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Chemistry 1 Final Exam 2011/1/14 Constants R = 8.314 J / mol K = 0.0821 L atm / K mol = 8.314 L kPa / K mol 1 atm = 760 Torr = 1.01x105 Pa c = 2.99108 m/s h = 6.6310-34 Js In case that you need thermodyanmics data to solve the problems, please find four tables, including Table1, Table2-1, Table2-2 and Table 3 1. An innovative engine consisting of 1 mol of monatomic perfect gas atoms is taken through the cycle, state 1 state 2 state 3 as shown in the following graph. Here 3 1 is an isothermal process. (a) Determine the temperature T1, T2 and T3 at the state 1, 2, and 3, respectively. (3%) (b) Calculate q, w and U for each step and for the overall cycle. (12%) 2. Answer the following questions. (2% each, 16% total) (a) Who did make foundation of the concept of a heat and a work for thermodynamics? Who did prove the heat and the work are a kind of the forms of the energy? Write the name of these French engineer and British physicist. (b) Define the standard state (c) What is H for an exothermic process, H=0, H>0 or H<0? (d) Give a relationship between Cv and Cp for an ideal gas. (e) Which of the following thermodynamic functions are extensive: pressure, work, entropy, enthalpy, internal energy, volume? (f) What is the Hess’s law? (g) What is a thermochemical equation? (h) What is the constant given by dividing the gas constant with Avogadro constant? 1 3. A sample consisting of 2.0 mol CO2 occupies a fixed volume of 15.0 L at 300 K. When it is supplied with 2.35 kJ of energy as heat its temperature increases to 341 K. Assume that CO2 is described by the van der Waals equation of state, and 2 -2 -1 calculate w, U and H. a = 3.640 L ∙atm∙mol , b = 0.04267 L∙mol . You may treat CO2 as an ideal gas to solve this problem, but only get 2 points on the calculation of ΔH. (2% for w , 3% for U , 4% for van der Waals solution of H, 2% for ideal gas solution of H, 9% total) 4. The bond enthalpy in NO is 632 kJ∙mol-1 and that of each nitric N-O bond in NO2 is 469 kJ∙mol-1. (a) Draw Lewis structures of NO and NO2 and show the bond order of each compounds. The mean bond enthalpies given in the table below. (b) Using Lewis structures, estimate the bond enthalpy of NO2 and (c) explain the reason of the difference between actual bond enthalpy and estimated enthalpy (3% each, 9% total) Table 1 Mean bond enthalpies (kJ∙mol-1). 5. The standard enthalpy of formation of metallocene biz(benzene)chromium was measured in a calorimeter. It was found for the reaction Cr(C6H6)2(s) Cr(s) + 2C6H6(g) that ΔUro(583 K) = +8.0 kJ∙mol-1. Find the corresponding reaction enthalpy at 583 K. (6%) 6. Using the standard enthalpy of formation of the following values, calculate the standard reaction enthalpy for each of the following reactions. (2% each, 6% total) (a) 3NO2(g) + H2O(l) 3HNO3(aq) + NO(g). (b) B2O3(s) + 3CaF2(s) 2BF3(g) + 3CaO(s). (c) H2S(aq) + 2KOH(aq) K2S(aq) + 2H2O(l). 2 7. In an experiment, 1.0 mole of O2 was compressed irreversibly from P1 to P2 by driving in a piston, and in the process its temperature was increased from T1 to T2. What is the entropy change of the gas? Assuming that the gas behalves ideally and express your answer in terms of P1, P2, T1, T2 and R only. (10 %) 8. Trouton’s rule states that the standard entropy of vaporization is ~ 85 J K-1 mol-1 for most substances. Based on this rule, estimate the standard enthalpy of vaporization of liquid bromine, which boils at 59 C. (4%) 9. Consider the super-cool water to form ice at -10 C , the molar entropy change of the system can be estimated as Using the principle of 2nd law to quantitatively explain why this process is spontaneous! Assuming that the heat capacitances are independent of temperature. (5%) 10. Explain (a) why are almost all combustion reactions are spontaneous? (2%) (b) how