# i. Define degree of dissociation. Derive Ostwald's dilution law for the CH3COOH.

### 4. Answer the following :

i. Define degree of dissociation. Derive Ostwald’s dilution law for the CH3COOH.

**i. **

Consider an equilibrium of weak acid CH_{3}COOH that exists in solution partly as the undissociated species CH_{3}COOH and partly H^{+} and CH_{3}COO^{-} ions. Then

\[CH_3COOH_{(aq)} \rightleftharpoons H^+_{(aq)} + CH_3COO^-_{(aq)}\]

**ii. **

The acid dissociation constant is given as:

\(K_a = \frac{{[H^+][CH_3COO^-]}}{{[CH_3COOH]}}\) ....(1)

**iii. **

Suppose 1 mol of acid CH_{3}COOH is initially present in volume V dm^{3} of the solution. At equilibrium, the fraction dissociated would be \(\alpha\), where \(\alpha\) is the degree of dissociation of the acid. The fraction of an acid that remains undissociated would be (1 - \(\alpha\)).

\(CH_3COOH_{(aq)} \rightleftharpoons H^+_{(aq)} + CH_3COO^-_{(aq)}\) | |||

The amount present at equilibrium (mol) | (1 - \(\alpha\)) | \(\alpha\) | \(\alpha\) |

Concentration at equilibrium (mol dm^{-3}) |
\((1 - \alpha)/V\) | \(\alpha/V\) | \(\alpha/V\) |

**iv.**

Thus, at equilibrium \([CH_3COOH] = (1 - \(\alpha\))/V\) mol dm^{-3},

\([H^+] = [CH_3COO^-] = \(\alpha\)/V\) mol dm^{-3}

**v. **

Substituting these in equation (1),

\(K_a = (\alpha / V)(\alpha / V) /((1 - \(\alpha\)) / V) = \alpha^2/(1 - \(\alpha\) V)\) ....(2)

**vi. **

If c is the initial concentration of CH_{3}COOH in mol dm^{-3} and V is the volume in dm^{3} mol^{-1} then c = 1/V. Replacing 1/V in equation (2) by c,

we get

\(K_a = (\alpha^2c)/(1 - \(\alpha\))\) ....(3)

**vii.**

For the weak acid CH_{3}COOH, \(\alpha\) is very small, or (1 - \(\alpha\)) \(\approx\) 1. With this, equation (2) and (3) become:

\(K_a = \(\alpha^2/V\)\) and \(K_a = \(\alpha^2c\) ....(4)

\(\alpha = \sqrt{K_a/c}\) or \(\alpha = \sqrt{K_aV}\) ....(5)

Equation (5) implies that the degree of dissociation of a weak acid (CH_{3}COOH) is inversely proportional to the square root of its concentration or directly proportional to the square root of the volume of the solution containing 1 mol of the weak acid.