of formation, ∆H ◦ 71.488 kJ mol−1 b ∆H ◦ ≈ −542 kJ mol−1 From enthalpy changes of formation, ∆H ◦ −545.092 kJ mol−1 3.5 ∆S 40.15 J K−1 ∆Ssurr −40.15 J K−1 ∆U q −w 11970 J 2.63 a ∆H ◦ 71.488 kJ mol−1 b ∆U ◦ 69.009 kJ mol−1 c EB (P-Cl) ≈ 156 kJ mol−1 3.6 ∆vap H 43.93 kJ 9.7 atm Fg /A ∆S 124.9 J K−1 2.65 a ∆H ◦ −311.42 kJ mol−1 b ∆U ◦ −306.46 kJ mol−1 c ∆U ≈ −323 kJ mol−1 ◦ d ∆H373 −315.11 kJ mol−1 2.67 a vs b vs γ 3.7 ∆S 3.8 a ∆S 12.26 J K−1 b ∆Ssurr −12.26 J K−1 346 m s−1 1016 m s−1 1.2117 2.69 a w ∆U q ∆H 180 J b same as part a 3.9 ∆Ssurr 3.11 ∆S 12.97 J K−1 ∆Ssurr −11.14 J K−1 ∆Suniv 1.83 J K−1 3.12 entropy production 3.13 a ∆Smix b ∆Smix 2.73 T2 217 K tC −56◦ C 3.14 b N c N Chapter Exercises 3.3 a ηr −9.85 J K−1 3.10 ∆S 24.47 J K−1 ∆Ssurr ∆Suniv 24.47 J K−1 2.71 a TRUE b FALSE c FALSE d FALSE e TRUE f FALSE g TRUE h FALSE i FALSE 3.2 ηc 29.149 J K−1 0.00274 J K−1 s−1 5.762 J K−1 4.322 J K−1 1296 21 3.15 24 Ω 106.61×10 0.378 3.19 b ∆H −565.990 kJ mol−1 c qsurr > and ∆Ssurr > 15.4 28 1314 K Answers to Numerical Exercises and Odd-Numbered Numerical Problems 1898.3 J K−1 1725.5 J K−1 d ∆Ssurr ∆Suniv 3.20 a ∆S ◦ b ∆S ◦ −326.607 J K−1 mol−1 −94.678 J K1 mol−1 3.21 Sst 14.90 J K−1 mol−1 3.22 ∆vap Hm 16240 J mol−1 Table A.7 value 15646 J mol−1 Chapter Problems 3.1 a η 0.211 V2 2.52 L V4 0.857 L b w1 −1411 J w2 −312 J w3 1113 J w4 312 J 3.3 h 14.1 km 3.5 a ηc 0.2114 b ηc 0.4107 percentage improvement c m 1.996 kg 3.7 a q(house) b q(house) c q(house) 8.4 × 107 J 4.68 × 108 J 4.00 × 107 J 3.11 a ηc 0.01649 b dV/dt 1.45 × 103 m3 s−1 3.13 a ∆S1 5.7632 J K−1 ∆S2 5.7587 J K−1 ∆S3 −2.3919 J K−1 ∆S4 −2.9612 J K−1 ∆S5 −3.3712 J K−1 ∆S6 −2.7985 J K−1 b All values are the same 94.3% 3.15 w −1227 J q ∆U −1227 J Tf 401.6 K ∆S 7.278 J K−1 ∆Srev qrev ∆Urev −3441 J wrev −3441 J 3.17 a ∆S b ∆S 217.98 J K−1 16.54 J K−1 3.19 a ∆S −5.7632 J K−1 ∆U q −1718.3 J w 1718.3 J ∆Suniv ∆Ssurr 5.7632 J K−1 b q ∆S ∆Ssurr ∆Suniv T2 473.3 K ∆U 2184.4 J w 2184.4 J c T2 > 473.3 K ∆U > 2184.4 K w > 2184.4 K q ∆S > ∆Ssurr ∆Suniv > d ∆S −5.7632 J K−1 ∆U w < 5066 J q > −5066 J ∆Suniv > ∆Ssurr > 5.7632 J K−1 3.21 a ∆S 23.55 J K−1 b ∆S 23.55 J K−1 c ∆Ssurr −23.55 J K−1 29 1315 K Answers to Numerical Exercises and Odd-Numbered Numerical Problems d ∆S 23.55 J K−1 ∆Ssurr −18.71 J K−1 ∆Suniv 4.84 J K−1 3.41 ◦ (270 K) Sm 3.23 a T2 271.4 K q ∆U −5702 J w −5702 J ∆S ∆Suniv b T2 439.1 K ∆S w −1520 J q −4183 J ∆U −5703 J ∆Suniv 12.00 J K−1 3.43 ammonia benzene carbon monoxide carbon tetrachloride ethane ethanol methane water 3.25 ∆S 18.71 J K−1 3.27 a Sst b Sst 3.47 ∆S ∆H qsurr 14.898 J K−1 11.526 J K−1 3.49 a q b h c h 3.29 Sst 3.7154 × 10−21 J K−1 3.31 ∆Smix 30.00 J K−1 mol−1 40.00 J K−1 mol−1 3.35 a ∆S ◦ b ∆S ◦ c ∆S ◦ d ∆S ◦ 100.97 J K−1 