Buffer Solutions

Types of buffer solutions

Buffer solutions can be acidic or basic. They are designed to keep the concentrations of hydrogen ions and hydroxide ions roughly the same by reacting with whatever substances are added to them, be it another acid or another base.

Acidic buffer solutions

Acidic buffer solutions are formed by mixing a weak acid with one of its salts in solution. The salt is also the acid’s conjugate base.

Let’s take a look at how acidic buffer solutions work.

Suppose we have the weak acid HA and its soluble salt MA. You should know from the article ‘Weak acids and bases’ that weak acids partially dissociate in solution. This is important for keeping a constant pH if we add an alkali. For our acid HA, that dissociation looks something like this:

$\mathrm{HA}\left(\mathrm{aq}\right)\rightleftharpoons {\mathrm{H}}^{+}\left(\mathrm{aq}\right)+{\mathrm{A}}^{-}\left(\mathrm{aq}\right)$

Because the acid only partially dissociates, the concentrations of H⁺ ions and OH^- ions are very small.

On the other hand, the soluble salt MA fully ionises in solution:

$\mathrm{MA}\left(\mathrm{aq}\right)\to {\mathrm{M}}^{+}\left(\mathrm{aq}\right)+{\mathrm{A}}^{-}\left(\mathrm{aq}\right)$

This is important for keeping a constant pH if we add an acid.

Adding an alkali to acidic buffer solutions

If we add an alkali to the buffer solution, we are essentially adding extra hydroxide ions, OH^-. We’d expect the pH to increase. However, the OH^- ions instead react with the weak acid in the buffer solution to form water and A^- ions:

${\mathrm{OH}}^{-}\left(\mathrm{aq}\right)+\mathrm{HA}\left(\mathrm{aq}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)+{\mathrm{A}}^{-}\left(\mathrm{aq}\right)$

This means that overall, the numbers of hydrogen ions and hydroxide ions haven’t changed, meaning [H⁺] and [OH^-] are the same. The buffer has resisted change in pH.

OH^- ions can also be removed by a second process – they react with the hydrogen ions produced when a tiny proportion of the weak acid HA dissociates, producing water. As soon as they react, the equilibrium shifts to the right and so more of the weak acid dissociates until all of the alkali is used up.

${\mathrm{H}}^{+}\left(\mathrm{aq}\right)+{\mathrm{OH}}^{-}\left(\mathrm{aq}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$

Adding an acid to acidic buffer solutions

If we add an acid to the buffer solution, we’d expect the pH to decrease as the acid donates protons, which are just hydrogen ions, to the solution. However, this is where the soluble salt MA comes in. Any protons react with the A^- ions produced when the salt ionises to form the weak acid HA:

${\mathrm{A}}^{-}\left(\mathrm{aq}\right)+{\mathrm{H}}^{+}\left(\mathrm{aq}\right)\to \mathrm{HA}\left(\mathrm{aq}\right)$

Overall, the concentrations of hydrogen ions and hydroxide ions have largely remained the same. The buffer has again resisted a change in pH.

An alternative acidic buffer solution

You can also create an acidic buffer by half-neutralising a weak acid with a strong base.

This forms the same solution we explored above – a solution containing a weak acid and its salt. However, because the acid is half-neutralised, the buffer solution has a unique property: its pK_a equals its pH.

Let’s look at this more closely. Take one mole of the weak acid HA and half a mole of the base MOH in a solution with a volume of 1000 cm³. At half-neutralisation, exactly half of the weak acid reacts with the base to form a salt, MA, and water, H₂O. The equation below shows the number of moles before the reaction, the change in the number of moles, and the number of moles after the reaction for each of the species:

Fig. 1 - The change in moles in a reaction between a weak acid and a strong base in a half-neutralisation reaction

We have half a mole for each of the weak acid HA and the salt MA. MA ionises in solution into M⁺ and A^-. This means that we also have half a mole of A^- ions. There are the same amount of HA molecules as A^- ions – their concentrations are equal. In other words, [HA] = [A^-].

Let’s now look at the equation for K_a:

${\mathrm{K}}_{\mathrm{a}}=\frac{\left[{\mathrm{A}}^{-}\right]\left[{\mathrm{H}}^{+}\right]}{\left[\mathrm{HA}\right]}$

Because [HA] and [A^-] are equal, we find that the [A^-] at the top of the equation cancels out with the [HA] at the bottom of the equation:

${\mathrm{K}}_{\mathrm{a}}=\frac{\sout{\left[{\mathrm{A}}^{-}\right]}\left[{\mathrm{H}}^{+}\right]}{\sout{\left[\mathrm{HA}\right]}}$

We are left with just K_a equalling H⁺. This means that the pH of this buffer solution equals the pK_a of the acid:

${\mathrm{K}}_{\mathrm{a}}=\left[{\mathrm{H}}^{+}\right]{\mathrm{pK}}_{\mathrm{a}}=\mathrm{<a\; data-course-subject-id="3783389"\; data-summary-id="25194273"\; href="/explanations/chemistry/physical-chemistry/ph/">pH</a>}$$$\begin{gathered} {\mathrm{K}}_{\mathrm{a}}=\mathrm{pH} \\ {\mathrm{pK}}_{\mathrm{a}}=\mathrm{pH} \end{gathered}$$

Basic buffer solutions

Similarly to acidic buffer solutions, basic buffer solutions are made from a weak base and one of its salts. This salt is the base’s conjugate acid.

