JEE Main 2025 Jan 28 Shift 1, Chemistry Q5: Ionization Of Acids And Bases

JEE Main2025Jan 28, Shift 1Chemistry

A weak acid HA has degree of dissociation $x$ . Which option gives the correct expression of $pH - pK_{a}$ ?

Solution

For a weak acid HA of initial concentration $a$ with degree of dissociation $x$ :

$HA ⇌ H^{+} + A^{-}$ , with equilibrium concentrations $a (1 - x), a x, a x$ .

$K_{a} = \frac{( a x ) ( a x )}{a ( 1 - x )} = \frac{a x \cdot x}{1 - x}$ , and $[H^{+}] = a x$ .

Taking $- lo g$ on $K_{a} = [H^{+}] \cdot \frac{x}{1 - x}$ :

$pK_{a} = pH - lo g (\frac{x}{1 - x})$

$∴ pH - pK_{a} = lo g (\frac{x}{1 - x})$ .

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