Autoionization of water | Acids and bases | AP Chemistry | Khan Academy

The autoionization of water refers to the reaction of water molecules to form two ions: the hydronium ion, which is H3O⁺, and the hydroxide ion, which is OH⁻. Water can function as an acid or base, and in this reaction, one water molecule functions as a Brønsted-Lowry acid and donates a proton, while another water molecule functions as a Brønsted-Lowry base and accepts a proton.

In the reaction, the base takes an H⁺ ion from the acid, and these two electrons are left behind on this oxygen. Adding an H⁺ to H₂O gives the hydronium ion (H3O⁺), and taking away an H⁺ from H₂O gives the hydroxide ion (OH⁻). We can write an equilibrium constant expression for this reaction.

So, we would write the equilibrium constant K as equal to: we would start with our products. We'd have the concentration of hydronium ions, and since we have a coefficient of one in front of hydronium in the balanced equation, it'd be the concentration of hydronium ions raised to the first power times the concentration of hydroxide ions. Once again, there's a coefficient of one in the balanced equation, so it's the concentration of hydroxide ions raised to the first power.

For the reactants, liquid water is left out of the equilibrium constant expression. Normally, we would write Kc, where the c stands for concentration for the equilibrium constant since we're dealing with concentrations. However, this is a special equilibrium constant expression for the autoionization of water, so instead of writing Kc, we're going to write Kw, where W stands for water.

Kw is equal to 1.0 times 10 to the negative 14th at 25 degrees Celsius. With such a low value for Kw, this value is much less than one, which tells us that at equilibrium we have an extremely small concentration of hydronium and hydroxide ions.

So, mostly we have H₂O molecules at equilibrium. Let's go ahead and solve for the concentration of hydronium ions and hydroxide ions at equilibrium. In the balanced equation, there's a coefficient of one in front of both hydronium and hydroxide. Therefore, at equilibrium, these two concentrations are equal. Since we don't know what those concentrations are, we're going to represent it by writing x.

So this would be x times x is equal to 1.0 times 10 to the negative 14. We would have x² is equal to 1.0 times 10 to the negative 14. Taking the square root of both sides, we would find that x is equal to 1.0 times 10 to the negative seventh. Therefore, if we had a sample of pure water at 25 degrees Celsius, the concentration of hydronium ions and the concentration of hydroxide ions would be equal to 1.0 times 10 to the negative seventh.

Instead of using two water molecules to show the autoionization of water, it's also possible to show it using only one water molecule. So, H₂O could break up to form H⁺ and OH⁻. The H⁺, which is the hydrogen ion, is sometimes used interchangeably with H3O⁺, which is the hydronium ion.

We've just seen that pure water has the concentration of hydronium ions equal to the concentration of hydroxide ions; therefore, pure water is a neutral substance. For any aqueous solution where the concentration of hydronium ion is equal to the concentration of hydroxide ion, we would classify that as a neutral solution.

If an aqueous solution has a concentration of hydronium ions that’s greater than the concentration of hydroxide ions, we would classify the solution as an acidic solution. If an aqueous solution has a concentration of hydronium ions that’s less than the concentration of hydroxide ions, or you could say the concentration of hydroxide ions is greater than that of hydronium, the solution would be considered a basic solution.

The equation that we've already talked about, the concentration of hydronium ions times the concentration of hydroxide ions, is equal to Kw, which is equal to 1.0 times 10 to the negative 14 at 25 degrees Celsius. This equation is true if you're dealing with an acidic solution, a neutral solution, or a basic solution, and I'll call this equation the Kw equation from now on.

Let's say we have an aqueous solution, and the concentration of hydronium ions in the solution is equal to 4.0 times 10 to the negative 6 molar at 25 degrees Celsius, and our goal is to calculate the concentration of hydroxide ions in this solution at 25 degrees Celsius. To solve for the concentration of hydroxide ion, we can use our Kw equation.

So, we need to plug in for the concentration of hydronium ion, so that gives us 4.0 times 10 to the negative six times the concentration of hydroxide ion, which we'll just go ahead and make x here, and all that's equal to Kw, which is equal to 1.0 times 10 to the negative 14.

Solving for x, we find that x is equal to 2.5 times 10 to the negative 9. Since x is equal to the concentration of hydroxide ion, the concentration of hydroxide ion is equal to 2.5 times 10 to the negative ninth molar for this aqueous solution. The concentration of hydronium ion is greater than the concentration of hydroxide ion; therefore, this is an acidic solution.

An equilibrium constant is only constant at a specific temperature. For example, at 25 degrees Celsius, Kw is equal to 1.0 times 10 to the negative 14. But if you change the temperature, you change the value for Kw. At 50 degrees Celsius, Kw is equal to 5.5 times 10 to the negative 14th. So, an increase in temperature from 25 degrees Celsius to 50 degrees Celsius causes an increase in the value for Kw.

An increase in temperature causes an increase in Kw, and we can use Le Chatelier's principle to predict if the autoionization of water is an endothermic reaction or an exothermic reaction. An increase in Kw means an increased concentration of hydronium ion and hydroxide ion at equilibrium; therefore, the net reaction must have gone to the right to increase the amount of our products.

If we treat heat as a reactant and we increase the temperature, it's as if we've increased the amount of one of our reactants. Therefore, according to Le Chatelier's principle, the net reaction is going to shift to the right to make more of the product since that's what we observe by increasing the value for Kw.

We know that the autoionization of water is an endothermic reaction. If we had put heat on the product side and treated this like an exothermic reaction, we would have gotten a shift in the wrong direction. We've got to shift back to the left, so we know it's not exothermic.

Finally, let's calculate the concentration of hydronium ions and hydroxide ions in a sample of pure water at 50 degrees Celsius. We can still use the Kw equation, so Kw is equal to the concentration of hydronium ions times the concentration of hydroxide ions. However, since the temperature is now 50 degrees Celsius, we can't use 1.0 times 10 to the negative 14 because that's the Kw at 25 degrees Celsius.

We need to use the Kw at 50 degrees Celsius, which is 5.5 times 10 to the negative 14th. For the autoionization of water, the mole ratio of hydronium ion to hydroxide ion is one to one. Therefore, the concentration of hydronium ion is equal to the concentration of hydroxide ion.

So when we plug in for hydronium, if you say that concentration is x, the concentration of hydroxide would also be x. So we have x times x is equal to Kw, which is equal to 5.5 times 10 to the negative 14. Thus, x² is equal to 5.5 times 10 to the negative 14th, and to solve for x, we simply take the square root of both sides.

So, x is equal to 2.3 times 10 to the negative seventh. The concentration of hydronium ions is equal to the concentration of hydroxide ions, which is 2.3 times 10 to the negative seventh molar. Notice that this is a higher concentration than we got at 25 degrees Celsius, which makes sense because the value for Kw has increased.

However, since the concentration of hydronium is still equal to the concentration of hydroxide ions, pure water is still neutral.