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1 CHEM 3411 MWF 9:00AM Fall 2010 Physical Chemistry I Exam #2, Version B (Dated: October 15, 2010) Name: GT-ID: NOTE: Partial Credit will be awarded! However, full credit will be awarded only if the correct answer is in marked boxes, when provided. (Do not write in the small boxes in the right margin; they are for grading purposes only.) Problem Max.Pts Actual Score TOTAL: 60 You MUST sign the honor pledge: On my honor, I pledge that I will not give or receive aid in examinations; I will not attempt to gain prior access to examinations; I will not represent the work of another as my own; and I will avoid any activity which will encourage others to violate their own pledge of honor. Your Signature: You may find the following information useful: Constant Symbol Value Units Speed of light in vacuum c E+10 cm sec 1 Electronic charge e E 10 esu e E 19 C (Coulombs) Avogadro s number N A E+23 molecules mole 1 Gas Constant R J K 1 mole 1 R E 2 L bar K 1 mole 1 R E 2 L atm K 1 mole 1 R E+1 L Torr K 1 mole 1 Boltzmann constant k B E 23 J, K 1 Electron mass m e E 4 amu Proton mass m p amu Neutron mass m n amu Planck Constant h E 27 erg sec h E 34 J sec h E 27 erg sec Bohr radius a E-11 m Atomic mass unit amu E 24 g Electron volt ev E 19 J ev E 12 erg Debye D E 30 C m Calorie cal J Rydberg Constant R E+5 cm 1 A sheet of possibly useful formulas is provided at the end. 1

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3 1. Concept Questions. Try to be concise, and correct! (6 pts) a. How does Gibbs free energy vary with pressure for a gas? Justify. (6 pts) b. According to a Maxwell s relation what derivative is Justify. ( S ) V T equal to? S: (8 pts) d. Suppose that you are making measurements of the two-phase coexistence between the liquid and gas phases of carbon tetrachloride. What is the difference, if any, in describing the coexistence point as being equilibrated or as being stable? Please also provide the criteria for equilibrium and stability using thermodynamic quantities. S: S: 3 :

4 2. Entropy. (5 pts) a. Suppose that 92.3 kj is transferred reversibly and isothermally to a block of aluminum at 389 K. Calculate the entropy change in the aluminum block. (5 pts) b. Suppose that heat is added reversibly to a block of aluminum from 389 K to 1751 K. During this process the heat transfer is measured to depend on temperature as { /(T/K)} kj. Calculate the entropy change. 4

5 (5 pts) c. Please refer to the thermodynamic table supplied at the end of this exam. What is the standard change in entropy of combustion of cyclohexane at 298K? (5 pts) d. At 2.09 kpa, the entropy S of a particular system in the temperature range between 591 K and 607 K is constant and equal to 45.5 kj/k. What is the change in Gibbs free energy for the system between these two temperatures at 2.09 kpa? 5 :

6 3. Phase diagrams. A pure sample of an unknown has the following properties at the triple point: T = 227 K, P = 87.1 kpa, H vap (T,P ) = 34.1 kj/mole, H fus (T,P ) = 25.2 kj/mole, V m (liquid) = L/mole, and V m (solid) = L/mole, (5 pts) a. What is the boiling point temperature of the pure unknown at kpa? (5 pts) b. What is the freezing point temperature of the pure unknown at kpa? 6

7 (5 pts) c. What is the vapor pressure of the pure unknown at 193.2K? (5 pts) d. What is the vapor pressure of the unknown at 193.2K if it is now placed in a closed container with argon at a partial pressure of kpa? 7 :

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9 (Possibly) Useful Formulas WARNING: Use at your own risk PV = nrt PV m = RTZ x a = na n T ( ( Z = 1 + BP + CP 2 + Z = 1 + B 1 + C V m ) P = nrt a ( ) n 2 1 Z = (a/rt) V nb V 1 (b/v m) V m ) 2 1 V m + U = q + w du = dq + dw H = q P U = w ad U = q V w = P ex Vf V i dv H = U + PV du = π T dv + C V dt dh = (µc P )dp + C P dt C V = ( ) U T V P = ( U V α 1 V C P = ( ) H T P w = P ex V ) ( V T κ T 1 V S,N ) P ( V P T V = ( ) H P S,N du = PdV + TdS ) dh = V dp + TdS C P C V = nr C V = 3 2 nr V T 1/c = constant c = C V,m PV γ = constant γ = 1 + R R C V,m i νr i R i j νp j P j r H = j νp j f H (P j ) i νr i f H (R i ) ds = dqrev T S = T 2 T 1 C p T dt r C P,m = j νp j C P,m (P j) i νr i C P,m (R i) S vap = Hvap T b 85 J mol S surr = Hsys T ( ) ǫ w q h = 1 Tc T h A = U TS G = U + PV TS da = dw max dg = dw add,max r S m = j νp j S m(p j ) i νr i S m(r i ) r G = j νp j f G (P j ) i νr i f G (R i ) ds dq 0 ds T U,V 0 du S,V 0 ds H,P 0 dh S,P 0 da T,V 0 dg T,P 0 ( ( G ) ) ( ) = H P G(P T T T P 2 f P i ) = V P G(P f P i ) = NRT ln f P i G(P) = G + NRT ln ( ) f f = φp ln φ = P Z 1 dp P 0 P dp = trss dt trsv µ = G N = G m dµ = S m dt + V m dp p = p e ( Vm P dp dt = trshm T trsv m ln ( ) ( ) P P = vaph m ( 1 ) 1 R T T RT ) ( ) [ P = P + fus H m fus ln ( ) ] T V T dw = γdσ P in = P out + 2γ r h = 2γ ρgr cos θ c = γsg γ sl γ lg w ad = γ sg + γ lg γ sl 9

10 Selected Thermodynamics Quantities (at 298 K) Substance f H /(kjmol 1 ) Cp,m/(JK 1 mol 1 ) Sp,m/(JK 1 mol 1 ) H 2 (g) H(g) H 2 O(l) H 2 O(g) CO 2 (g) O 2 (g) O 3 (g) C 6 H 12 (l), cyclohexane C 7 H 16 (l), heptane

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You MUST sign the honor pledge:

You MUST sign the honor pledge: Chemistry 3411 MWF 9:00AM Spring 2009 Physical Chemistry I Final Exam, Version A (Dated: April 30, 2009 Name: GT-ID: NOTE: Partial Credit will be awarded! However, full credit will be awarded only if the