an endothermic reaction can be spontaneous? (2%) (c) how to assist an originally non-spontaneous endothermic reaction becoming spontaneous? (2 %) 11. A scientist proposed the following two reactions to produce ethanol, a liquid fuel: C2H4(g) + H2O(g) CH3CH2OH(l) (A) C2H6(g) + H2O(g) CH3CH2OH(l) + H2(g) (B) Reaction B is preferred if spontaneous, because C2H6(g) is a cheaper starting material than C2H4(g). (a) Assume standard-state conditions and determine whether the above reactions are spontaneous. (5%) (b) Assuming that H and S are independent of temperature, estimate at what temperature ranges the above reactions would become spontaneous. (5%) 12. You wish to construct a fuel cell to do electrical work for you based on the oxidation of a hydrocarbon fuel. To understand how it works, you will (a) derive the relation between Gibbs free energy and the maximum non-expansion work at constant T and P (5%), (b) calculate the maximum non-expansion work available through the combustion of one mole octane fuel (C8H18, in liquid phase) at the standard-state conditions (5%) and (c) estimate the minimum heat that must be released to the environment which cannot be transferred to do the electrical work. (5%) 3 Table 2-1 Thermodynamic data of inorganic compounds at 25℃ 4 Table 2-2 Thermodynamic data of inorganic compounds at 25℃ 5 Table 3 Thermodynamic data of organic compounds at 25℃ 6 Solutions: 1. Ans. (a) From ideal gas law, T = PV/nR. T1 = P1V1/nR = 1 x22.4/1x0.0821 ([atm][L]/[mol][atm∙L∙K-1∙mol-1]) = 273 K T2 = P1V2/nR = 1 x44.8/1x0.0821 ([atm][L]/[mol][atm∙L∙K-1∙mol-1]) = 546 K T3 = T1 = 273 K (cycle 31 is isothermal. Thus, T3 = T1) (three correct: 2, one wrong:1, two&three wrong:0) (b) Cycle 12: w12 = -PV = -P1(V2-V1) = -1 x 22.4 = 22.4 atm∙L = -2.27 kJ U12 = 3nRT/2 = 3P1(V2-V1)/2 = +3.40 kJ (T21 = T2-T1 = P1(V2-V1)/nR) q12 = U12 - w12 = +5.67 kJ Another way to calculate Cycle 12 is also correct q12 = 5nRT/2 = +5.67 kJ U12 = 3nRT/2 = 3P1(V2-V1)/2 = +3.40 kJ w12 = U12 - q12 = -2.27 kJ Cycle 23: w23 = -PV =0, U23 = 3nRT/2 = -3P1(V2-V1)/2 = -3.40 kJ (T32 = T3-T2 = -P1(V2-V1)/nR), q23 = U23 = -3.40 kJ Cycle 31: w31 nRT1 V1 V3 V dV nRT1 ln 3 PV 1 1 ln 2 1.57kJ V V1 U31 = 0, q31 = – w31 = -1.57 kJ For overall cycle: w = -0.70 kJ, q = +0.70 kJ, U = 0, (one answer, 1 point) 2. Ans. (16% total, 2% each) (a) Carnot, and Joule. (b)Pure form at P = 1 bar. (c) H<0. (d) Cp = Cv + nR. (e) Entropy, enthalpy, volume, internal energy. (f) The overall reaction enthalpy is the sum of the reaction enthalpies of the steps into which the reaction can be divided. (g) Chemical equation written with a statement of reaction enthalpy. (h) Boltzmann constant. 7 3. Ans. Sample is in the fixed volume, i.e. under constant-volume condition. V = 0, thus, w = 0. 2.35 kJ of heat was supplied, thus q = +2.35 kJ. FromU = q + w, H = U + PV, van der Waals equation (P+an2/V2)(V-nb)=nRT, For initial state: (P1+an2/V2)(V-nb)=nRT1. For final state: (P2+an2/V2)(V-nb)=nRT2. Differential between final and initial state, (P2- P1)(V-nb)=nr(T2 - T1) and P = nRT/(V-nb). nRV T2 T1 2 0.082115 (341 300) H U V P q V P q 2.35 V nb 15 2 0.04267 = 2.35 [kJ] +(2x0.0821x15x41)/(15-2x0.04267) [atm] x 1.10x102 [J∙atm-1∙ L-1] = +3.03 kJ Thus, w = 0, U = +2.35 kJ, and H = +3.03 kJ. (2% for w , 3% for U , 4% for van der Waals solution of H, 2% for ideal gas solution of H) 4. Ans. (a) The Lewis structure for NO and NO2 show that the bond order in NO is a double bond and that in NO2 is 1.5 on average. (2%, if both Lewis structure is correct, then 1 point. If both bond order is correct, then 1 point) (b) Bond enthalpy of NO at 632 kJ∙mol-1 is close to N=O value listed in table, whereas the N-O bond enthalpy in NO2 is of 469 kJ∙mol-1 is slightly greater than the average of a N-O single and N=O double bond; ½ (630 kJ + 210 kJ) = 420 