Question

Acetic acid is 5% ionised in its decimolar solution. Calculate the dissociation constant of acetic acid.

Hint:

"Decimolar" means \( 0.1 \, M \), "Centimolar" means \( 0.01 \, M \), and "Millimolar" means \( 0.001 \, M \). Knowing these terms is essential for solving concentration problems.

Answer 1

Step 1: Understanding the Concept:
Ostwald's dilution law relates the dissociation constant (\(K_a\)) of a weak acid to its concentration (\(C\)) and degree of dissociation (\(\alpha\)).
Step 2: Key Formula or Approach:
\[ K_a = C\alpha^2 \]
(valid when \(\alpha<5%\))
Step 3: Detailed Explanation:
Given:
Percentage ionisation = 5%
Degree of dissociation, \(\alpha = 5/100 = 0.05\)
Decimolar solution means \(C = 0.1 \text{ M}\)
Now, calculate \(K_a\):
\[ K_a = 0.1 \times (0.05)^2 \]
\[ K_a = 0.1 \times 0.0025 \]
\[ K_a = 0.00025 = 2.5 \times 10^{-4} \]
Step 4: Final Answer:
The dissociation constant \(K_a\) is \(2.5 \times 10^{-4}\).