Autoionization of Water

Autoionization of Water Definition

In the article Acids and Bases, you learned that water has a pretty special property. Water is amphoteric, which means that it can act as both a Bronstead-Lowry acid (a proton donor) and a Bronstead-Lowry base (a proton acceptor). Take a look:

• Water molecules can act as acids by dissociating into hydroxide ions (OH^-) and hydrogen ions (H⁺). This is equivalent to losing a proton.
• Water molecules can also act as bases by combining with hydrogen ions to form hydronium ions (H₃O⁺). This is equivalent to gaining a proton.
• Both reactions are reversible - the hydronium ion and hydroxide ion can recombine to form water once more.
• This amphoteric nature means that two water molecules can even react with each other. In this case, the first loses a proton, which the second one then gains.

The ability of water to react with itself and form two ions is known as autoionization.

Autoionization of Water Equation

To better visualize what exactly happens in the autoionization of water, let’s write a chemical equation to show the process.

Firstly, a water molecule splits into H⁺ and OH^-. Then, a second water molecule reacts with the H⁺ produced to form H₃O⁺:

$$H_2O(l)\rightleftharpoons H^+(aq)+OH^-(aq)$$

$$H_2O(l)+H^+(aq)\rightleftharpoons H_3O^+(aq)$$

If we combine the two steps, we end up with one overall equation for the autoionization of water:

$$2H_2O(l)\rightleftharpoons H_3O^+(aq)+OH^-(aq)$$

Notice a few things about the equation:

• H₃O⁺ and OH^- are produced in an equal ratio. Therefore, in a solution of pure water, [H₃O⁺ ] and [OH^-] are the same.
• The reaction is reversible. This means that it eventually forms a state of dynamic equilibrium. Like with all equilibria, we can represent the autoionization of water using an equilibrium constant, which we'll look at in just a second.

Simplifying the equation

The aqueous hydronium ion, H₃O⁺(aq), is really nothing more than a hydrated proton. We can instead represent it using an aqueous hydrogen ion, H⁺(aq). This allows us to simplify the equation for the autoionization of water:

$$H_2O(l)\rightleftharpoons H^+(aq)+OH^-(aq)$$

Autoionization Constant of Water

So, we now know more about autoionization and have an equation to back it up. This equation shows that the autoionization of water is reversible, and so forms a dynamic equilibrium. Therefore, we can represent autoionization with an equilibrium constant.

The equilibrium constant for the autoionization of water is calculated using concentration, and so is based on K_c. This constant is important enough that it has its own name: K_w. K_w is also known as the ion-product constant of water.

K_w Expression

K_w is expressed by:

$$K_w=[H^+]_{eqm}[OH^-]{eqm}$$

K_w Properties

K_w is an equilibrium constant. As a result, it shares common properties with all forms of K_eq:

• K_w tells us about the position of the equilibrium reaction. Hence, it tells us about the extent of the autoionization of water.
• The value of K_w is fixed at a particular temperature. However, change the temperature, and you change the value of K_w.
• On the other hand, K_w is unaffected by factors such as concentration and pressure.

For example, at 25 °C (298 K), K_w always equals 1.0 × 10^-14. This is a small value and so tells us that the position of the equilibrium reaction lies far to the left - the vast majority of water molecules don't ionize.

But despite its diminutive size, K_w is still significant. This is because it allows us to calculate [H⁺], [OH^-], and pH for aqueous solutions. Let's find out how.

Autoionization of Water and pH

Remember that the value of K_w is fixed at a particular temperature. We say that it is temperature-dependent. At 25 °C, K_w equals 1.0 × 10^-14. Therefore, in all aqueous solutions, \( [H^+][OH^-]=1.0\times 10^{-14}\) . Provided we know information about any of [H⁺], [OH^-], or pH, we can use K_w to calculate the other values.

Notice that in pure water, the concentration of hydrogen ions equals the concentration of hydroxide ions. We'd expect this result - after all, the balanced chemical equation for the autoionization of water produces an equal ratio of H⁺ and OH^-. This makes pure water neutral.

At 25 °C, neutral substances (be it water or another aqueous solution) have a pH of exactly 7.0. But as temperature changes, the value of K_w changes, and the pH of neutral substances does too. One thing remains constant: no matter the temperature, neutral substances always have the same concentration of hydrogen ions as hydroxide ions.

Well, that's the pH of neutral substances covered. However, most aqueous solutions aren't neutral. Instead, they are either acidic or basic; in these solutions, [H⁺] ≠ [OH^-]. Let's see how this affects their acidity and pH:

• If [H⁺] > [OH^-], the solution is acidic. At 25 °C, it has a pH below 7.0.
• If [H⁺] < [OH^-], the solution is basic. At 25 °C, it has a pH above 7.0.

Fig.1-A diagram showing how the relative concentrations of hydrogen and hydroxide ions affect the pH of aqueous solutions.

Autoionization of Water Examples

Time to pull together what we have learned by practicing some example calculations involving the autoionization of water. Unless stated otherwise, assume that the temperature is 25 °C in all the following questions. First, have a go at finding pH using K_w and [OH^-]. Here are the steps:

1. Use the expression for K_w to find [H⁺].
2. Use [H⁺] to calculate pH.

Time to move on to a different sort of problem. Here, you need to work backwards and find both [H⁺] and [OH^-] using pH and K_w:

1. Use pH to find [H⁺].
2. Use [H⁺] and the expression for K_w to find [OH^-].

Try this problem:

Finally, have a go at finding the pH of pure water at a higher temperature. Remember that this changes the value of K_w. The method is similar to the one you used in the first problem.

Limitations of the Autoionization of Water

We've seen how we can use the autoionization of water and K_w to find the pH of an aqueous solution. This is handy for all sorts of acid-base calculations. In these problems, we ignore the H⁺ and OH^- ions from the ionization of water itself, and assume that they all come from the other acid or base involved. This typically isn't a problem. Remember that K_w is very low, meaning that only a small proportion of water molecules ionize at equilibrium. The ions that come from the autoionization of water have very little effect on the pH of the solution.

However, water's autoionization becomes an issue if working with extremely dilute acids or bases, such as those with [H⁺] or [OH^-] values less than two orders of magnitude away from 1.0 × 10^-7. Because these acids and bases also have such low values of [H⁺] or [OH^-], the H⁺ and OH^- ions from water become much more important, and you can't ignore their effect on pH.