MCQ
If $\alpha $ is the degree of ionization, $C$ the concentration of a weak electrolyte and ${K_a}$the acid ionization constant, then the correct relationship between $\alpha ,\,\,C$ and ${K_a}$is
  • A
    ${\alpha ^2} = \sqrt {\frac{{{K_a}}}{C}} $
  • B
    ${\alpha ^2} = \sqrt {\frac{C}{{{K_a}}}} $
  • $\alpha = \sqrt {\frac{{{K_a}}}{C}} $
  • D
    $\alpha = \sqrt {\frac{C}{{{K_a}}}} $

Answer

Correct option: C.
$\alpha = \sqrt {\frac{{{K_a}}}{C}} $
(c) According to the Ostwald’s dilution formula ${\alpha ^2} = \frac{{K(1 - \alpha )}}{C}$. But for weak electrolytes $ \alpha $  is very small. So that $(1 - \alpha )$ can be neglected. So that $\alpha = \sqrt {\frac{{{K_a}}}{C}} $.

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