Question

What molar ratio of acetic acid to sodium acetate is required to create a buffer solution having a pH of 4.93 at 25°C? Ka for HC2H3O2 is 1.8 × 10–5.

Answer 1

Answer:

0.65

Explanation:

$K_a$ = Acid ionization constant of acetic acid = $1.8\times 10^{-5}$

$pH$ = Potential of hydrogen of buffer solution = $4.93$

Acid ionization constant is given by

$K_a=\dfrac{[H+][A-]}{[HA]}\\\Rightarrow K_a=[H+]\dfrac{[A-]}{[HA]}$

Applying $-\log$ on both sides of the equation we get

$-\log K_a=-\log [H+]-\log\dfrac{[A-]}{[HA]}\\\Rightarrow pK_a=pH-\log\dfrac{[A-]}{[HA]}\\\Rightarrow pH=pK_a+\log\dfrac{[A-]}{[HA]}$

Here the acetic acid and acetate concentration are equal so we get

$4.93=-\log(1.8\times 10^{-5})+\log\dfrac{[A-]}{[HA]}\\\Rightarrow 4.93-4.74=\log\dfrac{[A-]}{[HA]}\\\Rightarrow 0.19=\log\dfrac{[A-]}{[HA]}\\\Rightarrow 1.55=\dfrac{[A-]}{[HA]}\\\Rightarrow \dfrac{[HA]}{[A-]}=0.65$

The ratio of acetic acid to sodium acetate is 0.65