Molecules are in constant motion. Sometimes the collision between two water molecules will result in a hydrogen ion from one water molecule being transferred to the other molecule. A water molecule that loses a hydrogen ion (H+) becomes a negatively charged hydroxide ion (OH-). A water molecule that + gains a hydrogen ion becomes a positively charge hydronium ion (H3O ).
O – H + O – H OH- + H – O – H + | | | H H H
In water or aqueous solutions, hydrogen ions are always joined to water molecules as hydronium ions + (H3O ). The concentration of hydrogen ions is exactly the same as the concentration of hydronium ions. + + When determining pH some chemistry books will refer to [H ] and others will use [H3O ]. It means the same thing.
In pure water at 25°C, the concentration of hydrogen ions [H+] and the concentration of hydroxide ions [OH-] are each equal to 1.0 x 10-7 mol/L.
Ion Concentrations in Aqueous Solutions
In any aqueous solution, the [H+] and the [OH-] are related to each other. If the [H+] increases, then the [OH-] decreases. If the [H+] decreases, then the [OH-] increases.
For aqueous solutions, the product of the hydrogen ion concentration and the hydroxide ion concentration -14 is equal to 1.0 x 10 mol/L. This is called the ion-product constant for water, Kw.
+ - -14 Kw = [H ] x [OH ] = 1.0 x 10 mol/L
When the concentration of hydrogen ions is greater than the concentration of hydroxide ions, the solution is acidic. [H+] > [OH-] Acidic solution
When the concentration of hydrogen ions is less than the concentration of hydroxide ions, the solution is basic. Basic solutions are also called alkaline.
[H+] < [OH-] Basic solution
Calculating pH
The strength of an acid or base can be expressed in moles per liter or molarity, but a more common scale for comparing acids and bases is the pH scale. It was developed in 1909 by a Danish scientist named Soren Sorensen. The pH of a solution is the negative logarithm of the hydrogen ion concentration.
pH = -log[H+]
Since [H+] and [OH-] are related to each other, you can also calculate the pH of a solution if you know the concentration of hydroxide ions [OH-].
pH = 14 + log[OH-]
Practice Problems 1. If [H+] = 1.0 x 10-5 mol/L, is the solution acidic, basic, or neutral? What is the [OH-] of the solution?
2. Calculate the pH of pure water at 25°C.
3. The hydrogen ion concentration of a solution is 1 x 10-10 mol/L. What is the pH of the solution?
4. Determine the pH of the following solutions: a. [H+] = 5.0 x 10-6 mol/L b. [H+] = 8.3 x 10-10 mol/L c. [OH-] = 2.0 x 10-5 mol/L d. [OH-] = 4.5 x 10-11 mol/L
5. Determine the [H+] and [OH-] for each solution: a. pH = 5.0 b. pH = 5.80 c. pH = 12.20 d. pH = 2.64
Answers: 1. pH = -log [H+] = -log [1.0 x 10-5] = 5
pH = 14 + log [OH-] 5 = 14 + log [OH-] -9 = log [OH-] To get rid of the log, raise 10 to the power on both sides of the equation. 10 -9 = 10 log [OH-] 1 x 10-9 = [OH-]
2. pH = 7
3. pH = -log [H+] = -log [1.0 x 10-10] = 10
4. a. pH = -log [H+] = -log [5.0 x 10-6] = 5.30 b. pH = -log [H+] = -log [8.3 x 10-10] = 9.08 c. pH = 14 + log [OH-] = -log [2.0 x 10-5] = 9.30 d. pH = 14 + log [OH-] = -log [4.5 x 10-11] = 3.65
5. a. 5 = -log [OH-] 10 -5 = 10 log [OH-] 1 x 10-5 = [OH-]
b. 1.6 x 10-6 c. 6.3 x 10-13 d. 0.0023