D28.3 Buffer Capacity

We can see how a buffer solution works by comparing quantitatively the pH of a buffered solution with the pH of an unbuffered solution upon addition of a strong acid or strong base.

Activity: Calculating pH Change for a Buffer Solution

As the activity above shows, for calculation purposes only, it is helpful to think of the addition of a strong acid or base as resulting in a “new” buffer solution being made. The “new” buffer’s starting concentrations of weak acid and weak base, [HA]0 and [A]0, are the original buffer’s starting concentrations modified by the reaction of weak acid with strong base (or weak base with strong acid). Artificially separating out the reactions like this helps us in figuring what is actually present in the final solution.

Next, we will calculate the pH change upon the addition of the same amount of NaOH to an unbuffered solution with the same initial pH as the buffered solution.

Activity: pH Change in an Unbuffered Solution

We can see from the above two activities that the change in pH is much more significant in the unbuffered solution compared to the buffered solution.

However, buffer solutions do not have unlimited capacity to keep the pH relatively constant (see figure below). For example, if we add a sufficient amount of a strong base to a buffer solution such that all the weak acid has reacted, no more buffering action is possible towards additional strong base. Similarly, if we add an excess of strong acid, the weak base would all be reacted, and no more buffering action would be possible towards any additional acid. In fact, we do not even need to react away all the weak acid or weak base in a buffer solution to make significant changes in pH: buffering action diminishes rapidly as either weak acid or weak base nears depletion.

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Figure: Adding acid to a buffer solution. (left) A buffered solution of pH 8 shows a yellow color from the indicator (methyl orange). (middle) When a small amount of acid is added to this buffered solution, there is little effect on the pH of the buffer. (right) However, a large amount of acid exhausts the buffering capacity of the solution and the pH changes dramatically. (credit: modification of work by Mark Ott)

The buffer capacity is the amount (moles) of acid or base that can be added to a given volume of a buffer solution before the pH changes by ±1 from the pKa of the weak acid. (Recall that if equal concentrations of weak acid and conjugate base are in a buffer solution, pHbuffer solution = pKa, weak acid.)

Buffer capacity depends on the amount (moles) of weak acid and its conjugate base that are in a buffer mixture. For example, a 1 L solution of 1.0 M CH3COOH and 1.0 M CH3COONa has a greater buffer capacity than a 1 L solution of 0.10 M CH3COOH and 0.10 M CH3COONa, even though both solutions have the same pH. The first solution has more buffer capacity because it contains more moles of acetic acid and acetate ion.

It takes 0.82 mol HCl to change the buffer pH from 4.74 to 3.74 in the first solution:

 \begin{array}{rcl} 3.74 &=& 4.74\;+\;\text{log}\dfrac{[\text{CH}_3\text{COO}^-]_0}{[\text{CH}_3\text{COOH}]_0}\\[1em] 10^{3.74-4.74} &=& \dfrac{[\text{CH}_3\text{COO}^-]_0}{[\text{CH}_3\text{COOH}]_0} \\[1em] 0.10 &=& \dfrac{(1.0\;\text{mol}\;-\;x)/(1\;\text{L})}{(1.0\;\text{mol}\;+\;x)/(1\;\text{L})} \\[1em] 0.10(1.0\;\text{mol}\;+\;x) &=& 1.0\;\text{mol}\;-\;x \\[0.5em] 1.1x &=& 0.90\;\text{mol}\\[0.5em] x &=& 0.82\;\text{mol} \end{array}

On the other hand, for the solution where the concentrations of weak acid and conjugate base are 0.10 M, it takes only one-tenth as much HCl, 0.082 mol HCl, to change the buffer pH from 4.74 to 3.74:

 \begin{array}{rcl} 3.74 &=& 4.74\;+\;\text{log}\dfrac{[\text{CH}_3\text{COO}^-]_0}{[\text{CH}_3\text{COOH}]_0}\\[1em] 10^{-1} &=& \dfrac{[\text{CH}_3\text{COO}^-]_0}{[\text{CH}_3\text{COOH}]_0} \\[1em] 0.10 &=& \dfrac{(0.10\;\text{mol}\;-\;x)/(1\;\text{L})}{(0.10\;\text{mol}\;+\;x)/(1\;\text{L})} \\[1em] x &=& 0.082\;\text{mol} \end{array}

If a buffer solution does not have equal concentrations of weak acid and weak base, the buffer capacity when strong acid is added is different from the buffer capacity when strong base is added.

Exercise: Calculating Buffer Capacity

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