The incorrect relation for isohydric solution | vedclass

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Question

(C) Isohydric solutions are those solutions which have the same concentration of hydrogen ions $([H^{+}])$.For a weak acid $HA$,the concentration of $

Vedclass · Accepted Answer

$\frac{K_{a_1}}{V_2} = \frac{K_{a_2}}{V_1}$

Vedclass · Answer

(C) Isohydric solutions are those solutions which have the same concentration of hydrogen ions $([H^{+}])$.For a weak acid $HA$,the concentration of $H^{+}$ is given by $[H^{+}] = \sqrt{K_a \cdot C}$.For two isohydric solutions,$[H^{+}]_1 = [H^{+}]_2$.Therefore,$\sqrt{K_{a_1} C_1} = \sqrt{K_{a_2} C_2}$,which implies $K_{a_1} C_1 = K_{a_2} C_2$.Since $C = \frac{1}{V}$ (where $V$ is dilution),we can write $K_{a_1} \cdot \frac{1}{V_1} = K_{a_2} \cdot \frac{1}{V_2}$,which simplifies to $K_{a_1} V_2 = K_{a_2} V_1$ or $\frac{K_{a_1}}{V_1} = \frac{K_{a_2}}{V_2}$.Option $C$ states $\frac{K_{a_1}}{V_2} = \frac{K_{a_2}}{V_1}$,which is mathematically incorrect.

The incorrect relation for isohydric solutions is $:-$

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