Total 5 pages 1 Thermodynamics Final Practice Exam 1. Thermodynamic processes are described by a few important parameters: U, H, S, A, G, and ., which are functions of each other as well as of T, P, and V. Please define these parameters. H = U + PV A = U – TS G = H – TS  = (𝜕𝑛) 𝜕𝐺 𝑇,𝑃 2. What states of matter (or chemical reactions) are chosen as the reference states for these following definitions: (a) Standard Gibbs free energy of formation, fGo = 0 most stable free elements at standard state (1 bar) (b) Absolute entropy, S = 0 Perfect crystals at 0 K (c) Standard potential, Eo = 0 2H+ (a = 1) + 2e  H2 (1 bar) 3. Please derive the four Maxwell’s equations See prelim II. Total 5 pages 4. Please devise cells in which the following are the reactions: (a) Fe (s) + CuSO4 (aq)  FeSO4 (aq) + Cu(s) (b) Hg2Cl2 (s) + H2 (g)  2Hg (l) + 2HCl (aq) (c) 2Co (NO3)3 (aq) + Co (s)  3Co(NO3)2 (aq) (d) 2H2 (g) + O2 (g)  2H2O (l) Show the half-cell reactions and the cell potentials. (a) Cathode Cu2+ + 2e  Cu (+0.337 V) Anode Fe2+ + 2e  Fe (0.447 V) Cell potential = +0.337  (0.447) = 0.784 V (b) Cathode Hg2Cl2 + 2e  2Hg + 2Cl (+0.268 V) Anode 2H+ + 2e  H2 (0 V) Cell potential = +0.268 – 0 =0.268 V (c) Cathode Co3+ + e  Co2+ (+0.453 V) Anode Co2+ + 2e  Co (-0.28 V) Cell potential = 0.453 – (-0.28) = 0.733 V (d) Anode 2H+ +2e  H2 (0 V) Cathode O2 + 4H+ + 4e  2H2O (1.23 V) Cell potential = 1.23 – 0 = 1.23 V 2 Total 5 pages 5 3 The dependence of the equilibrium constant of a reaction on temperature is shown below lnKeq = –5.39 – 768/T + 125/T2 Please calculate the standard molar enthalpy (rHo) and (rCpo) of the reaction at 570 K. Use Gibbs-Helmholtz equation (equation 6.64) rHo = RT2(768/T2 – 250/T3) = R(768 – 250/T) = 8.314 ×(768 – 250/570) = 6381.5 (J/mol) 𝜕∆𝑟 𝐻 𝑜 rCpo=( 𝜕𝑇 ) = 250𝑅/𝑇 2 = 250 × 8.314/5702 = 0.0064 J/molK 𝑃 5. (a) Please derive the Clapeyron equation that describe the phase boundary: dP/dT = trsS/trsV (b) For a substance, the densities of liquid and solid states are 1.00, and 0.92 g/cm3 respectively, please schematically draw the corresponding phase diagram (indicate the triple point). (a) ref to equations (8.8 – 8.13) (b) Because the density of liquid is higher than that of solid, the slope of the solid-liquid boundary is negative. The other two slopes are positive. Total 5 pages 4 6. (a) In an ideal solution, the addition of a nonvolatile solute (B) leads to the depression of the freezing point of the solvent (A). Please show that Tf = KfmB with Kf = RMATfusion2/Hfusion. (b) The addition of 5 g of a compound to 750 g of CCl4 lowered the freezing point of the solvent by 0.78 K. Normal freezing point of CCl4 is 22.92 C and fusion enthalpy 2.69 KJ/mol. Please calculate the molar mass of compound (B). (a) Ref to equations (9.25 – 33) 8.314×0.154×(273.15−22.92)2 (b) Kf = RMATfusion2/Hfusion = 2.69×103 5/𝑀 FromTf = KfmB, 0.78 = 29.80 × 0.750𝐵 MB = 254.7 g/mol = 29.80 𝐾𝑘𝑔/𝑚𝑜𝑙 Total 5 pages 5 7. The following is the phase diagram of the nearly ideal solution of hexane and heptane. (a) Please identify the phases in the P-z diagram below. (b) For a solution containing 1 mol each of hexane and heptane, estimate the vapor pressure on the pressure-composition diagram when vaporization on reduction of the pressure just begins. (c) What is the vapor pressure of the solution when one drop of liquid remains? (d) What will be the pressure, the composition of the liquid, and the composition of the vapor when 0.4 mole of the mixture has been vaporized? (a) Please see the diagram. (b) At zheptane = 0.5, from the diagram Ptotal = 617 torr, and yheptane = 0.30 where vaporization starts. (c) 477 torr (d) Lever rule: nvapor = 0.4 mole, this means nsolution = 2 – 0.4 = 1.6 mole. From Lever Rule, this corresponds to “ nvapor =  nsolution”, or :The corresponding pressure is 576 torr, yheptane = 0.34, and xheptane = 0.57. liquid 617 torr 576 torr    477 torr vapor 0.30 0.34 0.57