Short Answer Questions (10 points each)

Answer any five of the following six questions.

1. Phase Rule
For the following temperature-composition phase diagram for the liquid-solid equilibrium of a binary mixture at a fixed constant pressure, identify the number of degrees of freedom the system has at each of the labeled points (not counting P, which is held constant)
(a) c = 2, p=1 Þ f=2 (P const)
(b) c = 2, p=2 Þ f=1 (P const)
(c) c = 2, p=3 Þ f=0 (P const)
(d) c = 2, p=1 Þ f=2 (P const)
(e) c = 1, p=2 Þ f=0 (P const)

2. Tie Lines and the Lever Rule
The following diagram shows the phase behavior of copper and gold, which are completely miscible in both the solid and liquid phases.
(a) At what temperature would a mixture that is 30 mol% Cu begin to melt? 905°C

(b) At the composition and temperature in (a), what is the composition of the first liquid that forms?
63 mol% Au (37 mol% Cu)

(c) If the temperature is raised 50° above the initial melting point, what are the compositions of the phases present? If more than one phase is present, what is the relative number of moles in each?
Only the liquid phase is present at 70 mol% Au (30 mol% Cu)

3. Reaction Rates
Reactions 1 and 2 are each first order, and k₁ > k₂ at a certain temperature T. Must the reaction rate v₁ be greater than v₂ at temperature T? Explain your answer.
No. If v₁ = k₁[A] and v₂ = k₂[B] and k₁ > k₂, we can still have v₂ > v₁ if [B] >> [A].

4. Phase Equilibrium
True or false?
(a) Addition of a nonvolatile solute to a pure liquid always lowers the boiling point
(b) Addition of a volatile solute to a pure liquid always lowers the boiling point.
(c) A liquid solution of two substances will always freeze entirely at one temperature
(d) A liquid solution of two substances will never freeze entirely at one temperature
(e) The partial pressure of a component in a liquid binary mixture always increases when the mole fraction of that component in the liquid increases.

5.

F

T

T

F

T

F

F

F

F

T

Kinetics
True or false?
(a) The units of a second-order rate constant are moles per liter per second.
(b) The half-life is independent of initial concentration only for first-order reactions.
(c) Elementary reactions with molecularity greater than 3 generally don't occur.
(d) If the partial orders in a rate law are identical to the corresponding coefficients in the balanced reaction, the reaction must be simple.
(e) The activation energy of a reaction does not depend upon whether the reaction is exothermic or endothermic.

6.

B,C

E,H

F,G

A,B,C,D,E,G

F

A,B,C,D

D,H

None (G is high-P, lowT)

Phase Diagrams
Identify which (if any) of the phase diagrams above exhibit each of the following features:
(a) Ideal solution behavior in all phases (f) A high (T)-boiling azeotrope
(b) A eutectic point (g) Congruent melting B
(c) One or more invariant points (h) Incongruent melting C
(d) A critical or plait point (i) Partial miscibility in 1 or more phases
(e) Compound formation (j) Complete miscibility in all phases

Problems (25 points each)
Do any two of the following three problems. Be sure to show your work! Partial credit may be awarded for the correct approach even if your answer is wrong. Use the back of these sheets if necessary.

1. Liquid-Vapor Equilibrium
The vapor pressure of pure liquid A at 293 K is 68.8 kPa and that of pure liquid B is 82.1 kPa. These two compounds form ideal mixtures in the liquid and gaseous phases. Consider the equilibrium composition of a mixture in which the mole fraction of A in the vapor is 0.612. Calculate
(a) the total pressure of the vapor
(b) the composition of the liquid mixture

(a) Use line for vapor curve

(b) Raoult's Law (line for liquid curve)

2. Phase Diagrams
Iron(II) chloride (m.p. 677°C) and potassium chloride (m.p. 776°C) form the compounds KFeCl₃ and K₂FeCl₄ at elevated temperatures. KFeCl₃ melts congruently at 420°C and K₂FeCl₄ melts incongruently at 399°C. Eutectics are formed with composition x=0.38 (m.p. 351°C) and x = 0.54 (m.p. 393°C) where x is the mole fraction of FeCl₂. The KCl solubility curve intersects the K₂FeCl₄ curve at x = 0.34.
(a) Sketch the phase diagram on the axis system below (note the break in the temperature axis scale).
(b) State what phases are in equilibrium when a mixture of composition x = 0.36 is cooled from the liquid phase to 375°C.

(a)

3. Integrated Rate Law
A second order reaction of the type A+B ® P was carried out in a solution that was initially 0.050 M in A and 0.080 M in B. After 1.0 h the concentration of A had fallen to 0.020 M.
(a) Calculate the rate constant for the reaction
(b) Calculate the half life (or half lives) of the reactants

(a) Use integrated rate law for mixed second order reaction. If 0.03 M of A have reacted in 1 hr, then [B] =0.05 after 1 hour. Then

(b) For A,

For B,