Question

Sol. [Key Concept: For weak electrolyte $A_{x}B_{y}$, $K = x^{x}y^{y}C^{x + y - 1}\alpha^{x + y}$ (since $1 - \alpha \approx 1$); solve for $\alpha = (\frac{K}{c^{x + y - 1}x^{x}y^{y}})^{1/(x + y)}$.]

$${A_{x}B_{y} \rightleftharpoons {xA}^{y +} + {yB}^{x -} }{C(1 - \alpha)\ xC\alpha\ yC\alpha }{K = \frac{(xC\alpha)^{x}(xC\alpha)^{y}}{C(1 - \alpha)} }$$As $\alpha \ll 1 \Rightarrow (1 - \alpha) \simeq 1$

$${K = x^{x}y^{y}C^{x + y - 1}\alpha^{x + y} }{\alpha = \left( \frac{K}{C^{x + y - 1}x^{x}y^{y}} \right)^{\frac{1}{x + y}} }$$