Find the dissocation constant `K_(a)` of `HA` (weak monoabsic acid) which is `3.5%` dissociated in an`M//20` solution.

Answer

To find the dissociation constant \( K_a \) of the weak monobasic acid \( HA \) which is 3.5% dissociated in a \( \frac{1}{20} \) M solution, we can follow these steps:

### Step 1: Understand the given values
- The degree of dissociation \( \alpha \) is given as 3.5%.
- The concentration \( C \) of the solution is \( \frac{1}{20} \) M.

### Step 2: Convert the degree of dissociation to decimal
Convert the percentage of dissociation to a decimal:
\[ \alpha = \frac{3.5}{100} = 0.035 \]

### Step 3: Calculate the concentration \( C \)
The concentration \( C \) is already given as \( \frac{1}{20} \) M. To express this in decimal:
\[ C = \frac{1}{20} = 0.05 \, \text{M} \]

### Step 4: Use the formula for the dissociation constant \( K_a \)
The dissociation constant \( K_a \) for a weak acid is given by the formula:
\[ K_a = C \cdot \alpha^2 \cdot \frac{1}{1 - \alpha} \]

### Step 5: Substitute the values into the formula
Substituting \( C = 0.05 \, \text{M} \) and \( \alpha = 0.035 \):
\[ K_a = 0.05 \cdot (0.035)^2 \cdot \frac{1}{1 - 0.035} \]

### Step 6: Calculate \( (0.035)^2 \)
First, calculate \( (0.035)^2 \):
\[ (0.035)^2 = 0.001225 \]

### Step 7: Calculate \( 1 - \alpha \)
Calculate \( 1 - 0.035 \):
\[ 1 - 0.035 = 0.965 \]

### Step 8: Substitute and calculate \( K_a \)
Now substitute these values back into the formula:
\[ K_a = 0.05 \cdot 0.001225 \cdot \frac{1}{0.965} \]

Calculating \( K_a \):
\[ K_a = 0.05 \cdot 0.001225 \cdot 1.035 \approx 0.0000635 \]
or
\[ K_a \approx 6.35 \times 10^{-5} \]

### Final Result
Thus, the dissociation constant \( K_a \) of the weak monobasic acid \( HA \) is approximately:
\[ K_a \approx 6.35 \times 10^{-5} \]

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