$p K_{a}$ value of acetic acid is $4.76$ at room temperature. How do you obtain buffers of $4.40$ and $5.40 p H$ values from acetic acid and sodium acetate?

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Solution

To obtain $p H$ of 4.4
$p H = p K_{a} + log \frac{[S o d i u m a c e t a t e]}{[A c e t i c A c i d]}$
$4.4 = 4.76 + log \frac{[S o d i u m a c e t a t e]}{[A c e t i c A c i d]}$
$- 0.36 = log \frac{[S o d i u m a c e t a t e]}{[A c e t i c A c i d]}$
$\frac{A c e t a t e}{A c i d} = 0.4365$
To obtain $p H$ of 5.4
$p H = p K_{a} + log \frac{[S o d i u m a c e t a t e]}{[A c e t i c A c i d]}$
$5.4 = 4.76 + log \frac{[S o d i u m a c e t a t e]}{[A c e t i c A c i d]}$
$0.64 = log \frac{[S o d i u m a c e t a t e]}{[A c e t i c A c i d]}$
$\frac{A c e t a t e}{A c i d} = 4.364$

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