We saw in a previous study guide that water is amphoteric — it can act as an acid or a base. In pure water, a molecule can donate a proton to another molecule according to the following reaction.
The reaction is the dissociation of water. This is known as the self-ionization of water or in some texts as the auto-ionization of water. An equilibrium constant expression can be written for the reaction. The equilibrium constant is called the ion-product constant for water and is represented by Kw.
It has been shown experimentally that at 25°C, the value of Kw is 1.0 x 10-14. Keep in mind, Kw varies with temperature. From the value of Kw we see the eqilibrium lies far to the left. Only about 2 molecules out of one billion molecules will dissociate. But, just like all equilibria, the equilibrium is dynamic.
From, Kw, we see the concentrations of H3O+ and OH– are equal.
Let [H3O+] = [OH–] = x
1.0 x 10-14 = x2
x = 1.0 x 10-7 M
At 25°C both H3O+ and OH– in pure water are 1.0 x 10-7 M. If an acid or a base is added to pure water at 25°C the hydroxide and hydronium ion concentrations will change in order to keep Kw constant at 1.0 x 10-14 at 25°C.
At 25°C, if both [H3O+] and [OH–] are both equal to 1.0 x 10-7 M, we have a neutral solution. If [H3O+] is greater than the [OH–] concentration, we have an acidic solution. If [H3O+] is less than the [OH–] concentration, we have a basic solution.
If [H3O+] > [OH–] the solution is acidic
If [H3O+] < [OH–] the solution is basic
If a strong acid or a strong base is added to pure water at 25 °C, we can determine the concentration of [H3O+] or [OH–] using Kw.
If we were to add 0.015 M HCl to pure water at 25°C, we can calculate the [OH–] concentration.
Solve for [OH–]
\(\displaystyle [OH^-]\;=\;\frac{1.0\;\times 10^{-14}}{0.015}\;=\;6.7\times\;10^{-13}\;M\)
This solution is acidic because 0.015 M H3O+ is greater than 1.0 x 10-7 M, and the OH– concentration is less than 1.0 x 10-7 M.
If we added 0.0010 M NaOH to pure water we can calculate the H3O+ concentration. This time solve Kw for [H3O+].
In this case, the solution is basic because 0.0010 M is greater than a hydroxide ion concentration of 1.0 x 10-7 M, and a hydronium ion concentration of 1.0 x 10-11 M is less than 1.0 x 10-7 M H3O+.
Exercises
Exercise 1. A shampoo has [H3O+] = 3.2 x 10-8 M. What is the hydroxide ion concentration at 25°C? Is the shampoo acidic, neutral, or basic?
Exercise 2. What are the concentrations of H3O+ and OH– in 0.16 M Ba(OH)2 at 25°C? Is the solution acidic, basic, or neutral?
Exercise 3. At 25°C, Kw is 1.0 x 10-14. What is Kw at 30°C if the hydroxide concentration of pure water at this temperature is 1.2 x 10-7 M?
Exercise 4. What is the hydronium ion and hydroxide ion concentrations of 0.025 HNO3 at 25°C?
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