R = 0.08206 L Atm/Mole KNA = 6.022 X 1023 F = 96485. C/Mol
CHM 3410 - Physical Chemistry 1
Final Exam
December 3, 2012
There are seven problems on the exam. Do all of the problems. Show your work.
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R = 0.08206 Latm/moleKNA = 6.022 x 1023 F = 96485. C/mol
R = 0.08314 Lbar/moleK1 Latm = 101.3 J
R = 8.314 J/moleK1 atm = 1.013 bar = 1.013 x 105 N/m2
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1. (28 points) Consider a substance that obeys the following equation of state
p(V – nb) = nRT (1.1)
a) The isothermal compressibility of a substance, T, is defined as
T = - (1/V) (V/p)T(1.2)
Find an expression for T for a substance whose equation of state is given by equation 1.1. Give your final expression in terms of p, T, and constants.
b) 2.00 moles of substance whose equation of state is given by equation 1.1 (and with b = 0.052 L/mol), undergoes a change in pressure from an initial value pi = 10.00 bar to a final value pf = 20.00 bar at a constant temperature T = 400.0 K. Find H for the process. You may use the following general relationship for enthalpy as a starting point for the problem.
dH = Cp dT + { V – T(V/T)p } dp (1.3)
2. (36 points) Sulfur dioxide (SO2), is an air pollutant produced by the combustion of trace sulfur impurities in fossil fuels. Its oxidation to sulfuric acid (H2SO4) leads to the formation of acid precipitation.
In coal burning electric power plants one method used to reduce emissions of sulfur dioxide is to convert it into calcium sulfite (CaSO3), which, upon further oxidation, forms calcium sulfate (gypsum, CaSO4), a substance with a variety of practical applications.
The conversion reaction that removes SO2 from waste gases is
CaCO3(s) + SO2(g) CaSO3(s) + CO2(g) (2.1)
Thermochemical data for the reactants and products are given below for T = 25. C, p = 1.00 bar.
a) Give the general expression for K, the equilibrium constant for the above reaction, in terms of reactant and product activities.
b) Give the expression that K reduces to if ideal behavior of the reactants and products is assumed to occur.
c) Using the thermochemical data given below, find the numerical value for K at T = 25. C.
d) Using the thermochemical data given below, find the numerical value for K at T = 250. C.
Substance Hf (kJ/mol) Gf (kJ/mol) S (J/mol.K)
CO2(g) - 393.51- 394.36 213.74
SO2(g) - 296.83 - 300.19 248.22
CaCO3(s) - 1206.9 - 1128.8 92.9
CaSO3(s) - 1156.0 - 1072.7101.4
3. (32 points) Consider the following process carried out on a 1.000 mol sample of nitrous oxide gas (N2O, M = 44.01 g/mol), which we can assume obeys the ideal gas law. The initial temperature and pressure of the gas are Ti = 300.0 K and pi = 0.500 atm. Heat is slowly added to the gas under conditions of constant pressure until a final temperature Tf = 400.0 is reached. Over the temperature range of the process the constant pressure molar heat capacity of nitrous oxide is given by the expression
Cp,m = a + bT (3.1)
where a = 26.70 J/molK and b = 0.040 J/molK2.
Find the following for the process: q, w, U, H, and S.
4. (30 points) The solid-liquid phase diagram for a mixture of two substances A and B is given below. Use the phase diagram to answer the following questions.
a) What is the normal melting point for substance A?
b) How many eutectic points (if any) are present in the system? Give the temperature and mole fraction A for each eutectic point that is present.
c) Consider a system containing 8.00 moles of A and 2.00 moles of B at temperatures in the range 350. K to 600. K. Give the temperature or range of temperatures (if any) where there will be three phases present in the system. Justify your answer.
d) A second system contains 2.00 moles of A and 8.00 moles of B at a temperature T = 500. K. At this temperature there are two phases present, a solid phase and a liquid phase. The mole fraction of A in the liquid phase present at this temperature is 0.368. Based on this information, find the total number of moles of liquid present in the system.
5. (30 points) When precise experimental data are available the standard cell potential for a galvanic cell is often fit to the expression
Ecell = a + bT + cT2(5.1)
where a, b, and c are constants.
Consider a galvanic cell whose standard cell potential is given by equation 5.1, with a = 0.328 v, b = 1.4 x 10-4 v/K, c = 8.5 x 10-8 v/K2, and = 2, where is the moles of electrons transferred per mole of reaction. Find numerical values for Grxn, Hrxn, Srxn, and Cprxn, (the free energy change, enthalpy of reaction, change in entropy, and difference in constant pressure molar heat capacity), for the chemical reaction taking place in the galvanic cell, at T = 300. K.
6. (28 points) The gas phase compound SO2Cl2 is thermally unstable, and decomposes by the process
SO2Cl2(g) SO2(g) + Cl2(g) (6.1)
The decomposition reaction follows first order homogeneous kinetics
v = - d[SO2Cl2]/dt = k [SO2Cl2] (6.2)
The rate constant for the above reaction is k = 1.96 x 10-6 s-1 at T = 560. K.
a) A gas mixture at T = 560. K initially contains 2.40 x 1011 molecules/cm3 of SO2Cl2. What concentration of SO2Cl2 will be present in the gas mixture after 24 hours?
b) The activation energy for the above reaction is Ea = 210.0 kJ/mol. At what temperature, in K, will the rate constant for the above reaction be k = 1.0 x 10-2 s-1?
7. (16 points) According to collision theory, the Arrhenius pre-exponential factor for a bimolecular gas phase reaction is given by the expression
A = P AB (8RT/AB)1/2 (7.1)
where P is a steric factor, AB is the A-B collision cross-section, and AB = MAMB/(MA+MB) is reduced mass.
Consider the bimolecular gas phase reaction between hydrogen atoms (H, M = 1.01 g/mol) and hydrogen bromide molecules (HBr, M = 80.91 g/mol)
H(g) + HBr(g) H2(g) + Br(g) (7.2)
Assuming P = 1, T = 300. K, and using H,HBr = 0.54 nm2 for the collision cross section, find the value for A predicted from collision theory. Give your final answer in units of cm3/molecules.