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1 10/06/08, Chem433 Exam # 1 Last Name or Student ID 1. (3 pts) 2. (3 pts) 3. (3 pts) 4. (2 pts) 5. (2 pts) 6. (2 pts) 7. (2 pts) 8. (2 pts) 9. (6 pts) 10. (5 pts) 11. (6 pts) 12. (12 pts) 13. (22 pts) 14. (30 pts) Extra(?) Total: (100pts) This exam consists of two parts: The first part is close book close notes with mostly conceptual problems. Give a brief explanation for maximum credit. You can submit corrections to your answers online before midnight 10/06/08. If answered correctly online, you get half the face value credit. The second part is take-home. You can submit your answers online before midnight of 10/07/08 or bring it to class on Wednesday to be submitted no later than 9 am.

2 N A = mol -1 ; R = 8.31 J K -1 mol -1 = L atm mol -1 K -1 ; 1 atm = 760 torr = Pa = 1.01 bar; 1 cal = J du =δq + δ w = TdS - pdv ; H = U + PV; A = U - TS; G = H - TS; ΔH = q p = C p ΔT ; ΔU = q V = C v ΔT ; δqrev w = pext dv ΔS = T Adiabatic reversible: PV γ = const, γ = C p /C V ; For ideal gases: C p,m = R + C V,m ; Equipartition theorem: C V,m = NR/2 M 2 2 Ms Maxwell distribution: f s s 3RT ( ) = 4π exp Δs 2 RT RT ; c π 2 rms = ; M vdw Equation of State: (P + a/v 2 m )(V m - b) = RT Δ r H(T) = Δ r H + Δ r C p ΔT; Δ r U(T) = Δ r U + Δ r C v ΔT; Δ S = Δ rc r dt T ΔG = VΔP - SΔT; Clapeyron: dp dt Δ 3/ 2 Δ G Δ = G = Δ Vdp r r r T r 2 T T P T = Δtr S ΔtrV Clausius-Clapeyron: P Δ 2 vap H 1 1 ln = P1 R T1 T2 H c = 8RT πm ; Δ mix G ideal = nrtσx i lnx i w Heat engine efficiency: ε =. Refrigerator coefficient of performance q h c = q c w n+ 1 n ax adx ax dx = ; = aln x; n + 1 x π = [C]RT; ΔT f = - K f m, ΔT b = K b m, ln ( ax) dx = xln( ax) x; udv = uv vdu Water: ΔH fus (H 2 O; 0 C) = 6.01 kj/mol; ΔH vap (H 2 O; 100 C) = kj/mol C p (H 2 O, vapor) = J K -1 mol -1 ; C p (H 2 O, liquid) = J K -1 mol -1 ; ΔH o f (H 2 O(l)) = kj/mol; ΔH o f (H 2 O(g)) = kj/mol ; ΔH o f (CO 2 (g)) = kj/mol K f (H 2 O) = 1.86 C/m; K b (H 2 O) = C/m,

3 Part I. In class and collected after 1 hour. It is close book close notes portion with conceptual problems. Give a brief explanation for full credit. 1. (3 pts) Which statements about chemical potentials are correct? Circle ALL correct properties for the Gibbs free energy, explain to secure partial credit a) at equilibrium between vapor and liquid, μ(g) = μ(l) b) in solution of substances A and B, μ A = μ B c) for a pure substance, it always decreases with temperature d) for a pure substance, it always increases with temperature e) for a pure substance, it always decreases with pressure f) for a pure substance, it always increases with pressure 2. (3 pts) A real gas at its Boyle temperature, T b, has the first virial coefficient 0. Identify ALL correct statements below: Explain briefly if necessary. a) at T = T b, the compression factor, Z, equals 1 at all pressures b) Z > 1 always for T > T b b) Boyle temperature depends on pressure c) Z < 1 at all pressures for T < T b d) if Z = 1, the behavior of a real gas is identical to that of an ideal gas in ALL aspects 3. (3 pts) List ALL correct properties for the Gibbs free energy: a) it is a state function b) it characterizes a spontaneity of a reaction c) it characterizes the amount of energy released or consumed in the course of a reaction d) it describes the maximum amount of work that can be obtained from a reaction e) it describes the maximum amount of work that can be obtained from a reaction at constant pressure and constant temperature f) it describes the maximum amount of nonexpansion work that can be obtained from a reaction at constant pressure and constant temperature e) it describes the maximum amount of nonexpansion work that can be obtained from a reaction at constant volume and constant temperature f) the more negative Δ r G, the faster is the reaction

