Dissociation constant of 0.01 M weak acid is $10^{-4}$. What is percent dissociation of acid?
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Ostwald's shortcut $\alpha = \sqrt{K_a/C}$ is incredibly fast and works perfectly for 99% of competitive exam problems where $K_a \le 10^{-4}$. Always try the shortcut first!
Step 1: Understanding the Concept:
For a weak acid, the degree of dissociation ($\alpha$) is related to the dissociation constant ($K_a$) and concentration ($C$) by Ostwald's Dilution Law. Step 2: Formula Application:
$\alpha = \sqrt{\frac{K_a}{C}}$
Percent dissociation = $\alpha \times 100$. Step 3: Explanation:
Given $K_a = 10^{-4}$ and $C = 0.01 = 10^{-2}$ M.
$\alpha = \sqrt{\frac{10^{-4}}{10^{-2}}} = \sqrt{10^{-2}} = 0.1$.
Percent dissociation = $0.1 \times 100 = 10%$. Step 4: Final Answer:
The percent dissociation is 10%.