Answer to Question #138705 in General Chemistry for John

Question

A buffer consisting of lactic acid and sodium lactate has the pH = 4.30. Given that the –4
concentration of lactic acid is 0.12 M, and Ka = 1.4 × 10 , calculate the concentration of sodium lactate

Answer 1

pH = 4.30

$HC_3H_5O_3$ - (weak acid)

$C_3H_5O_3^-$ - (Conjugate base of HC3H5O3)

$Na^+$- (spectator ion )

$H_2O$ - (Very weak acid or base )

$K_a = 1.4× 10^{-4}$

$\begin{aligned} [H^+] &= 10^{-pH}\\ &= 10^{-4.30}\\ &=5.01× 10^{-5}M \end{aligned}$

$HC_3H_5O_{3(aq)} \ ^\leftarrow_\rightarrow \ H^+_{(aq)} + C_3H_5O_{3(aq)}^-$

Using ICE

Initial -> 0.12M = 0M + yM

Change ->. -x = +x +x

Equilibrium -> 0.12-x = x y+x

$\therefore x = [H^+] = 5.01× 10^{-5}M$

$K_a = \dfrac{[H^+][C_3H_5O_3^-]}{[HC_3H_5O_3] }$

$1.4 × 10^{-4} = \dfrac{[5.01× 10^{-5}M][y+5.01× 10^{-5}M]}{[0.12 - 5.01× 10^{-5}M] }$

$1.68×10^{-5}= 5.01× 10^{-5}y + 2.51× 10^{-9}$

y = 0.337M

$\therefore$ The concentration of sodium lactate is 0.34M.