## Absolute Concentrations of the Acid and Conjugate Base

#### Learning Objective

• Calculate the final pH of a solution when a strong acid or base is added to a buffer solution.

#### Key Points

• The pH of an effective buffer changes very little when a small amount of strong acid or base is added to it.
• The change in the pH of a buffer upon the addition of an acid or base can be calculated using the balanced equation and the formula for the equilibrium acid dissociation constant.
• Any buffer will lose its effectiveness if too much strong acid or base is added.

#### Terms

• acid dissociation constantQuantitative measure of the strength of an acid in solution; typically written as a ratio of the equilibrium concentrations.
• conjugate baseThe species that is created after the donation of a proton.
• conjugate acidThe species created when a base accepts a proton.

## Identifying Acid and Conjugate Base Pairs

A buffer is an aqueous solution consisting of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid. Therefore, it is very important to be able to identify acid and conjugate base pairs. The conjugate acid is created by accepting (adding) a proton (H+) donated by the conjugate base.

A buffer’s pH changes very little when a small amount of strong acid or base is added to it. Therefore, it can be used to prevent change in the pH of a solution. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of situations.

One of the main requirements of a buffer is that it have the capacity to control pH after the addition of a reasonable amount of acid or base. In other words, there must be a large-enough concentration of acetic acid in an acetic acid/acetate ion buffer, for example, to consume all of the hydroxide ions that may be added.

## Calculating the Final pH

A concentrated buffer can neutralize more added acid or base than a dilute buffer, because it contains more acid/conjugate base. However, any buffer will lose its effectiveness if too much strong acid or base is added.

## Example:

Calculate the pH change when you add 1.0 mL of 1.0 M HCl to 1.0 L of acetic acid/sodium acetate buffer with [HC2H3O2] = 0.70 M and [C2H3O2] = 0.60 M.

Next, calculate the pH change for a buffer with [HC2H3O2] = 7 mM (7 x 10-3 molar) and [C2H3O2] = 6 mM (6 x 10-3 molar). The Ka for acetic acid is 1.8 x 10-5.

## Solution:

The balanced equation for the buffer is:

$HC_2H_3O_2 \rightleftharpoons H^+ + C_2H_3O_2^-$

The ICE table for the reaction is: ICE table for the reaction of acetic acid in waterICE table showing the concentrations of acetic acid, a hydrogen ion, and the acetate ion.

The acid dissociation constant is:

$K_a=\frac{[H^+][CH_3CO^-_2]}{CH_3CO_2H]}=\frac{(x)(0.60+x)}{0.70-x}=1.8\times 10^{-5}$

Solving for x using the quadratic equation, we get [H+] = 2.1 x 10-5 M. Therefore, the pH for the buffer with an acid/base concentration of 0.7/0.6M is 4.68.

HCl is a strong acid that is fully ionized in water. We only need to account for the fact that it supplies [H+] and reacts completely with the base in solution. The change in the concentrations after the reaction is:

$H^+(\text{from HCl})+C_2H_3O^-_2\leftrightarrow HC_2H_3O_2$