112

Another T/F exercise. The points
made are subtle, but very important. In
part (b) of this problem it is important to know that the activity
coefficient calculated from the Davies equation is the same for the cation
and its associated anion, but that the molality of the cation and the
molality of the anion must each be
multiplied by that activity coefficient.
Part (d) is rather subtle.
Remember that if a very small amount of HCl
is added to water so that the molality is 1.0 x 10^{8} mol/kg then the solution is acidic and the pH < 7.00.

116

Exercise in calculating ionization constants from data in thermodynamic
tables. Note that very small and very large equilibrium constants are seldom
known very well.

118

A quick calculation to show that the –log_{10}m_{H+} of a NaCl(aq) solution is not
7.00, even if the temperature is 298 K. Neither the Na^{+}(aq) ion nor the Cl^{}(aq)
undergoes hydrolysis, but they change the ionic strength, which lowers the
activity coefficients of the H^{+}(aq)
and OH^{}(aq) ions and so increases
their concentrations.
NB/ It is true
that log_{10}a_{H+}
of aqueous solutions at 298 K is 7.00.
The pH is defined as log_{10}a_{H+} rather than as log_{10}m_{H+} or as log_{10}[H^{+}].

119

It is important to remember that K_{w}
changes with temperature; the only temperature at which the value is 1.0 x 10^{14}
is 298 K.
(a) Use an empirical expression to get K_{w} at normal body
temperature.
(b) Estimate K_{w} at normal body temperature by using the
expression for the temperature dependence of ln K° that was introduced
earlier in the semester.



119

It is important to remember that K_{w} changes with
temperature; the only temperature at which the value is 1.0 x 10^{14}
is 298 K.
(a) Use an empirical expression to get K_{w} at normal body
temperature.
(b) Estimate K_{w} at normal body temperature by using the
expression for the temperature dependence of ln K° that was introduced
earlier in the semester.

114

(Not a short problem, but very important).
All parts require solving an equilibrium problem for a reaction involving ions.
Solutions containing ions are not ideal; activity coefficients for uncharged
molecules are usually assumed to be 1, but activity coefficients for ions
must be determined experimentally or estimated using an equation like the
Davies equation.
(a) Dissociation of formic acid in pure water.
(b) Dissociation of formic acid in a solution containing an electrolyte that
changes the ionic strength but that does not participate in the chemical
reaction being considered.
(c) Dissociation of formic acid in a solution that also contains the formate ion, which (along with the accompanying Na^{+}
ion) changes the ionic strength, and which also participates in the chemical
reaction being considered (common ion effect). Note that this third solution
is a buffer because the concentrations of the formic acid (undissociated acid) and formate
ion (conjugate base) are similar.
See how including the activity coefficient for the uncharged, undissociated acid affects the calculations. See problem 11.36 for the equation.

(extra)

Calculate the pH =  log_{10}a_{H+} for a 1.00 x 10^{8}
m HCl(aq) solution at 298 K.
Assume complete dissociation of the HCl. Use K_{w}° = 1.00 x 10^{14}.
Use activity coefficients or show that they are not necessary.
NB/ Solution
by the method of successive approximations may not work well so it may be
better to solve by some more exact method.
