课程名称︰普通化学二 课程性质︰系内必修 课程教师︰郑原忠 开课学院：理学院 开课系所︰化学系 考试日期（年月日）︰101年3月28日 考试时限（分钟）：120分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : General Chemistry (II) Mid-term Exam #1 Date: 3/28/2012 (A total of 110 points) ***Refer to the last page for thermodynamic data and physical constants.*** 1. (15%) Given that the mean-square speed of an ideal gas molecule is <u^2>=3kT/2 , answer the following questions: (a) Calculate the molar heat capacity of an ideal-gas system in constant vo- lume (C_v) and constant pressure (C_p), respectively. You need to give the details, not just the answers. (b) Thermodynamics yields that ┌δE ┐ ┌δV ┐ C_p - C-v = [ p - │--- │ ] * │--- │ . └δV ┘T └δT ┘P Show that the result is in agreement with that obtained from the kinetic theory. (c) Calculate the absolute entropy S of 1 mole of ideal gas in its standard state. Give the mathematical expression if you cannot obtain a number. (d) Does the result you obtained in (c) agree with the third law of thermo- dynamics? Explain. (e) Suppose you want to consider a quantum model for an ideal-gas system, which simple model will you choose? Describe the state of a bosonic ide- al gas system at absolute zero temperature and relate your description to the third law of thermodynamics. 2. Suppose 1.0 mol of an ideal gas is initially at P=4.0 atm and T=400 K. It is expanded irreversibly and adiabatically against a constant pressure of 1.0 atm until the volume has doubled. (a) (3%) Calculate the final volume of the gas. (b) (3%) Calculate w, q, and energy change ΔU of this process, in joules. (c) (3%) Calculate the final temperature of the gas. (d) (8%) Calculate the entropy change ΔS of the ideal gas in the process. (e) (3%) What is the entropy change of the surroundings, ΔS_surr, during this process? Does the results in (c) and (d) in combination satisfy the second law of thermodynamics? Explain. 3. (15%) Suppose 1.0 mol ice at -30°C is heated slowly at 1 atm until it is conver- ted to stream at 140°C. For ice, water, and stream, c_p is 38, 75, and 36 J/K-mol, respectively, and can be taken to be approximately temperature in- dependent. ΔH_fus for ice is 6.007 kJ/mol, and ΔH_vap for water is 40.66 kJ/mol. Use the ideal gas law for stream, and assume that the volume of 1 mol ice or water is negligible relative to that of 1 mol stream. (a) Calculate w, q, ΔH, and ΔU of this process. (b) Calculate ΔS of the system in this process. (c) Sketch the entropy of the system as a function of temperature from -30°C to 120°C. 4. (5%) The dissolution of calcium chloride in water is spontaneous at 25°C. Howe- ver, ΔS°of the reaction is ΔS°= -44.7 J/K. What conclusion can you draw about the sign and magnitude of the standard enthalpy change of the reaction ? You must state your reasoning clearly. 5. Consider wquilibrium states of a thermodynamic system that does only preesu- re-volume work. (a) (4%) Use the first law of thermodynamics to derive the total derivative of internal energy U, and then use the results to obtain the total deri- vatives of H, A, and G, respectively. Definitions of thermodynamic ener- gy functions are given in the last page. (b) (3%) Show that at constant temperature, pressure-induced Gibbs free ene- rgy change can be calculated from P_2 ΔG = ∫ V dP . P_1 (c) (3%) Derive the two Maxwell's relations from the total derivatives of A and G, respectively, 6. (10%) Gibbs free enerfy change for n mol of a solute whose concentration changes from c_1 to c_2 M in an ideal solution is ΔG = G(c=c_2) - G(c=c_1) = nRT ln(c_2/c_1) . Consider the simple reaction: aA(sol) → bB(sol) . (a) Give the thermodynamic cycle that relates the free energy change when a mol of A in concentration [A] reacts to produce b mol of B in concen- tration [B] to the standard-state reaction free energy ΔG°. Clearly define the states in your thermodynamic cycle. (b) Show that in equilibrium, lnK = - ΔG°/RT. Clearly state the definition of the thermodynamic equilibrium constant L. 7. (20%) Solid ammonium chloride is in equilibrium with ammonia and hydrogen chloride gases: NH4Cl(s) <---> NH3(g) + HCl(g) . The eauilibrium constant at 275°C is 1.04*10^(-2). When 0.98 g of solid NH4Cl, 0.1 g of NH3, and 0.1 g of HCl are placed into a closed vessel with volume 1.000 L and heat to 275°C, answer the following questions. (a) In what direction does the reaction proceed? (Hint: you need to calcul- ate the reaction quotient) (b) What is the partial pressure of each gas at equilibrium? (c) What is the mass of solid NH4Cl at equilibrium? (d) After the equilibrium is established at 275°C, we further increase the temperature to 375°C. In what direction does the reaction proceed dur- ing this process? Explain your answer. 8. (15%) Consider the reaction: N2(g) + 3H2(g) <---> 2NH3(g) (a) Use the thermofynamic data in the next page to calculate the thermodyna- mic equilibrium constant at 25°C. Is conversion of nitrogen and hydrog- en into ammonia at standard conditions spontaneous? (b) Suppose we measure the equilibrium constant K of the reaction around 25 °C and then plot lnK against the inverse temperature 1/T. Sketch the plot. You must pay attention to the slope and intercept of the curve and give numerical values whenever possible. (c) In reality, mixing nitrogen and hydrogen at 25°C does not produce ammo- nia readily. Explain why this reaction is difficult? Does this agree with the result in (a)? Explain your answer. --- Thermodynamic functions: H=U+PV A=U-TS G=H-TS ΔH°_f (25°C) S°(25°C) ΔG°_f (25°C) C_p (25°C) substance kJ/mol J/K-mol kJ/mol J/K-mol ------------------------------------------------------------------------------ N2(g) 0 191.50 0 29.12 N(g) 472.70 153.19 455.58 20.79 NH3(g) -46.11 192.34 -16.48 35.06 NH4+(aq) -80.29 111.3 -26.50 --- N2H4(l) 50.63 121.21 149.24 98.87 N2H4(aq) 34.31 138 128.1 --- Physical constants: R= 0.082 L-atm/K-mol = 8.3 J/mol-K --

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