Physical Chemistry Third Edition

7.5 Buffer Solutions 331

with the separated ions. For example

Na++Cl−
Na+Cl−

The ion pair Na+Cl−isnota molecule. A chemical bond is not formed between the

ions, which are held together by electrostatic attraction. Each ion retains at least part of

its attached water molecules (hydration sphere) and one or more water molecules can

lie between the ions. Equilibrium constants have been determined for the formation of

some ion pairs. Multiply charged ions have a greater tendency to form ion pairs than

do singly charged ions. For example,

Mg^2 ++Cl−
Mg^2 +Cl−

has a relatively large equilibrium constant. We will not discuss these equilibria, but

will regard them as one of the reasons that the activity coefficients deviate from unity.

Exercise 7.12

Write expressions forγ±andm±for Mg 3 (PO 4 ) 2 in terms of the stoichiometric molality and

the activity coefficients of the ions. Neglect hydrolysis (a poor approximation).

PROBLEMS

Section 7.4: Equilibria in Solutions of Strong Electrolytes

7.38 Find the partial vapor pressure of HCl over a
0.85 mol kg−^1 aqueous HCl solution at 298.15 K. Use the
Davies equation to estimateγ±.

7.39 Write the expressions forγ±andm±for each of the
following solutes (assume strong electrolytes):
a.Na 2 SO 4
b.AlCl 3

c.MgSO 4

d.Mg(NO 3 ) 2

7.40 Evaluatem±for each of the solutes in the

previous problem if the stoichiometric molality is

0.100 mol kg−^1. Use the Davies equation to

estimateγ±for each of the solutes in the previous

problem if the stoichiometric molality is

0.100 mol kg−^1.

7.5 Buffer Solutions

A solution that resists changes in pH is called abuffer solution. A typical buffer solution

contains both a weak acid and its conjugate base, which is a weak base. If acid is added

to the solution, the weak base can react with part of it, and if base is added, the weak

acid can react with part of it, minimizing the effect of the addition. Consider a solution

produced by addingnamoles of a weak acid (abbreviated by HA) andnsmoles of its

salt to 1.000 kg of water (the anion of the salt is the conjugate base, abbreviated by

A−). The acid will ionize slightly, and the anion will hydrolyze slightly. These effects

will nearly cancel, and we can write to a good approximation

meq(HA)

na

1 .000 kg

(7.5-1)