Download CHEMISTRY 231 — Tellinghuisen 2nd Hour Exam — 3/14/01

CHEMISTRY 231 — Tellinghuisen
2nd Hour Exam — 3/14/01
NAME:
(please print)
Honor Code Pledge and Signature:
Fundamental Constants:
R (mol–1 K–1) = 8.31451 J = 0.0820578 L atm = 1.9872 cal; F = 96485.3 C/mol
I. (30) Colligative Properties and Activity. A solution of K2SO4 (M = 174.27) in water (M = 18.015)
is 4.00 % K2SO4 by mass.
A. Calculate the molality of K2SO4 in this solution and predict the freezing point using the simplest colligative
properties approach: (1) first treating the solute as undissociated; and (2) treating the solute as fully
dissociated into ions in solution. [k f = 1.860 K kg/mol]
B. The observed freezing point is –0.950˚C. Use this information to calculate the activity aA of the solvent
water in this solution. [∆Hfus,A = 6007 J/mol, independent of T over this range.]
C. The van't Hoff i factor is defined as the amount by which the colligative property is multiplied due to
dissociation of solute. Give (1) the expected, or simple theoretical value of i, and (2) the observed i.
D. In recommended problem 12.10 we showed that ∆Tf ≈ –k f φ ν mi, where φ is the practical osmotic
coefficient. [The van't Hoff i factor is the quantity φ ν in this expression.] Calculate φ from this relation,
and compare with a value predicted from your results for aA in part B above.
-2II. (30) Low-V Sparks.
A.
The force exerted by a He2+ ion on an electron 100.0 Å away in a vacuum is calculated to have a
magnitude of 4.61×10–12 N.
1.
What is the direction of this force on the electron, toward the He2+ or away from it?
2.
What is the force if the electron is moved to a distance of 10.0 Å?
3.
Back at a distance of 100.0 Å, the system is put in the dielectric medium H2O, having ε r = 80.
What is the force now?
4.
The He2+ ion is replaced by a Be4+ ion. What is the force on an electron 100.0 Å away in vacuum?
B.
Copper and zinc are both good electrical conductors. If a piece of Cu is brought into contact with a piece
of Zn, are the electric potentials φ Cu and φ Zn the same or different?
C.
(1) Give the definition of the electrochemical potential of component i in phase α, µ~ αi , defining all terms.
(2) Then state the condition for phase equilibrium for two phases (α and β) in physical contact in an
electrochemical system. (3) Finally, state the condition for reaction equilibrium in a closed
electrochemical system.
D.
Apply the condition for phase equilibrium in an electrochemical system to the electrons in the
electrochemical cell, Cu'|Zn|Ag|Cu'', to determine whether the emf E [E ≡ φ (Cu'') – φ (Cu')] of this
cell is positive, negative, or zero.
I
II
III
IV
V
-3E.
Now consider a piece of Zn metal dipping into an aqueous ZnSO4 solution. The process, Zn →
←
2+
–
Zn (aq) + 2 e (Zn), occurs to a very slight extent. Apply the reaction equilibrium condition from C to
this process to obtain an expression for the electric potential difference, φ (Zn) – φ (aq. ZnSO4 ).
III. (35) Multicomponent Phase Diagrams. The accompanying figure shows the phase diagram for the
binary Mg-Ni system in the solid-liquid region. This system forms two solid compounds, Mg2Ni and
MgNi2. Use this diagram to answer the following questions.
A. What is the melting point of pure Mg?
_______ of pure Ni ? ________
B. How many liquid phases are there? _______
How many solid phases? ________
C. Identify the euctectic point(s) by giving its
(their) composition(s) and melting
temperature(s).
D.
Identify a congruent melting point by giving its
T and x Ni.
E.
Identify an incongruent melting point by
giving its T and the composition of the
substance involved.
F.
Suppose you start with 1.00 mol of Mg at
700˚C and add Ni. What is the maximum
amount of Ni that can be dissolved in Mg at
this T without producing a solid phase?
G.
In the previous question, what is the composition of the solid that first precipitates as Ni is added?
H.
Suppose you repeat the dissolution experiment of F starting at 1400˚C. How much Ni can you now
dissolve in 1.00 mol of Mg without observing the formation of a solid phase?
I.
By how much is the freezing point of Ni depressed by the addition of 2.00 mol of Mg to 8.00 mol of
Ni?
-4J.
What phases are present at labeled point R, and in what amounts, if the system contains 2.00 mol total of
Ni and Mg? Also, give nMg and nNi for each phase present. (Show work clearly.)
K.
Continuing with the theme of the preceding question, analyze the composition of a system containing
2.00 mol total of Ni and Mg, at the point x Ni = 0.60, T = 900˚C. (I.e., determine the compositions of
the phases, their amounts, and the amounts of Ni and Mg in each.)
IV. (35) Galvanic cells. The cell Pt L |H 2(g)|HCl(aq)|AgCl(c)|Ag(c)|Pt R, was referred to frequently in
class, in the text, and in homework problems.
A. Write the half reactions that occur at each electrode.
B. Write the overall electrochemical reaction, and the overall chemical reaction.
C. Which electrode is the anode and which the cathode, for the cell as written?
D. Is this a cell with or without transference.
-5-
F.
Give an expression that relates E for this cell to E˚
and the activities of all reactants and products. At
P = P˚, several of the activities are very well
approximated as unity. Rewrite the expression
accordingly.
E for this cell was studied at P H2 = 1.00 atm and
25˚C in homework problem 6-4. The
accompanying figure illustrates a least-squares fit
of these data. From these results,
1.
2.
3.
Determine E˚.
Obtain an expression for the stoichiometric
activity coefficient of HCl(aq).
Calculate γ i at m = 0.200 m˚.
y (= E' ) = E - 1.691e-4 + .0513856*ln(m/m˚)
0.236
0.234
0.232
y = a + b m1/2 + c m
E' (V)
E.
0.230
y = a + b*x + c*x^ 2
Value
Error
a
0.22219 0.00014
b
0.05353 0.00128
c
-0.05276 0.00244
Chisq
0
NA
R
0.99974
NA
0.228
0.226
0.224
0.222
0.220
0.0
0.1
0.2
0.3
m1/2
0.4
0.5