Question

What is the concentration of hydroxide ions in pure water at 30.0°C, if `K_w` at this temperature is `1.47*10^-14`?

Answer 1

We interrogate the equilibrium: `"2H_2O(l) rightleftharpoons H_3O^(+) + HO^-`.

`[HO^-]=1.21xx10^-7*mol*L^-1`

Explanation:

We interrogate the equilibrium:

`"2H_2O(l) rightleftharpoons H_3O^(+) + HO^-`,

where the ion product, `K_w=1.47xx10^-14`, at `303*K`. Note that this is slightly higher than `K_w=10^-14` at `298*K`, and given that this is a bond breaking reaction this is perhaps reasonable.

From the equation, `[H_3O^+][HO^-]=1.47xx10^-14`.

Given that this is a neutral solution, `[H_3O^+]=[HO^-]`.

Thus `[HO^-]^2=1.47xx10^-14`

And `[HO^-]=sqrt(1.47xx10^-14)=1.21xx10^-7*mol*L^-1`