mol−1 −169.4 J K−1 mol−1 −232.72 J K−1 mol−1 1330.0 J K−1 mol−1 3.37 ◦ a Sm,473K ◦ b Sm,473K 39.99 J K−1 mol−1 ∆S/J k−1 mol−1 97.44 121.47 82.72 91.27 84.80 115.12 81.57 108.99 −145.11 J K−1 44.004 kJ−1 44.004 kJ −1.225 × 105 kJ 7.08 km 6.03 km 3.51 a FALSE b FALSE c TRUE d FALSE e FALSE f TRUE g TRUE h FALSE 5.763 J K−1 3.33 ◦ (CO ) Sm ◦ (H O) Sm −172.864 J K−1 mol−1 b ∆S ◦ 3.53 a ∆Smix 9.351 J K−1 b five types of molecules n(C35 Cl4 ) 0.316406 mol 0.421876 mol n(C35 Cl37 Cl) 35 37 n(C Cl2 Cl2 ) 0.210936 mol n(C35 Cl37 Cl3 ) 0.046875 mol n(C37 Cl4 ) 0.003906 mol c ∆Smix 10.157 J K−1 204.9 J K−1 mol−1 204.7 J K−1 mol−1 3.39 a ∆f S ◦ (CO) 89.340 J K−1 mol−1 ∆f S ◦ (CO2 ) 2.908 J K−1 mol−1 ∆f S ◦ (O2 ) 30 1316 K Answers to Numerical Exercises and Odd-Numbered Numerical Problems 3.55 Sst 20.66 J K−1 4.17 a µi − µ◦i b µi − µ◦i 0.0326 kJ mol−1 5.741 kJ mol−1 Chapter Exercises Chapter Problems 4.1 a (∂V /∂S)P,n 8124 K m−3 b (∂V /∂S)P,n 4062 K m−3 c (∂V /∂S)P,n 16248 K m−3 4.3 a ∆H ◦ −571.660 kJ mol−1 b wsurr 101.9 kJ c ∆S ◦ −326.607 J K−1 mol−1 ∆G◦ −474.282 kJ mol−1 d wnet,surr,max 474.282 kJ wtotal,surr,max 469.314 kJ 4.2 a (∂V /∂S)P,n 0.00118 K Pa−1 b Same as part a 4.3 b (∂S/∂P)T,n −8.226 × 10−5 J K−1 Pa−1 4.4 ∆S 19.37 J K−1 ∆S(ideal) 19.14 J K−1 4.5 (∂U/∂V )T,n 4.6 a (∂U/∂V )T,n 4.7 b (∂H/∂P)T,n 309 J m−3 4.11 a f b f c f 309 Pa 4.13 vs 1302 m s−1 1113 atm −7.54 × 10−5 J Pa−1 0.4418 J K−1 g−1 504.2 kPa 496900 Pa 1.434 × 106 Pa 4.12 a Gm − G◦m b Gm − G◦m 11.376 J K−1 4.9 b ∆S 23.157 J K−1 ∆Sideal 23.053 J K−1 4.8 a CV,m 74.841 J K −1 mol−1 b CP,m − CV,m d γ 1.0106 For argon gas, γ 1.667 4.9 CV 4.7 b ∆S 7.09 × 10−2 J mol−1 6.38 J mol−1 4.13 a ∆G383.15K ≈ −1090 J mol−1 b ∆G383.15K ≈ −1090 J mol−1 4.15 c lim àJT 7.441 J atm1 P0 4.3 ì 106 K Pa−1 4.17 a Hm (P2 ) − Hm ( P1 ) 91.04 J mol−1 b Hm (P2 ) − Hm (P1 ) 92.64 J mol−1 c ∆fus Hm 6004 J mol−1 4.21 a w −1716 J b ∆S 5.736 J K−1 c ∆U 0.0099 J d w ∆U 0.0099 J q 0.0099 J ∆S 5.736 J K−1 4.23 ◦ b Sm − Sm −7.53434 J K−1 mol−1 4.25 b ∆U 123.8 J 4.27 b ∆S −0.0374 J K−1 31 ... ∆S ◦ 10 0.97 J K? ?1 mol? ?1 ? ?16 9 .4 J K? ?1 mol? ?1 −232.72 J K? ?1 mol? ?1 1330.0 J K? ?1 mol? ?1 3.37 ◦ a Sm ,47 3K ◦ b Sm ,47 3K 39.99 J K? ?1 mol? ?1 ∆S/J k? ?1 mol? ?1 97 .44 12 1 .47 82.72 91. 27 84. 80 11 5 .12 81. 57 10 8.99... Pa? ?1 0 .4 418 J K? ?1 g? ?1 5 04. 2 kPa 49 6900 Pa 1. 43 4 × 10 6 Pa 4 .12 a Gm − G◦m b Gm − G◦m 11 .376 J K? ?1 4. 9 b ∆S 23 .15 7 J K? ?1 ∆Sideal 23.053 J K? ?1 4. 8 a CV,m 74. 8 41 J K ? ?1 mol? ?1 b CP,m − CV,m d γ 1. 010 6... × 10 −5 J K? ?1 Pa? ?1 4. 4 ∆S 19 .37 J K? ?1 ∆S(ideal) 19 . 14 J K? ?1 4. 5 (∂U/∂V )T,n 4. 6 a (∂U/∂V )T,n 4. 7 b (∂H/∂P)T,n 309 J m−3 4 .11 a f b f c f 309 Pa 4 .13 vs 13 02 m s? ?1 111 3 atm −7. 54 × 10 −5 J Pa−1