Q.The dissociation constant of a weak acid is $1 \times 10^{-3}$. In order to prepare a buffer solution with a pH = 4, the $\frac{[Acid]}{[Salt]}$ ratio should be

Henderson's equation links the pH of a buffer to the $pK_a$ of the weak acid and the ratio of conjugate base (salt) to acid, making it the working formula for all practical buffer calculations.

Derivation (brief): For a weak acid $HA$ in equilibrium: $HA \rightleftharpoons H^+ + A^-$, $K_a = \dfrac{[H^+][A^-]}{[HA]}$.

Taking $-\log$ of both sides and rearranging: $pH = pK_a + \log\dfrac{[A^-]}{[HA]} = pK_a + \log\dfrac{[\text{salt}]}{[\text{acid}]}$

(For a basic buffer of weak base and its salt: $pOH = pK_b + \log\dfrac{[\text{salt}]}{[\text{base}]}$.)

Significances:

1. Calculating buffer pH: Given $pK_a$ of the weak acid and the concentrations (or moles) of the salt and acid used to prepare the buffer, the pH of the resulting buffer solution can be directly calculated.
2. Determining $pK_a$/$K_a$ of a weak acid: If the pH of a buffer of known salt/acid ratio is measured experimentally, the equation can be rearranged to find $pK_a$ (and hence $K_a = 10^{-pK_a}$) of the weak acid — a practical method of determining dissociation constants. …