Physical Chemistry II
Spring, 2017
Homework Set #6
1.
Calculate the ionic strengths of 0.02 M solutions of KNO3, K2SO4, 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 e− r/rD
4π rD2 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 4π r
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 ρ 4π r 2 .
c) Plot ρ 4π r 2 vs. r for a Debye length of 16 Å.
3.
Aqueous SrSO4 has a solubility product K sp of 3.44 x 10-7 at 298 K.
a) Assuming that the DHLL applies calculate the solubility of SrSO4 in water at 298 K.
b) Assuming that the DHLL applies calculate by successive approximations the solubility of
SrSO4 in 0.10 M MgCl2.
c) Assuming that the DHLL applies estimate by successive approximations the solubility of
SrSO4 in 0.10 M MgSO4.
d) Consider the cell : Cu’ | Sr(s) | SrSO4 (sat’d, aq), MgSO4(0.100 M) | Ag2SO4(s) | Ag(s) | Cu
__
RHE: Ag2SO4(s) + 2e- <__> 2Ag(s) + SO42-(aq) E° = 0.654 V
__
LHE: Sr2+(aq) + 2e- <__> Sr(s)
E° = -2.899 V
Calculate the EMF of this cell at 298 K using the information found in part (c).
4.
Given E° for the following two reactions
__
NO3- + H2O + 2 e- <__> NO2- + 2 OH__
NO2- + H2O + e- <__> NO + 2 OH-
E° = 0.01 V
E° = -0.47 V
Find E° (in volts) for the reaction
__
NO3- + 2 H2O + 3 e- <__> NO + 4 OH5.
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 t 2 + 5.869 x 10−9 t 3
Given that ΔG of ( AgCl ) = −109.8 kJ / mol and ΔH of ( AgCl ) = −127.0 kJ / mol calculate the
standard Gibbs free energy and enthalpy of formation of Cl-(aq) at 298 K.