kJ. The extra stability is due to resonance stabilization. (5%) (c) The bond energies are the same for the two bonds, because the bonds are equivalent due to resonance. (2%) 5. Ans. Reaction enthalpy is obtained from H = U + ngasRT. Thus, H = U + ngasRT = 8.0 + 2x8.314x583 =17.7 kJ. (6%) 8 6. Ans. (6%, 2% each) (a) 3NO2(g) + H2O(l) 3HNO3(aq) + NO(g). Hor = 2Hof(HNO3) + Hof(NO, g) –[3Hof(NO2, g) + Hof(H2O, l)] = 2(-207.36)+90.25 – [3(+33.18) +(-285.83)] =-138.13 kJ. (b) B2O3(s) + 3CaF2(s) 2BF3(g) + 3CaO(s). Hor = 2Hof(BF3, g) +3Hof(CaO, s) –[Hof(B2O3, s)+Hof(CaF2, s)] = 2(-1137.0)+3(-635.09) – [-1272.8 + 3(-1219.6)] = +752.3 kJ. (c) H2S(aq) + 2KOH(aq) K2S(aq) + 2H2O(l). Hor = Hof(K2S, aq) +2Hof(2H2O, l) –[Hof(H2S, aq)+Hof(KOH, aq)] = -417.5+2(-285.83) – [-39.7 + 2(-482.37)] = +15.28 kJ. 7. Ans: For this irreversible process, we may construct two (reversible) steps first, (1) and (2), and then to calculate their individual entropy changes. We then sum them up to obtain the total entropy change of the system. (1) Compression from P1 to P2 at constant temperature (T1): (must be a reversible process) (5%) (2) Heating from T1 to T2 at constant pressure (P2): (can be either reversible or irreversible) (3) The total entropy change from P1 T1 to P2 T2: Note that if one considers the compression in terms of volume change (V 1 to V2 are not specified in the problem, so they MUST be transferred to T1/P1 and T2/P2 using the ideal gas law). Alternatively, one may construct the following steps and obtain exactly the SAME answer: (1) Compression from V1 to V2 at constant temperature (T1): (must be a reversible process) (2) Heating from T1 to T2 at constant volume (V2): (can be either reversible or irreversible) (3) The total entropy change from P1 T1 to P2 T2: 9 8. Ans: (4%) Hvap = 85 × (273.15+59) /1000 = 28.2 kJ mol-1 9. Ans: (5%) Therefore, It is a spontaneous process! 10.Ans: The criterion for spontaneous process is G = H - TS < 0 at constant T and P. (a) For most combustion reactions, H < 0, and H overwhelms the contribution of the –TS term for the G being always negative. (b) For endothermic reactions, H > 0, the only way for G < 0 is TS > H, so S must be positive to overcome the positive contribution of H. (c) Following (b), increasing T for TS > H is a way to assist the original non-spontaneous reaction to be spontaneous. 11.Ans: (5% each, 10% Total) For (A) C2H4(g) + H2O(g) CH3CH2OH(l), Hr0 = -277.69 – 52.26 + 241.82 = -88.13 kJ mol-1 < 0 Sr0 = 160.7-219.56 – 188.83 = -247.69 J K-1mol-1 < 0 Gr0 = Hr0 - TSr0 = -88.13 - 298×(-247.69/1000)= -14.32 kJ mol-1 < 0 For (B) C2H6(g) + H2O(g) CH3CH2OH(l) + H2(g), Hr0 = 0 - 277.69 + 84.68 + 241.82 = +48.81 kJ mol-1 > 0 Sr0 = 130.68 + 160.7 – 229.6 – 188.83 = -127.05 J K-1mol-1 < 0 Gr0 = Hr0 - TSr0 = 48.81 - 298×(-127.05/1000)= +86.67 kJ mol-1 > 0 (a) A is spontaneous but B is non-spontaneous. (b) B is never spontaneous because Hr0 > 0 and Sr0 <0. For reaction A, the criterion for spontaneous is Gr0 = Hr0 - TSr0 = -88.13 - T×(-247.69/1000) < 0, T < 88.13/0.2477 = 355.8 K When T < 355.8 K reaction A would become spontaneous, so it is spontaneous at 298 K. 10 12. Ans: (a) Starting from G ≡ H - TS G = H - TS (at constant T and P) = U + PV - TS (U ≡ H + PV) = q + w + PV - TS (U = q + w) = TS + (-PV + we,max) + PV - TS (for reversible process, q = TS and w = -PV + we,max ) = we,max (5%) Meaning that the maximum non-expansion work is equal to the Gibbs free energy for a reversible process. (b) C8H18(l) + 25/2 O2(g) 8 CO2(g) + 9 H2O(l) we,max = Gr0 = [9×(-237.13) + 8×(-394.36)] [(+6.4) + 0] = -5295.5 kJ mol-1 or | we,max | = 5295.5 kJ mol-1 (5%) (c) Hc0 = -5471 kJ mol-1, the minimum heat that must be released to the environment (cannot be used to do the electric work) is qTS =Hc0 - Gr0 = -5471 + 5296 = -175 kJ mol-1 or | q | = 175 kJ mol-1 (5%) 11