Introduction to and use of Kw
H2O can act as both an acid and a base, and the proton transfer reaction shown below occurs to a very small extent in pure water. The presence of the two ions can be demonstrated by very sensitive conductivity experiments.
H2O(l) + H-OH(l)
H3O+(aq) + –OH(aq)
The equilibrium expression for this proton transfer shows only hydronium and hydroxide product ions as the concentration of the water is constant. This equilibrium constant is known as Kw.
Proton transfer reactions are fast, and pure water or any aqueous solution is at equilibrium with respect to the concentrations of the hydronium and hydroxide ions and the product of [H3O+] and [OH–] must therefore equal Kw.
Kw can be used to calculate [OH–] if [H3O+] is known and vice versa.
Example:
If pH = 10,
[H3O+] = 1 × 10–10
THEN at 25°C
Kw = 1 × 10–14 = 10–10 × [OH–]
THUS [OH–] = 1 × 10–4
If pH is 9.46.
[H3O+] = 3.45 × 10–10
[OH–] = 2.89 × 10–5
Note that the sum of the exponents is -15 in this case because 3.45 × 2.89 is equal to 10.
Try this on your calculator to practice!!
H2O(l) + H-OH(l)
H3O+(aq) + –OH(aq)Kw = [H3O+][OH–]
At 25 °C
Kw = 1 × 10–14
At 25 °C
Kw = 1 × 10–14
The equilibrium expression for this proton transfer shows only hydronium and hydroxide product ions as the concentration of the water is constant. This equilibrium constant is known as Kw.
The proton transfer reaction above is endothermic; therefore Kw is larger at temperatures higher than 25 °C.
Proton transfer reactions are fast, and pure water or any aqueous solution is at equilibrium with respect to the concentrations of the hydronium and hydroxide ions and the product of [H3O+] and [OH–] must therefore equal Kw.
In pure water at 25 °C the reaction above is the only source of these ions
[H3O+] = [OH–] = 10–7
In a solution where an acid has been dissolved in water
[H3O+] > [OH–] BUT the product of the concentrations is equal to Kw
These solutions are referred to as being acidic, and they turn blue litmus red.
In a solution where a base has been dissolved in water
[H3O+] < [OH–] BUT the product of the concentrations is equal to Kw
These solutions are referred to as being alkaline, and they turn red litmus blue.
[H3O+] = [OH–] = 10–7
In a solution where an acid has been dissolved in water
[H3O+] > [OH–] BUT the product of the concentrations is equal to Kw
These solutions are referred to as being acidic, and they turn blue litmus red.
In a solution where a base has been dissolved in water
[H3O+] < [OH–] BUT the product of the concentrations is equal to Kw
These solutions are referred to as being alkaline, and they turn red litmus blue.
Kw can be used to calculate [OH–] if [H3O+] is known and vice versa.
| Useful maths: | |
| 10a × 10b = 10a+b | and 10a ÷ 10b = 10a-b |
Example:
If pH = 10,
[H3O+] = 1 × 10–10
THEN at 25°C
Kw = 1 × 10–14 = 10–10 × [OH–]
THUS [OH–] = 1 × 10–4
If pH is 9.46.
[H3O+] = 3.45 × 10–10
[OH–] = 2.89 × 10–5
Note that the sum of the exponents is -15 in this case because 3.45 × 2.89 is equal to 10.
Try this on your calculator to practice!!