Weak Acids and Bases

Defining weak acids and bases

What are weak acids and bases? Let's look at a few definitions to make this clear.

Weak acids

To understand weak acids, we first need to define strong acid, so that you can accurately compare the two.

All acids are proton donors. Every molecule of a strong acid donates a proton when it reacts. We can represent this using the following equation. Note how the reaction isn’t reversible:

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

On the other hand, weak acids behave a little differently.

Weak acids form an equilibrium, in which the majority of the molecules present are acid molecules and only a tiny fraction donate their protons and dissociate into ions. The stronger an acid is, the more the equilibrium shifts to the right and the greater the concentration of hydrogen ions in solution.

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

Weak bases

We can also find strong and weak bases. Remember that a base is a proton acceptor.

An example of a strong base is sodium hydroxide, NaOH. Every molecule of NaOH accepts a proton from water, dissociating in solution to form sodium ions and hydroxide ions:

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

In contrast to sodium hydroxide, ammonia is only a weak base.

Like with weak acids, weak bases form an equilibrium in which the backward reaction is strongly favoured, and only a small proportion of the molecules ionise. This means not every molecule of the weak base accepts a proton. We represent the dissociation of ammonia with the following equation:

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

The general equations for the dissociation of a strong base and weak base are shown below, with the dissociation of a strong base first:

$$\begin{gathered} \mathrm{B}\left(\mathrm{aq}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\to {\mathrm{BH}}^{+}\left(\mathrm{aq}\right)+{\mathrm{OH}}^{-}\left(\mathrm{aq}\right) \\ \mathrm{B}\left(\mathrm{aq}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\leftrightharpoons {\mathrm{BH}}^{+}\left(\mathrm{aq}\right)+{\mathrm{OH}}^{-}\left(\mathrm{aq}\right) \end{gathered}$$

Fig. 1 - Strong and weak concentrated and dilute acids

pH of weak acids and bases

Weak acids have higher pH values than strong acids. Likewise, weak bases have lower pH values than strong bases. This is because weak acids and bases only partially ionise in solution.

Fig. 2 - The pH of acids and bases

Strong and weak acids and bases

Let's now take some time to compare strong and weak acids and bases. This table should recap the differences we've already mentioned, as well as introduce you to their reactions with metals and conductivities.

Weak acids and bases chart

You’ll encounter both strong and weak acids and bases in everyday life. For example, concentrated hydrochloric acid, a strong acid, is used to remove algae from the bottoms of boats, whilst a more dilute solution is used in toilet cleaners. Hydrochloric acid is also the acid found in our stomachs that helps digest our food. Citric acid and ethanoic acid, the acids found in lemons and malt vinegar respectively, are both weak acids. Basic sodium bicarbonate is also known as baking soda, a useful leavening agent in baking, whilst the base calcium hydroxide is used to help neutralise acidic soil.

Here's a handy chart with common chemical examples of strong and weak acids and bases.

Fig. 3 - Strong and weak acid and base chart

Weak acids and K_a

Now let's move on to calculations involving weak acids and bases. We'll start by focusing on K_a.

In The Ionic Product of Water, we discussed K_w. K_w is a modified equilibrium constant for the dissociation of water. We can also get K_a, a modified equilibrium constant for the dissociation of weak acids.

The general equation of the equilibrium constant for the reaction $\mathrm{aA}+\mathrm{bB}\leftrightharpoons \mathrm{cC}+\mathrm{dD}$ is shown below:

${\mathrm{K}}_{\mathrm{c}}=\frac{{\left[\mathrm{C}\right]}^{\mathrm{c}}{\left[\mathrm{D}\right]}^{\mathrm{d}}}{{\left[\mathrm{A}\right]}^{\mathrm{a}}{\left[\mathrm{B}\right]}^{\mathrm{b}}}$

Square brackets represent concentration, and the small letter represents the number of moles of each species in the chemical equation. For example, the equilibrium reaction, ${\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{I}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{HI}\left(\mathrm{g}\right)$, has the following equilibrium constant:

