Ion-Product of Water

Learning Objectives

  • Define the ion-product constant of water.
  • Define acidic solution.
  • Define basic solution.
  • Use the constant to calculate [H+] or [OH−] when the other is known.

What’s inside?

At one time, you could take the little caps off the top of a car battery and check the condition of the sulfuric acid inside. If it got low, you could add more acid. But, sulfuric acid is hazardous stuff, so the batteries are now sealed to protect people. Because of the acid’s dangerous nature, it is not a good idea to cut into a battery to see what it looks like—you could get acid burns.

Car batteries contain sulfuric acid

The Ion-Product of Water

The self-ionization of water (the process in which water ionizes to hydronium ions and hydroxide ions) occurs to a very limited extent. When two molecules of water collide, there can be a transfer of a hydrogen ion from one molecule to the other. The products are a positively charged hydronium ion and a negatively charged hydroxide ion.

text{H}_2text{O}(l)+text{H}_2text{O}(l) rightleftarrows text{H}_3text{O}^+(aq)+text{OH}^-(aq)

We often use the simplified form of the reaction:

text{H}_2text{O}(l) rightleftarrows text{H}^+(aq)+text{OH}^-(aq)

The equilibrium constant for the self-ionization of water is referred to as the ion-product for water and is given the symbol K_w .

K_w = [ text{H}^+ ][ text{OH}^- ]

The ion-product of water  (K_w) is the mathematical product of the concentration of hydrogen ions and hydroxide ions. Note that H 2 O is not included in the ion-product expression because it is a pure liquid. The value of  K_w is very small, in accordance with a reaction that favors the reactants. At 25°C, the experimentally determined value of  K_w in pure water is 1.0 × 10 -14 .

K_w=[text{H}^+][text{OH}^-]=1.0 times 10^{-14}

In pure water, the concentrations of hydrogen and hydroxide ions are equal to one another. Pure water or any other aqueous solution in which this ratio holds is said to be neutral. To find the molarity of each ion, the square root of  K_w is taken.

[text{H}^+]=[text{OH}^-]=1.0 times 10^{-7} text{M}

An acidic solution is a solution in which the concentration of hydrogen ions is greater than the concentration of hydroxide ions. For example, hydrogen chloride ionizes to produce H + and Cl − ions upon dissolving in water.

text{HCl}(g) rightarrow text{H}^+(aq) + text{Cl}^-(aq)

This increases the concentration of H + ions in the solution. According to LeChâtelier’s principle, the equilibrium represented by text{H}_2text{O}(l) rightleftarrows text{H}^+(aq)+text{OH}^-(aq) is forced to the left, towards the reactant. As a result, the concentration of the hydroxide ion decreases.

A basic solution is a solution in which the concentration of hydroxide ions is greater than the concentration of hydrogen ions. Solid potassium hydroxide dissociates in water to yield potassium ions and hydroxide ions.

text{KOH}(s) rightarrow text{K}^+(aq)+text{OH}^-(aq)

The increase in concentration of the OH − ions causes a decrease in the concentration of the H + ions and the ion-product of [H + ][OH − ] remains constant

Sample Problem: Use of  K_w for an Aqueous Solution

Hydrochloric acid (HCl) is a strong acid, meaning it is 100% ionized in solution. What is the [H + ] and the [OH − ] in a solution of 2.0 × 10 3  M HCl?

Step 1: List the known values and plan the problem .

Known

  • [HCl] = 2.0 × 10 -3 M
  • K_w=1.0 times 10^{-14}

Unknown

  • [H + ] = ? M
  • [OH – ] = ? M

Because HCl is 100% ionized, the concentration of H + ions in solution will be equal to the original concentration of HCl. Each HCl molecule that was originally present ionizes into one H + ion and one Cl − ion. The concentration of OH − can then be determined from the [H + ] and K_w .

Step 2: Solve .

left [ text{H}^+ right ]&=2.0 times 10^{-3} text{M} \K_w &=left [ text{H}^+ right ] left [ text{OH}^- right ]=1.0 times 10^{-14} \left [ text{OH}^- right ] &=frac{K_w}{left [ text{H}^+ right ]}=frac{1.0 times 10^{-14}}{2.0 times 10^{-3}}=5.0 times 10^{-12} text{M}

Step 3: Think about your result.

The [H + ] is much higher than the [OH − ] because the solution is acidic. As with other equilibrium constants, the unit for  K_w is customarily omitted.

Summary

  • The self-ionization of water is described and an ionization constant for the process is stated.
  • Acidic and basic solutions are defined.
  • Calculations using  K_w are illustrated.

Practice

Read the first two pages of this handout on Water Ionization and do those practice problems.

Review

  1. What is an acidic solution?
  2. What is a basic solution?
  3. What is the [OH – ] of a solution which has a [H + ] of 1 times 10^{-5} M ?

Glossary

  • acidic solution: A solution in which the concentration of hydrogen ions is greater than the concentration of hydroxide ions.
  • basic solution: A solution in which the concentration of hydroxide ions is greater than the concentration of hydrogen ions.
  • ion-product of water (K_w) : The mathematical product of the concentration of hydrogen ions and hydroxide ions.
  • self-ionization of water: The process in which water ionizes to hydronium ions and hydroxide ions.