A weak acid HA is found to be 3% dissociated in 0.1 M solution . Calculate the value of `K_a `

Answer

To calculate the acid dissociation constant \( K_a \) for the weak acid \( HA \) that is 3% dissociated in a 0.1 M solution, we can follow these steps:

### Step 1: Understand the given information
- The degree of dissociation \( \alpha \) is given as 3%, which can be expressed as a decimal:
\[ \alpha = \frac{3}{100} = 0.03 \]
- The concentration of the acid solution \( C \) is given as 0.1 M.

### Step 2: Write the formula for \( K_a \)
The formula for the acid dissociation constant \( K_a \) is given by:
\[ K_a = \frac{C \cdot \alpha^2}{1 - \alpha} \]
Since \( \alpha \) is small (3% or 0.03), we can approximate \( 1 - \alpha \) as 1. Thus, the formula simplifies to:
\[ K_a \approx C \cdot \alpha^2 \]

### Step 3: Substitute the values into the formula
Now, we can substitute the values of \( C \) and \( \alpha \) into the simplified formula:
\[ K_a \approx 0.1 \cdot (0.03)^2 \]

### Step 4: Calculate \( \alpha^2 \)
First, calculate \( \alpha^2 \):
\[ \alpha^2 = (0.03)^2 = 0.0009 \]

### Step 5: Calculate \( K_a \)
Now substitute \( \alpha^2 \) back into the equation for \( K_a \):
\[ K_a \approx 0.1 \cdot 0.0009 = 0.00009 \]

### Step 6: Express \( K_a \) in scientific notation
To express \( K_a \) in scientific notation:
\[ K_a = 9 \times 10^{-5} \]

### Final Answer
Thus, the value of \( K_a \) for the weak acid \( HA \) is:
\[ K_a = 9 \times 10^{-5} \]

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