Let’s look at an example, such as the buffer solution formed when ammonia is mixed with ammonium chloride. Ammonia is a weak base. This means that it partially dissociates in solution, as shown by the following equation:

${\mathrm{NH}}_3\left(\mathrm{aq}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\rightleftharpoons {{\mathrm{NH}}_4}^{+}\left(\mathrm{aq}\right)+{\mathrm{OH}}^{-}\left(\mathrm{aq}\right)$

Aammonium chloride is a salt and so fully ionises in solution:

${\mathrm{NH}}_4\mathrm{Cl}\left(\mathrm{aq}\right)\to {{\mathrm{NH}}_4}^{+}\left(\mathrm{aq}\right)+{\mathrm{Cl}}^{-}\left(\mathrm{aq}\right)$

Let’s now explore how the buffer solution reacts to extra acids and bases.

Adding an acid to basic buffer solutions

If we add an acid, the H⁺ ions it releases react with aqueous ammonia to form ammonium ions:

${\mathrm{NH}}_3\left(\mathrm{aq}\right)+{\mathrm{H}}^{+}\left(\mathrm{aq}\right)\to {{\mathrm{NH}}_4}^{+}\left(\mathrm{aq}\right)$

There may also be a second reaction. Remember, a small proportion of the ammonia in solution dissociates into ammonium ions, NH₄⁺, and hydroxide ions, OH^-. The acid’s hydrogen ions can also react with the hydroxide ions to form water:

${\mathrm{H}}^{+}\left(\mathrm{aq}\right)+{\mathrm{OH}}^{-}\left(\mathrm{aq}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$

Because the hydrogen ions have reacted and been used up, the overall concentrations of hydrogen ions and hydroxide ions remain constant. The buffer solution has resisted change in pH.

Adding an alkali to basic buffer solutions

If we add an alkali to our buffer solution, it reacts with the ammonium ions in solution to form ammonia and water:

${{\mathrm{NH}}_4}^{+}\left(\mathrm{aq}\right)+{\mathrm{OH}}^{-}\left(\mathrm{aq}\right)\to {\mathrm{NH}}_3\left(\mathrm{aq}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$

Overall, the hydroxide ion concentration remains largely unchanged. The buffer solution has resisted change in pH.

Examples of buffer solutions

Let’s now look at an example of a buffer solution in action. A typical buffer solution can be made from ethanoic acid and sodium ethanoate. The ethanoic acid partially dissociates in solution:

${\mathrm{CH}}_3\mathrm{COOH}\left(\mathrm{aq}\right)\rightleftharpoons {\mathrm{CH}}_3{\mathrm{COO}}^{-}\left(\mathrm{aq}\right)+{\mathrm{H}}^{+}\left(\mathrm{aq}\right)$

The sodium ethanoate fully ionises in solution:

${\mathrm{CH}}_3\mathrm{COONa}\left(\mathrm{aq}\right)\to {\mathrm{CH}}_3{\mathrm{COO}}^{-}\left(\mathrm{aq}\right)+{\mathrm{Na}}^{+}\left(\mathrm{aq}\right)$

If we add hydrogen ions, H⁺, they react with the ethanoate ions, CH₃COO^-, that came from the sodium ethanoate:

${\mathrm{CH}}_3{\mathrm{COO}}^{-}\left(\mathrm{aq}\right)+{\mathrm{H}}^{+}\left(\mathrm{aq}\right)\to {\mathrm{CH}}_3\mathrm{COOH}\left(\mathrm{aq}\right)$

If we add hydroxide ions, OH^-, they either react with the ethanoic acid, CH₃COOH, to form ethanoate ions and water, or they react with the hydrogen ions produced when a small proportion of ethanoic acid dissociates:

${\mathrm{CH}}_3\mathrm{COOH}\left(\mathrm{aq}\right)+\hspace{0.17em}{\mathrm{OH}}^{-}\left(\mathrm{aq}\right)\to {\mathrm{CH}}_3{\mathrm{COO}}^{-}\left(\mathrm{aq}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right){\mathrm{H}}^{+}\left(\mathrm{aq}\right)+\hspace{0.17em}{\mathrm{OH}}^{-}\left(\mathrm{aq}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$

Overall, the pH of the solution remains roughly the same. The buffer solution has resisted change in pH.

Buffer solution calculations

Now that we understand how buffer solutions work, we can have a go at calculating their pH.

Not too tricky, right? Now let’s take another example, this time calculating the pH of a buffer solution formed in the reaction between a weak acid and a strong base.

Well done! You made it through buffer solutions. The following flow charts show how you calculate the pH of an acidic buffer solution to help summarise your knowledge:

Fig. 2 - A flowchart showing you how to calculate the pH of buffer solutions