Name
This
examination contains two sections: (1) Short answer questions worth 50% of the
total score, and (2) Problems worth 50%of the total score. A choice of
questions is given in each section: it would be wise to read all the questions
before starting to answer.
Short Answer Questions (10
points each)
Answer
any five of the following six
questions.
1. Phase
Rule
At temperatures approaching 1000°C, equilibrium is
established in the two reduction reactions
FeO(s) + H2(g) = Fe(s) + H2O(g)
and FeO(s) + CO(g) = Fe(s) + CO2(g).
(a) If a reaction chamber is charged with FeO(s) and H2(g),
how many components, phases, and degrees of freedom does the system have?
(b) If the reaction chamber is charged with FeO(s), H2(g), and
CO(g), how many components, phases, and
degrees of freedom does the system have?
2. Phase
Behavior
True or false?
(a)
Addition
of a tiny amount of soluble impurity to a pure liquid always lowers the
freezing point
(b)
Addition
of a tiny amount of a soluble impurity to a pure liquid must lower the freezing
point if only pure solvent freezes out
(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 PB of B
vapor (assumed ideal) in equilibrium with a nonideal solution of B and C must
always increase when the B mole fraction is increased at constant temperature.
(f) For a binary two-phase system, the closer a point on a tie line is to a phase, the more of that phase is present.
3. Method
of Initial Rates
A reaction obeys the stoichiometric equation A + 2B ® 2C. Rates of formation of C at various
concentrations of A and B are as follows:
|
[A]/M |
[B]/M |
r/(M s-1) |
|
|
3.5´10-2 |
2.3´10-2 |
5.0´10-7 |
|
|
7.0´10-2 |
4.6´10-2 |
2.0´10-6 |
|
|
7.0´10-2 |
9.2´10-2 |
4.0´10-7 |
|
(a)
What
are a and b in the rate equation r = k[A]a[B]b?
(b)
What
is the rate constant, k (full credit
requires correct units!)
4. Kinetics
True or false?
(a)
The
half-life of a reaction is independent of initial concentration only for
first-order reactions.
(b)
The
units of a first-order rate constant are s-1.
(c)
Changing
the temperature of a reaction changes its rate constant.
(d)
Elementary
reactions with a molecularity greater than 3 generally do not occur.
(e)
If
the partial orders (i.e., orders with respect to each concentration in the rate
law) of a reaction are equal to the corresponding stoichiometric coefficients
in the balanced reaction, the reaction must be elementary.
(f)
If
the partial orders in a rate law differ from the corresponding stoichiometric
coefficients in the balanced reaction, the reaction cannot be elementary.
5. Phase Diagrams
Draw phase
diagrams for the following types of systems. Label the regions and intersection
points of the diagrams, stating what materials (possibly compounds or azeotropes)
are present and whether they are solid, liquid, or gas.
(a)
Two-component,
temperature composition, solid-liquid diagram; one compound of formula AB2
that melts incongruently, negligible solid-solid solubility.
(b)
Two-component,
temperature-composition, liquid-vapor diagram; formation of an azeotrope at xB = 0.333; complete
miscibility.
|
|
6. At right is a miscibility diagram for
aniline
in water. Use the diagram to estimate the ratio of the mass of the water-rich layer
to that of the aniline-rich layer for 30 wt.% aniline in water at 400 K.
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. First
Order Reactions and Half-Life
The uranium present in the earth today is 99.28% 238U, and 0.72%
235U. The half-lives are 4.51´109 years for 238U
and 7.00´108 years for 235U.
How long ago was the earth’s uranium 50% 238U and 50% 235U?
(Isotopic abundance are given on an atom-percent basis; you may assume that the
nuclear decay is a first-order reaction)
2. Complex
Phase Diagrams
The following is an example of a liquid-solid phase diagram in which
there is partial miscibility in both liquid and solid phases.
(a) Label all regions indicating the number and identity of each of the phases present
(b) Sketch either a cooling curve or a DSC (differential scanning calorimeter) trace for the isopleth indicated by the dotted line starting at the indicated point.
(c)
The points X and Y on the diagram are invariant (that is, they occur at a
definite composition and temperature) at constant pressure. Why is that so?
Identify the phase or phases present at each point.
3.
Binary Liquid Vapor Equilibrium
Assume that
benzene and toluene form ideal solutions. The normal boiling point of benzene
is 80°C. At that temperature, toluene has a vapor
pressure of 350 torr.
(a) Calculate the partial and total pressures of a solution at 80°C when the mole fraction of benzene is 0.2.
(b) What composition of the solution would boil at 80°C under a reduced pressure of 500 torr?
Formulas and Constants for
Chapters 8 and 25 in Atkins
Physical Constants
R=8.3145 J K-1 mol-1;
L=6.022´1023 mol-1; kB
= R/L
1
atm = 760 torr = 1.01325 bar = 1.01325´105 Pa
Raoult’s Law: xi,liq = Pi,gas/Pi*
Ideal
solution phase boundaries:
Phase Rule: f=c-p+2; c=s-r-a Lever Rule: na la = nb lb
Kinetic Rate
Laws:
k =
[A]a [B]b [C]g [D]d¼ for total order a+b+g+d+¼
Integrated Rate Laws
First order reaction: 
Order n (¹1) reaction:
Competing 1st order reactions: 
Arrhenius Law
k
= A exp[ -Ea/RT ]
Half-Life
1st order reaction: t1/2 = (ln 2)/k
Order n (¹1) reaction: 