Question

A solution of sodium citrate (monobasic) is prepared to a formal concentration of 0.2 M. If the pKa's for the triprotic citric acid molecule are 3.13, 4.76, 6.40 what is the approximate pH of this solution

Answer 1

Consider equilibira of citric acid as shown below.

H₃Cit H ⁺ + H₂Cit ^-   H ⁺ + HCit ^2- H ⁺ + Cit ^3-

Sodium citrate mono basic is a intermediate form of Citric acid and disodium citrate.

We know that, for intermediate form, [H⁺ ] = K ₁ K ₂ F + K ₁ K _w / K ₁ + F

We have , pK ₁ = 3.13

We know that, pK ₁ = -log K ₁ . Therefore, K ₁ = 10 ^{- pK} ₁ = 10 ^{- 3.13} = 7.413 10 ^-04

Similarly , K ₂ = 10 ^{- pK} ₂ = 10 ^{- 4.76} = 1.738 10 ^-05

Here F = 0.2 M and K _w = 1 10 ^-14

[H⁺ ] = (7.413 10 ^-04) (1.738 10 ^-05 ) 0.2 + (7.413 10 ^-04 1  10 ^-14 ) / 7.413 10 ^-04 + 0.2

= 2.577 10 ^-09 / 0.20074

= 1.284 10 ^-08

= 1.133 10 ^-04 M

We have, pH = - log [H⁺ ] = - log 1.133 10 ^-04 = 3.946

ANSWER : Approximate pH of 0.2 M solution of mono sodium citrate solution = 3.946