The dissociation constant of a weak acid HA is `4.9 xx 10^(-8)`. Calculate for a decimolar solution of acid:.
`% ` of ionisation

Answer

To calculate the percentage of ionization of the weak acid HA with a dissociation constant \( K_a = 4.9 \times 10^{-8} \) in a decimolar solution (0.1 M), we can follow these steps:

### Step 1: Define the Initial Concentration
The concentration of the acid \( HA \) is given as a decimolar solution, which means:
\[ C = 0.1 \, \text{M} \]

### Step 2: Write the Dissociation Equation
The dissociation of the weak acid \( HA \) can be represented as:
\[ HA \rightleftharpoons H^+ + A^- \]

### Step 3: Set Up the Expression for Ionization
Let \( \alpha \) be the degree of ionization. At equilibrium, the concentrations will be:
- Concentration of \( HA \) = \( C(1 - \alpha) \)
- Concentration of \( H^+ \) = \( C\alpha \)
- Concentration of \( A^- \) = \( C\alpha \)

### Step 4: Write the Expression for the Dissociation Constant
The expression for the dissociation constant \( K_a \) is given by:
\[ K_a = \frac{[H^+][A^-]}{[HA]} = \frac{(C\alpha)(C\alpha)}{C(1 - \alpha)} = \frac{C^2\alpha^2}{C(1 - \alpha)} \]
This simplifies to:
\[ K_a = \frac{C\alpha^2}{1 - \alpha} \]

### Step 5: Assume \( \alpha \) is Small
Since \( K_a \) is small, we can assume that \( \alpha \) is very small, which allows us to approximate \( 1 - \alpha \approx 1 \). Thus, the equation simplifies to:
\[ K_a \approx C\alpha^2 \]

### Step 6: Solve for \( \alpha \)
Rearranging the equation gives:
\[ \alpha^2 = \frac{K_a}{C} \]
Taking the square root:
\[ \alpha = \sqrt{\frac{K_a}{C}} \]

### Step 7: Substitute Values
Substituting the values of \( K_a \) and \( C \):
\[ \alpha = \sqrt{\frac{4.9 \times 10^{-8}}{0.1}} = \sqrt{4.9 \times 10^{-7}} \approx 7 \times 10^{-4} \]

### Step 8: Calculate Percentage Ionization
The percentage ionization is given by:
\[ \text{Percentage Ionization} = \alpha \times 100\% \]
Substituting the value of \( \alpha \):
\[ \text{Percentage Ionization} = (7 \times 10^{-4}) \times 100\% = 0.07\% \]

### Final Answer
The percentage of ionization of the weak acid HA in a decimolar solution is:
\[ \boxed{0.07\%} \]

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