CHEM 4300 homework chapter 3 + solution PDF

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Chem 4300 - Fall 2009- Take Home 4 1. The molar volume of a certain solid is 161.0 cm 3 mol-1 at 1.00 atm and 350.75 K, its melting temperature. The molar volume of the liquid at this temperature and pressure is 163.3 cm 3 mol-1. At 100 atm the melting temperature changes to 351.26 K. Calculate the molar enthalpy and entropy of fusion of the solid. 2. What is the vapor pressure of water at 90.0 oC if the standard boiling is 99.6 oC? The enthalpy of vaporization of water is 40.656 kJ/mol? 3. What is the vapor pressure of a sample of water at 298 K when a pressure of 10.0 bar is applied externally? The vapor pressure of water at 298 without external pressure is 0.0315 bar and the molar volume of the liquid at 298 is 18.07 cm 3 mol-1? 4. What is the mole fraction of water in the vapor over a solution of 2.00 moles of water and 2.00 moles of methanol at 50.0 oC, if the vapor pressure of methanol and water at this temperature are 100.0 torr and 92.51 torr respectively? (Assume an ideal solution)

Chem 4300 - Chapter 4 Note: subscripted m denotes a molar quantity Chem 4300 - Fall 2009- Take Home 4 1. The molar volume of a certain solid is 161.0 cm 3 mol-1 at 1.00 atm and 350.75 K, its melting temperature. The molar volume of the liquid at this temperature and pressure is 163.3 cm 3 mol-1. At 100 atm the melting temperature changes to 351.26 K. Calculate the molar enthalpy and entropy of fusion of the solid. ΔP/ΔT = ΔSm,f/ΔVm,f ΔSm,f =(ΔP*ΔVm,f)/ΔT=[(100.-1.00 atm)(163.3-161.0 cm 3 mol-1)]/(351.26-350.75K) ΔSm,f = 446.5 atm cm3 mol-1 K-1 = 45.2 Pa m3 mol-1 K-1 = 45.2 J mol-1 K-1 ΔSm,f =ΔHm,f/Tf, therefor Hm,f = ΔSm,f * Tf = (45.2 Jmol -1K-1)(350.75K) = 15900 J/mol 2. What is the vapor pressure of water at 90.0 oC if the standard boiling is 99.6 oC? The enthalpy of vaporization of water is 40.656 kJ/mol? ln(P2/P1) = (-ΔH/R)(1/T2 - 1/T1) = (ΔH/R)(T2 - T1)/(T2T1) P2 = P1 exp{(ΔH/R)(T2 - T1)/(T2T1)} P = 1.00 exp{(40656/8.314)(363.15-372.75)/(363.15*372.75)} = 0.707 bar 3. What is the vapor pressure of a sample of water at 298 K when a pressure of 10.0 bar is applied externally? The vapor pressure of water at 298 without external pressure is 0.0315 bar and the molar volume of the liquid at 298 is 18.07 cm 3 mol-1? RT ln(P2/P1) = V * ΔP = Vm,l * Papp P2 = P1 * exp{(Vm,l * Papp)/RT} P2 = 0.0315*exp{(1.807 x 10-5 m3/mol*1.0 x 106 Pa)/[(298 K)(8.314 Pa m3/mol K)]} P2 = 0.0317 bar 4. What is the mole fraction of water in the vapor over a solution of 2.00 moles of water and 2.00 moles of methanol at 50.0 oC, if the vapor pressure of methanol and

water at this temperature are 100.0 torr and 92.51 torr respectively? (Assume Ideal solution) XH2O = 2/(2+2) = 0.500 = XCH3OH YH2O = (XH2OP*H2O)/(XH2OP*H2O + XCH3OHP*CH3OH) YH2O = (0.5*92.51)/(0.5*92.51 + 0.5* 100.0) = 0.481...