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K_w : Ion Product for Water

Key Concepts

Water undergoes self-dissociation, also referred to as self-ionization or autodissociation.
H₂O H⁺ + OH^-
The equilibrium constant for the self-dissociation of water is:

K = [H⁺][OH^-]

[H₂O]
The concentration of water is essentially constant at any given temperature, and is incorporated into the equilibrium constant:
K_w = [H⁺][OH^-]
K_w is called the ion product for water or the dissociation constant for water.
K_w, like all equilibrium constants, is temperature dependent.
For any given temperature, [H⁺] = [OH^-] for water, so water is neutral at all temperatures.
For any given temperature, pH = pOH for water.
Water is only pH=7 at 25^oC (298K)
Water is only pOH=7 at 25^oC (298K)
pH + pOH = 14 is only true at 25^oC (298K)

K_w Calculations at 25^oC (298K)

Calculate the hydroxide ion and hydrogen ion concentration of water at 25^oC (~298K), K_w = 10^-14.

Write the equation for the ion product for water:
K_w = [H⁺][OH^-]
Substitute in the value for K_w:
10^-14 = [H⁺][OH^-]
Since [H⁺] = [OH^-]
10^-14 = [H⁺]²
Take the square root of both sides of the equation to find [H⁺]:
√10^-14 = [H⁺]
[H⁺] = 10^-7M
Since [H⁺] = [OH^-],
[OH^-] = 10^-7M

Calculate the pH and pOH of water at 25^oC (298K).

Write the equation for calculating pH:
pH = -log[H⁺]
Substitute in the value for [H⁺] calculated above:
pH = -log[10^-7] = 7
Write the equation for calculating pOH:
pOH = -log[OH^-]
Substitute in the value for [OH^-] calculated above:
pOH = -log[10^-7] = 7

Temperature Dependence of K_w

The reaction

H₂O

H⁺ + OH^-

is endothermic, it absorbs heat.

By Le Chatelier's Principle if the temperature of the system is increased, the equilibrium position will shift to the right to minimise the effect of the increased temperature.

The forward reaction is favoured resulting in the production of more H⁺ and more OH^-, so the value of K_w will increase.

Since the concentration of hydrogen ions is greater at higher temperatures, the pH of water will be lower at higher temperatures.

Temperature (^oC) K_w [H⁺] (mol L^-1) pH acidity

0 0.114 x 10^-14 3.376 x 10^-8 7.47 [H⁺] = [OH^-] = neutral

10 0.293 x 10^-14 5.413 x 10^-8 7.27 [H⁺] = [OH^-] = neutral

20 0.681 x 10^-14 8.252 x 10^-8 7.08 [H⁺] = [OH^-] = neutral

25 1.008 x 10^-14 1.004 x 10^-7 7.00 [H⁺] = [OH^-] = neutral

30 1.471 x 10^-14 1.213 x 10^-7 6.92 [H⁺] = [OH^-] = neutral

40 2.916 x 10^-14 1.708 x 10^-7 6.77 [H⁺] = [OH^-] = neutral

50 5.476 x 10^-14 2.340 x 10^-7 6.63 [H⁺] = [OH^-] = neutral

100 51.3 x 10^-14 7.162 x 10^-7 6.14 [H⁺] = [OH^-] = neutral

Note that the value of K_w at each of the temperatures above is very small so water undergoes very little self-dissociation. The percentage of dissociation (percent ionization) is small.

Practice Questions

For AUS-e-TUTE members: