CHM 3410 – Problem Set 8
Due date: Wednesday, November 2nd
Do all of the following problems. Show your work.
“There is nothing to be learnt from a Professor which is not to be met with in Books.” – David Hume
1) Self-ionization of water is the reaction
H2O()  H+(aq) + OH-(aq)
(1.1)
At T = 25.0 C, the equilibrium constant for the above reaction is Kw = 1.011 x 10-14.
If we assume that aH2O = 1, as is approximately true for dilute solutions, then
Kw = (aH+) (aOH-)  [H+] [OH-] ()2 = KM ()2
(aH2O)
KM = [H+] [OH-]
(1.2)
where KM is the product of the concentrations of hydrogen and hydroxide ions and () = ( H+ OH-)1/2 is the mean
activity coefficient for hydrogen and hydroxide ion.
The value for KM has been measured for a series of aqueous solutions of potassium chloride, KCl, a 1:1
strong electrolyte (Harned, H. S. and W. J. Hamer, J.Amer.Chem.Soc. 55, 2194 (1933)). Some of the data are given
below.
bKCl (mol/kg)
KM
bKCl (mol/kg)
KM
0.01
0.02
0.03
0.04
1.24 x 10-14
1.33 x 10-14
1.39 x 10-14
1.44 x 10-14
0.06
0.11
0.21
0.51
1.51 x 10-14
1.64 x 10-14
1.76 x 10-14
1.89 x 10-14
a) For each of the above solutions find the experimental value for , the mean activity coefficient.
b) Theoretical vales for the mean activity coefficient can be found using Debye-Huckel theory
log10() = - A |z+ z-| I1/2
(1.3)
I = (1/2) i zi2 bi
(1.4)
where
For water at T = 25.0 C, A = 0.509. For solutions of potassium chloride (ignoring the small contribution to I from
H+ and OH- ions), I = bKCl.
Find the value for  predicted using Debye-Huckel theory for each of the above solutions.
c) Plot the experimental values for log10() vs I1/2. Also indicate in the plot the line that represents the
values for log10() predicted using Debye-Huckel theory. Briefly discuss the agreement (or lack of agreement) of
Debye-Huckel theory with the experimental results.
2) For the galvanic cell
Pt(s)|H2(g)|H+(aq)||Cl-(aq)|Cl2(g)|Pt(s)
(2.1)
it is found (at T = 25.0 C) that Ecell = 1.362 v and (Ecell/T)p = - 1.20 x 10-3 v/K.Using only this information find
Grxn, Hrxn, and Srxn for the reaction
H2(g) + Cl2(g)  2 HCl(aq)
(2.2)
3) For carbon dioxide (CO2, M = 44.01 g/mol) at T = 400.0 C, find the following
a) crms, the rms average speed of a CO2 molecule
b) f(450. m/s < v < 550. m/s), the fraction of CO 2 molecules with speeds between 450. m/s and 550. m/s.
4) The two dimensional Maxwell-Boltzmann distribution, which would apply, for example, to the free motion of
particles adsorbed onto a surface, is
f(v) dv = N v exp( - Mv2/2RT) dv
(4.1)
where N is a constant.
a) Find the value for N that makes f(v) dv a normalized distribution. This means finding the value for N
that makes the distribution satisfy the following requirement
0 f(v) dv = 1
(4.2)
b) Find cave, crms, and cmp for the two dimensional Maxwell-Boltzmann distribution.
Also do the following from Atkins:
Exercises.
5.18a Calculate the ionic strength of a solution that contains 0.100 mol/kg KCl(aq) and 0.200 mol/kg
CuSO4(aq).
6.20b Find the half-cell reactions, the net cell reaction, and the cell potential for standard conditions for the
following galvanic cells
Pt(s)|Cl2(g)|HCl(aq)||K2CrO4(aq)|Ag2CrO4(s)|Ag(s)
Pt(s)|Fe3+(aq), Fe2+(aq)||Sn4+(aq), Sn2+(aq)|Pt(s)
C(s)|Cu2+(aq)||Mn2+(aq), H+(aq)|MnO2(s)|Pt(s)
6.23b Calculate the equilibrium constants of the following reactions at T = 25.0 C from standard half-cell
potential data
Sn(s) + CuSO4(aq)  Cu(s) + SnSO4(aq)
Cu2+(aq) + Cu(s)  2 Cu+(aq)
EXTRA CREDIT.
Starting with equn 2.2 from Handout 20 (the three-dimensional Maxwell-Boltzmann distributions of speeds)
find an expression for f(z), the fraction of molecules with speed v > z c rms, where crms is the rms average speed of a
molecule, that is approximately correct for values of z >> 1. Note that such an expression is useful both in gas phase
chemical kinetics and atmospheric chemistry. (Hint: The integral you need to do is
zcrms f(v) dv
which unfortunately does not have a closed form solution. However, there is a solution to this integral which is
approximately correct for the case z >> 1. Also note that this is a difficult problem (it is a problem I sometimes ask
in my graduate class in atmospheric chemistry).