0.6 Buffers

When acid or base is added to water, the pH can change rapidly. For example, at 298 K the pH of 1 L of neutral water is 7.00. Adding just 0.10 mol of HCl to this water would decrease the pH to 1.0. Many processes are sensitive to such large changes in pH, particularly in biological systems. For example, the pH of our blood must remain close to 7.40 for our proteins to maintain their 3D structure and function. To protect against large changes in pH upon the addition of an acid or base, our blood contains a buffer. A buffer is a solution that minimizes changes in pH upon the addition of acid or base. A buffer solution contains a weak conjugate acid-base pair, where both the weak acid and weak base components are present in significant amounts. For example, an acetic acid/acetate buffer is comprised of significant amounts of both CH₃COOH and CH₃COO⁻. If a base, such as NaOH, were added to this solution then it would be neutralized through reaction with the weak acid component

Likewise, if an acid such as HCl were added to this solution then it would be neutralized through reaction with the weak base component

In both cases, the neutralization of the added acid or base minimizes the overall pH change of the solution. Of course, there is a limit to how much acid or base can be added to the solution: if more NaOH is added than there is CH₃COOH to react with, for example, then the buffer will no longer function. This maximum amount of acid or base that can be added before the buffer is no longer effective is called the buffer capacity. Buffers with high buffer capacity contain large amounts of both the weak acid and weak base components and can thus resist a large pH change upon the addition of relatively large amounts of acid or base.

Identifying a buffer
Buffers need to contain a significant amount of both a weak acid and its conjugate base so that they can minimize pH change upon the addition of either base or acid. Significant amounts of each here means that the weak acid and its conjugate base are within a 10:1 ratio of each other at equilibrium. That is, for each molecule of the weak acid, a buffer should contain between 0.1 and 10 molecules of the conjugate base. When considering this ratio, compare the amount of weak acid and conjugate base using either the number of moles of each or concentrations based on the total volume of the buffer.

 
Determining the pH of a buffer
There are two common methods to determine the pH of a buffer solution:

1. The first method uses the same ICE tables that were introduced in the previous section for determining the pH of mixtures of acids and bases. In fact, the second example in the previous section (reaction between a strong acid and weak base) was a buffer solution. An abridged solution is repeated below for your review.
   Example: What is the pH of the buffer solution made by adding 12 mL of 1.2 M HCl to 23 mL of 2.3 M CH₃COO⁻? The K_a of CH₃COOH is 1.8 x 10⁻⁵ at 298 K.

   View solution (Method 1):

   The concentrations of HCl and CH₃COO⁻ based on the total volume are:

   

   

   Strong acids like HCl react completely with weak bases like CH₃COO⁻, so the strong acid (limiting reagent) will react completely here:

   

   At the end of this reaction, we have a weak acid, CH₃COOH, and its conjugate base, CH₃COO⁻, within a 10:1 ratio, so this is a buffer solution. To determine the pH, we'll consider the equilibrium that is established between the weak acid and its conjugate base in water. A second ICE table shows how the CH₃COOH produced in the first reaction goes on to react with water:

   

   Notice that we included initial amounts of both CH₃COOH and CH₃COO⁻, since both were still present after the reaction in the first ICE table. The equilibrium constant of this reaction, K_a, is equal to the concentrations of the products divided by the reactants:

   

   Since CH₃COOH is a weak acid, we can make the simplifying assumption that x is small such that and . This simplifies our equation to

   

   And thus x is given by

   

   This value of x is less than 5% of either 0.4114 M or 1.100 M, so our assumption that x is small was valid. Since x represents the [H₃O⁺] at equilibrium, the pH is given by

   
   

 

2. The second method uses the Henderson-Hasselbalch equation. This method is valid whenever the ‘x is small’ approximation is valid. To derive the Henderson-Hasselbalch equation, consider a generic weak acid, HA, and its conjugate base, A⁻. The reaction between HA with water is

   

   and the K_a for this reaction is

   

   Taking the negative logarithm of both sides gives

   

   Since and , we can substitute these terms in to give

   

   and thus the pH of a buffer solution is given by

   

   In a buffer, the weak acid (HA) and conjugate base (A⁻) are in the same solution, so the volume used to calculate the concentration is also the same. If C_a is the number of moles of conjugate acid, C_b is the number of moles of conjugate base, and V is the volume of the solution, then

   

   Substituting this in above gives the Henderson-Hasselbalch equation

   

   Note that it’s equally valid to input as either the ratio of the moles or the concentrations of the weak conjugate acid-base pair, since both will give the same result.

   The question below is the same as the example given above, except the solution uses the Henderson-Hasselbalch equation rather than a second ICE table to calculate the pH. Solve the problem yourself, then expand the solution and check your work, to confirm that both methods give the same pH.

   Example: What is the pH of the buffer solution made by adding 12 mL of 1.2 M HCl to 23 mL of 2.3 M CH₃COO⁻? The K_a of CH₃COOH is 1.8 x 10⁻⁵ at 298 K.

   View solution (Method 2):

   The concentrations of HCl and CH₃COO⁻ based on the total volume are:

   

   

   Strong acids like HCl react completely with weak bases like CH₃COO⁻, so the strong acid (limiting reagent) will react completely here:

   

   At the end of this reaction, we have a weak acid, CH₃COOH, and its conjugate base, CH₃COO⁻, within a 10:1 ratio, so this is a buffer solution. To determine the pH of a buffer solution, use the Henderson-Hasselbalch equation. We'll need the pK_a for the Henderson-Hasselbalch equation:

   

   Next, insert this value into the Henderson-Hasselbalch equation along with the amounts of weak acid and conjugate base from the equilibrium row in the ICE table above:

   
   

 
Buffer range
From the Henderson-Hasselbalch equation, we know that the pH of a buffer depends on the ratio of . We also know that a solution is only an effective buffer when the weak base and its conjugate acid are within a 10:1 (or 1:10) ratio. It follows, then, that each particular weak conjugate acid-base pair could only form an effective buffer over a limited pH range. The pH range of a buffer is the range of pH values over which the buffer is effective. We can determine the pH range of any buffer using the Henderson-Hasselbalch equation. Consider the extreme where is 10:1. By the Henderson-Hasselbalch equation, at this ratio the pH of the buffer will be

At the other extreme, where where is 1:10, the pH of the buffer will be

That is, any buffer made of a weak acid with a particular pK_a and its conjugate base will be effective from over the pH range spanning from to .

 
pH of a buffer after strong acid/base addition
At the top of this page we saw that adding 0.10 mol of HCl to pH 7.00 water would decrease the pH to 1.00. What would happen to the pH, though, if we instead added the same 0.10 mol of HCl to a solution buffered at pH 7.00? To answer this question, try to solve the example below yourself, then expand to see the solution.

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