Name

130 possible points (Exam will be graded out of 125).

Short answer questions

Answer any five of the following six questions (10 points each)

1. For any closed system at constant T and P, dG < 0 for a spontaneous change. Use this to derive a short mathematical expression showing that if for substance A in phases a and b, then A will flow spontaneously from phase b to phase a.

2. What is the major source of inaccuracy when colligative properties such as osmotic pressure are used to determine the molar mass of a macromolecule? Describe what steps can be taken to reduce or eliminate such inaccuracies.

3. Will the rate of an enzyme-catalyzed reaction generally be more sensitive to temperature or less sensitive to temperature than that of the same uncatalyzed reaction? Explain your answer.

4. How can you determine whether a given balanced chemical reaction proceeds via a complex or via a simple (elementary, single-step) mechanism?

5. Each of the plots of m vs. T or P for a pure substance shown below has at least one fault. Identify what is wrong with each.

6. Two optical isomers are mixed as liquids, and they obey Raoult’s law.
(a) For vaporization of this mixture at a constant T, will the solution exhibit a range of vaporization pressures for different compositions, or will any mixture vaporize at a single pressure? Why?
(b) What can you say about the composition of the gas phase over the solution?

PART 2: Material from Atkins Chapters 6, 7, 8, and 25

Answer any two of the following three questions (1 through 3: 20 points each)

1. Colligative Properties
The addition of 2.58 g of a compound to 100 g of CHBr₃ lowers the freezing point of the solvent by 2.374 K. For CHBr₃, K_fp = 14.4 K m^-1.
(a) Find the apparent molar mass of the compound. (8 pts)
(b) Estimate the osmotic pressure of this solution at 298 K. (8 pts)
(c) The compound added was phenol (C₆H₅OH). Give a qualitative explanation for the molar mass you found in (a), and explain what effect if any this result has on the accuracy of your estimate in (b). (4 pts)

2. Gibbs-Duhem Equation
The general form of the Gibbs-Duhem equation for a binary mixture at constant T and P is

where is any partial molar thermodynamic quantity. Use this relation to show that the Gibbs-Duhem equation can also be applied to activity coefficients at constant T and P as follows:

(Hint: recall that chemical potential is the partial molar Gibbs free energy)

3. Arrhenius Law
The second-order rate constants for the reaction of oxygen atoms with benzene are 1.44´10⁷ M^-1 sec^-1 at 300.3 K and 3.03´10⁷ M^-1 sec^-1 at 341.2 K.
(a) Estimate the pre-exponential factor and activation energy for this reaction. (10 pts)
(b) At 400 K, the DG^o for this reaction is -35.2 kJ mol^-1. Estimate the equilibrium constant and the rate constant for the reverse reaction at this temperature. (10 pts)

PART 3: Complex Kinetics

Answer any two of the following three questions (4 through 6: 20 points each).

4. Chain Reaction Rate Law
A simplified version of the CH₃CHO decomposition mechanism is

(the CHO reacts to form minor amounts of various species and may be neglected)
(a) Identify the initiation, propagation, and termination steps, and propagators (5 pts)
(b) Write the net reaction, neglecting minor products formed during initiation and termination steps (3 pts)
(c) Use appropriate approximations to derive a rate law for this reaction in terms of the concentration of the reactant, [CH₃CHO]. (12 pts)

5. Deriving Possible Reaction Mechanism from Rate Law
The redox reaction is catalyzed by Ag⁺ ions. Under certain conditions, the rate law is given by

Suggest a mechanism consistent with this behavior. [Hint: Double oxidations such as Tl⁺ ® Tl³⁺ +2e^-, are almost unknown in a single elementary step.]

6. Uncompetitive Enzyme Inhibition
The mechanism known as uncompetitive inhibition of a simple Michaelis-Menten type of reaction occurs according to the following scheme:

(a) Write the rate equations for each of the intermediates involved in this mechanism and for the appearance of product. (5 pts)

(b) Identify the simplifying assumptions that can be used to derive an overall rate law for this reaction. (3 pts)

(c) Starting from the material balance condition for the total enzyme concentration, [E]₀=[E]+[ES]+[ESI], obtain a rate law for the net reaction S®P in terms of [E]₀, [S],.[I], and constants. (12 pts)

Useful Constants

L = 6.022´10²³ mol^-1; R = 8.315 J^-1 K^-1 mol^-1

R = 0.08206 atm dm³ K^-1 mol^-1

1 torr = 1 mm Hg = 133.322 Pa;

1 atm = 1.01325´10⁵ Pa = 760 torr

Clapeyron Equation:

Partial Molar Quantities
for Y = G, V, H, A, U, S...

Gibbs-Duhem Equation: for Y = G, V, H, A, U, S,...

Kinetic Rate Laws: r = k[A]^a [B]^b [C]^g [D]^d¼ for total order a+b+g+d+¼

Free Energy of Mixing

Molality:

Ideal Gas	mA = mA°+RT ln P/P°	xA,vap = PA/Ptot	P°= 1 bar
Ideal Solution	mA = mA*+RT ln xA,soln	xA,soln = PA/PA*	pure substance
Ideal-Dilute Solution	mB = mB°+RT ln xB,soln	xB,soln = PB/KB*	behavior at xB®0 extrapolated to xB=1
Nonideal Solution	mA = mA°+RT ln aA,soln	aA,soln = PA/PA* OR aB,soln = PB/KB	pure substance, OR behavior at xB®0 extrapolated to xB=1

Derivative Relations Equilibrium and Free Energy

Michaelis-Menten Equation:

Arrhenius Law ; for an elementary reaction

Condition for Phase Equilibrium: for substance I between phases a and b

Raoult’s Law: x_i,liq = P_i,gas/P_i*

Ideal solution phase boundaries: