Physical Chemistry II Homework Set #6

1. Calculate the ionic strengths of 0.01 M solutions of KNO3, Ca(NO3)2, ZnSO4, ZnCl2,

K4Fe(CN)6, Fe(porphyrin)Cl.

2. The concept of the ionic atmosphere can be made clearer by calculating the charge density

as a function of distance from the ion. At low ionic strength the charge density around a

single positive ion is given by

ρ = −z+e

4πrD2

e−r /rD

r

where the Debye length rD is a constant.

a) SHOW that the total counter charge in all space around the ion is −z+e .

*HINT: Integrate the charge density over all space, i.e., ρ 4πr 2 dr

0

∞

∫ .

b) SHOW that the maximum charge density per unit width dr around the central positive

ion occurs at the Debye length rD .

*HINT: The charge density per width dr is 4πr 2ρ .

c) Plot 4πr 2ρ vs. r for a Debye length rD of 18 Å.

3. Aqueous CaSO4 has a solubility product

Ksp of 7.10 x 10-5 at 298 K.

a) Assuming that the DHE applies calculate the solubility of CaSO4 in water at 298 K.

b) Assuming that the DHE applies calculate by successive approximations the solubility of

CaSO4 in 0.10 M MgCl2.

c) Assuming that the DHE applies estimate by successive approximations the solubility of

CaSO4 in 0.10 M MgSO4.

*NOTE: the ionic size parameter a is 8.0 x 10-8 cm for Ca2+ and 4.0 x 10-8 cm for SO42-.

4. Consider the cell : Pt | Mn | MnI2(aq., 0.01 M) | CuI2 | Cu | Pt

The EMF for this cell is +1.53 V. Assume that DHLL applies and calculate Ksp(CuI2) for

the cell at 298 K given the following information:

Mn2+ + 2e- <__ __> Mn E° = -1.185 V

Cu2+ + 2e- <__ __> Cu E° = 0.521 V

5. Given E° for the following two reactions

H3IO6 + 4 e- IO3− + 3 OH- E° = + 0.700 V

IO3− + 6 H+ + 6 e- I- + 6 H2O E° = + 1.085 V

Find E° (in volts) for the reaction: H3IO6 + 6 H+ + 10 e− I− + 3 OH− + 6 H2O

6. The standard potential, E°, for the Ag,Cl-/AgCl(s) couple has been measured very carefully

over a range of temperatures (R.G. Bates and V. E. Bowers, J. Res. Nat. Bur. Stand. 53,

283 (1954)) and the results (t = °C) were found to fit the expression

E°(V) = 0.23659 - 4.8564 x 10-4 t - 3.4205 x 10-6 t2 + 5.869 x 10-9 t3

Calculate the standard Gibbs free energy and enthalpy of formation of Cl-(aq) and its

entropy at 298 K.