${\mathrm{K}}_{\mathrm{c}}=\frac{{\left[\mathrm{HI}\right]}^2}{\left[{\mathrm{H}}_2\right]\left[{\mathrm{I}}_2\right]}$

Let’s look at this from the point of view of a weak acid. It dissociates in solution with the equation $\mathrm{HA}\left(\mathrm{aq}\right)\leftrightharpoons {\mathrm{H}}^{+}\left(\mathrm{aq}\right)+{\mathrm{A}}^{-}\left(\mathrm{aq}\right)$. The reactant is the acid and the products are the hydrogen ions and the negative ions. This gives us the following equilibrium constant, known as K_a:

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

The units of K_a

To find the units of K_a, we multiply and cancel down the units of all the species involved in the equation. All three species, [H⁺], [A^-], and [HA], have the units mol dm^-3. The equation now looks like this:

$\frac{\mathrm{mol}{\mathrm{dm}}^{-3}\mathrm{x}\mathrm{mol}{\mathrm{dm}}^{-3}}{\mathrm{mol}{\mathrm{dm}}^{-3}}$

One of the mol dm^-3 from the top of the fraction cancels out with the one on the bottom, leaving just one mol dm^-3:

$\frac{\mathrm{mol}{\mathrm{dm}}^{-3}\mathrm{x}\sout{\mathrm{mol}{\mathrm{dm}}^{-3}}}{\sout{\mathrm{mol}{\mathrm{dm}}^{-3}}}$

K_a and pK_a

Just as pK_w is the negative log of K_w, pK_a is the negative log of K_a:

$$\begin{gathered} {\mathrm{pK}}_{\mathrm{a}}=-\log \left({\mathrm{K}}_{\mathrm{a}}\right) \\ {\mathrm{K}}_{\mathrm{a}}={10}^{-{\mathrm{pK}}_{\mathrm{a}}} \end{gathered}$$

You should note the following relationships between K_a, pK_a, acid strength and pH:

• As K_a increases, pK_a and pH both decrease.
• As K_a increases, acid strength increases.

Finding Ka from pH

To calculate the pH of weak acids, you use the relationships between K_a, PK_a, and the concentration of the acid in solution. You’ll be given information about the acid’s PK_a or K_a. There are a few more steps compared to working out the pH of a strong acid, but it isn’t too tricky. Let’s have a look at an example together.

Weak bases and K_b

We know what a weak base is - a base that only partially dissociates in solution. It forms an equilibrium reaction. Just like for acids, we can find an equilibrium constant, this time known as K_b. The equation for K_b is given below using B to represent the base:

${\mathrm{K}}_{\mathrm{b}}=\frac{\left[{\mathrm{BH}}^{+}\right]\left[{\mathrm{OH}}^{-}\right]}{\left[\mathrm{B}\right]}$

Units of K_b

Like K_a , K_b has the units mol dm^-3.

Kb and pKb

You can probably guess how we calculate pK_b. It is simply the negative log of K_b:

$$\begin{gathered} {\mathrm{pK}}_{\mathrm{b}}=-\log \left({\mathrm{K}}_{\mathrm{b}}\right) \\ {\mathrm{K}}_{\mathrm{b}}={10}^{-{\mathrm{pK}}_{\mathrm{b}}} \end{gathered}$$

Finding the pH of weak bases

Finding the pH of a weak base is similar to finding the pH of a weak acid. However, there are a few differences. Let’s look at an example together.

Steps for finding the pH of weak acids and bases

Congratulations! You made it through some tricky calculations. You should now be able to work out the pH values for all sorts of acids, bases, and mixtures.

The following flowchart provides a summary of the steps taken to work out the pH of weak acids and bases. Remember to check out all of the other articles we mentioned here for more information about various acid-base calculations.

Fig. 4 - Finding the pH of weak acids and bases

Weak acid and base titrations

We've learned that weak acids have higher pH values than strong acids, whilst weak bases have lower pH values than storng bases. This means that they produce slightly different pH curves in titration experiments. You can explore this more in pH Curves and Titrations.