Page 107 - Basic physical chemistry for the atmospheric sciences

Acids and bases 1) 1

of a weak base (NH3) and a strong acid (HCI). Therefore, we would
expect it to hydrolyze to produce an acidic solution. The reactions arc
NH4Cl(s) + H 0(1)� C l - (aq) + NH !(aq) + H 0(1)
2
2
NH !(aq) + H20(1) � N HJ(aq) + H30 + (aq)
The hydrolysis constant for the last reaction is
[N H 3(aq)][H30 +(aq)] Kw
K h -
[NH4 + ( aq)] Kb

where Kw = 1 0 - 14 and Kb is the base-dissociation constant for
1
N H J(aq), which is given as l . 8 x 0 - 5 • Therefore, Kh = 5 . 6 x 1 0 - IO. We
see from the reaction equations that equal numbers of NH (aq)
3
and H30 + (aq) are formed. If x = [NH3(aq)] = [H30 + (aq)], then
[N H !(aq)] = 0 . 1 0 - x . Hence,
x 2
K = 5 6 X 1 0 - IO = ---
h • 0 . 1 0 -x

Solving this as a quadratic equation and taking the positive root, we
1
get x = 0.75 x 0 - 5 M . (Note: If we had anticipated that x would be
small, we could have obtained the value of x much more quickly by
writing 0. 1 0 - x = 0 . 1 0 in the above expression for Kh. Generally, it is
quicker to make such approximations at the outset and then check to
determine if the value of x that is obtained is small enough to justify
the approximation. ) The pH of the solution is

pH = - log[H30 + (aq)] = - logIOx

.
1
= - l og(0 7 5 x 0 - 5 ) = - ( - 5 . 1 )
5
= . 1 (acidic, as predicted)
The fraction of NH4Cl(s) hydrolyzed is
1
N
Amount of H 3(aq) x 0. 75 x 0 - 5
Original amount of H 4Cl(s) 0. 1 0 0. 1 0
N
= 7 .5 x 1 0 - 5 o r 0.0075%

5.9 Buffers
If the pH of a solution is not greatly affected by the addition of small
amounts of acids or bases, the solution is said to be buffered. This will
be the case if the solution contains a relatively large amount of an