4 4. (2 pts) Reversible isothermal expansion produces greater amount of work than irreversible isothermal. 5. (2 pts) Molar entropy of a liquid is greater than that of its solid at all temperatures 6. (2 pts) Endothermic reactions are always nonspontaneous 7. (2 pts) The entropy of a system can not decrease 8. (2 pts) Any adiabatic process is isentropic. 9. (6 pts) A balloon for hot-air traveling of 5 m in diameter can be filled either with hot air or with He instead. In the latter case, there will be buoyancy even without heating. Neglect the weight of the balloon and its load and calculate at what temperature the air-filled balloon will have the same buoyancy as the He-filled one at 25 o C. Is it reachable?

5 10. (5 pts) A sample consisting of 2.0 mol CaCO 3 (s) was heated to 800 C, when it decomposed. The heating was carried out in a container fitted with a piston which was initially resting on the solid. Calculate the work done during complete decomposition at 1.0 atm. What work would be done if instead of having a piston the container was open to the atmosphere? 11. (6 pts) Calculate ΔG o and ΔS o of mixing 2 moles of N 2 with 2 moles of O 2 at 25 o C, as well as, 1 mole of N 2 with 3 moles of O 2 at 25 o C. Explain the difference (preferably in one phrase). 12. (12 pts) Carbon monoxide is a poisonous gas that can be burned to make CO 2. a) (3 pts) What is the combustion enthalpy of CO(g), Δ c H o m, if its formation enthalpy is Δ f H o m (CO) = kj/mol and the enthalpy of combustion of C(graphite) is Δ c H o m (CO 2 ) = kj/mol b) (2 pts) In the reaction CO(g) + ½ O 2 (g) CO 2 (g), will the enthalpy increase or decrease with temperature? Why? c) (2 pts) In the same reaction, does the entropy increase or decrease? Why? d) (5 pts) Estimate Δ c H o m(co(g)) at 50 o C by presuming that vibrational contributions to heat capacity can be ignore for all substances.

6 13. (22 pts) Standard entropy of argon gas is S m o (298K) = J mol -1 K -1. Presuming that argon can be treated as an ideal gas, a) (8 pts) calculate the entropy of 2 moles at 300 o C and 3 bar. b) (6 pts) calculate its formation enthalpy Δ f H for the same condition. Clue: recall that the U internal energy of an ideal gas does not depend on its pressure, = 0 p T c) (8 pts) Calculate the Gibbs energy, Δ f G, for the same condition.

7 Part II. Take home and collected on Friday in class or online. I encourage you to try answering these questions without any help. If submitted in class, each correct answer gets 1.5 times of its face value. 14. (30 pts total) One mole of N 2 is subjected to a cyclic change A--> B -->C A, as shown in the Figure. Points A and B have the same temperature, T! ; transition B C is isochoric with volume, V 2 ; transition C A is adiabatic. Presume that N 2 can be treated as an ideal gas. Provide the numerical answers for P 1 = 2 atm, P 2 = 1 atm, V 1 = 1 L. a) (5 pts) Finish the sketch for the variation of temperature vs entropy in the cycle. Show qualitatively the changes, i.e., is the line connecting A and B straight or curved up or down? Similarly - for the line connecting B and C. b) (7 pts) Calculate the work on each step, w AB, w BC, and w CA, and for the whole cycle. c) (4 pts) Calculate ΔU for each step and the whole process.

8 d) (4 pts) Calculate ΔH for each step and the whole process. e) (4 pts) Calculate ΔS for each step and the whole process. c) (6 pts) Derive the expression for the thermodynamic efficiency, ε, of a thermal engine employing such a cycle.

9 Extra Credit. (up to 15 pts) you would have show it to me in person. Calculate the fugacity of van der Waals gas.

The Second Law of Thermodynamics (Chapter 4)

The Second Law of Thermodynamics (Chapter 4) First Law: Energy of universe is constant: ΔE system = - ΔE surroundings Second Law: New variable, S, entropy. Changes in S, ΔS, tell us which processes made