Buffer Solutions

Learning Goals

You will learn how a buffer solution functions to maintain the pH of a solution upon the addition of an acid or base. You will also learn how to make buffer solutions for some particular applications and how to use the very important Henderson-Hasselbalch equation.

Synopsis

A buffer solution is one that will maintain a rather constant pH value even if an acid or a base is added to the solution. A very common buffer solution is blood which maintains its pH at about 7.4 within about 1.35% even upon the addition of an amount of acid which would lower an unbuffered acid solution by about 71%. A buffer must contain some hydroxyl ions (base) that can counter the addition of hydronium ions, and it must contain some hydronium ions (acid) that can counter the addition of hydroxyl ions. Also the acids and bases of the buffer must not react with each other. A buffer then usually consists of roughly equal quantities of a conjugate acid-base pair. We could use either a weak acid and its conjugate base or a weak base and its conjugate acid. Table 18.2 shows some common buffer systems and the pH range over which they are effective.

Let's first set up a table to calculate the pH of a buffer solution by examining a buffer made of a weak acid and its conjugate base: WA(aq) + H2O(°) 9 H3O+(aq) + A-(aq). We will let the initial concentration of the weak acid be "a" and the initial concentration of the conjugate base be "b".

concentration [WA] H2O [H3O+] [A-]

Before ionization a 0 b

Change -x x x

At equilibrium a - x x b + x

Then at equilibrium we will have Ka = x(b + x)/(a - x) = bx/a if x is much less than b and if x is much less than a. This then will give

x = [H₃O⁺] = [weak acid]Ka/[conjugate base]

from which we can obtain the pH of the buffer solution. Similarly, for a weak base and its conjugate acid we would obtain [OH^-] = [weak base]Kb/[conjugate acid] from which we can also obtain the pH of the buffer solution. We would then need to set up another table to calculate the pH of the buffer solution after adding a strong acid.

We can rearrange these equations by taking the negative logarithm of each side:

-log[H₃O⁺] = - logKa - log ( [weak acid]/[conjugate base] )

and this can be written as

pH = pKa - log ( [weak acid]/[conjugate base] ), one form of the Henderson-Hasselbalch equation. The usual practice is to change the sign in front of the log by inverting the ratio of acid to base, and then we obtain the usual form of the Henderson-Hasselbalch equation:

pH = pKa + log ( [conjugate base]/[weak acid] ).

If the concentration of weak acid and its conjugate base are the same then we have that pH = pKa. The Henderson-Hasselbalch equation is valid for [conjugate base]/[weak acid] less than 10 and > 0.1. Because we want the buffer solution to be a buffer for added acid or base, we generally want [conjugate base] to be approximately equal to [weak acid]. Because the pH would then be equal to the pKa we would choose a weak acid whose pKa is close to the pH at which we wish to maintain the solution. Appendix H and Table 17.4 contain needed Ka values.

If we wish to keep a solution at a pH which is not equal to the pKa of an appropriate acid then we will have to vary the [conjugate base]/[weak acid] ratio until the Henderson-Hasselbalch equation gives the appropriate value for the pH. Note that in the [conjugate base]/[weak acid] ratio the numerator and the denominator contain "per liter" so the resultant units of the ratio are moles of conjugate base to moles of the weak acid. Thus it is the mole ratio which is important.

Review Questions

Use Table 17.3 to determine an appropriate acid to use for a buffer solution to maintain the pH at about 10.8
Calculate the pH of a buffer solution containing 0.350-M lactic acid and 0.225 M sodium lactate
What pH change on the buffer solution of question 2 would occur if we add 1 mL of 0.10 M HCl?
What ratio of [conjugate base]/[weak acid] would be needed to maintain a buffer solution at a pH of 4.20 if we are using lactic acid as the weak acid

On-Line Activity

Go to this site to practice some more buffer problems:

Buffers

concentration	[WA]	H2O	[H3O+]	[A-]
Before ionization	a		0	b
Change	-x		x	x
At equilibrium	a - x		x	b + x