The Ion Product of Water (HL IB Chemistry)

pH of water

• An equilibrium exists in water, where a few water molecules dissociate into proton and hydroxide ions

H₂O (l) ⇌ H⁺ (aq) + OH^– (aq)

• The equilibrium constant for this reaction is:

${\mathit{K}}_{\mathbf{c}}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{\left[}{\mathbf{H}}^{\mathbf{+}}\mathbf{\right]}\mathbf{\left[}\mathbf{O}{\mathbf{H}}^{\mathbf{-}}\mathbf{\right]}}{\left[H_{2}O\right]}$

K_c x [H₂O] = [H⁺][OH^–]

• Since the concentration of the H⁺ and OH^- ions is very small, the concentration of water is considered to be a constant
• This means that the expression can be rewritten as:

K_w = [H⁺] [OH^-]

• • Where K_w (ion product of water) =  K_c x [H₂O] =  1.00 10^-14 at 298K

• The product of the two ion concentrations is always 1.00 x 10^–14 
• This makes it straightforward to see the relationship between the two concentrations and the nature of the solution:

[H⁺] & [OH^–] Table

[H+]	[OH–]	Type of solution
0.1	1 x 10–13	acidic
1 x 10–3	1 x 10–11	acidic
1 x 10–5	1 x 10–9	acidic
1 x 10–7	1 x 10–7	neutral
1 x 10–9	1 x 10–5	alkaline
1 x 10–11	1 x 10–3	alkaline
1 x 10–13	0.1	alkaline

How does temperature affect the ion product of water, K_w?

• The ionisation of water is an endothermic process

2H₂O (l) ⇌ H₃O⁺  (aq) + OH^- (aq) 

• In accordance with Le Châtelier's principle, an increase in temperature will result in the forward reaction being favoured
  • This causes an increase in the concentration of the hydrogen and hydroxide ions
  • This leads to the magnitude of K_w increasing
  • Therefore, the pH will decrease
• Increasing the temperature decreases the pH of water (becomes more acidic)
• Decreasing the temperature increases the pH of water (becomes more basic)

Graph to show how K_w changes with temperature

As temperature increases, K_w increases so pH decreases