Question

What is the ratio of lactic acid (Ka = 1.37x10-4) to lactate in a solution with pH =4.59?

Answer 1

Approximately 1:5

Explanation:

If `pH=4.59`

Then the `[H_3O^(+)]` is approximatley `2.57 times 10^-5 moldm^-3` as

`pH=-log_10[H_3O^(+)]`

Hence

`[H_3O^(+)]=10^(-pH)`

Because each lactic acid molecule must dissociate to from one lactate ion and one oxonium ion, `[H_3O^(+)]=[lactate]`

If we set up a `K_a` expression we can thus find the concentration of the lactic acid:

`K_a=([H_3O^(+)] times [lactate])/([Lactic.])`

`(1.37 times 10^-4)=(2.57 times 10^-5)^2/(x)`

(as it can be assumed that `[H_3O^(+)]=[lactate]`)

Hence

`x=[Lactic]=4.82 times 10^-6`

So,

`[[Lactic]]/[[Lactate]]=(4.82 times 10^-6)/(2.57 times 10^-5)approx 0.188 approx 0.2 approx (1/5)`

So from this approximation, it seems that the concentration of lactate is almost 5 times higher than that of the lactic acid, so the lactic acid to lactate is (approximately) in a 1:5 ratio.