What will be the ionisation constant of formic acid if its 0.01 M solution is `14.5%` ionised ?

Options

A. a. `2.1xx10^(-4)`
B. b.`14.5`
C. c.`0.145`
D. d.`1.45xx10^(-4)`

Explanation

To find the ionization constant (Ka) of formic acid given that its 0.01 M solution is 14.5% ionized, we can follow these steps:

### Step 1: Identify the given values
- Concentration of formic acid (C) = 0.01 M
- Degree of ionization (α) = 14.5%

### Step 2: Convert the degree of ionization from percentage to decimal
To convert the percentage of ionization to a decimal:
\[ \alpha = \frac{14.5}{100} = 0.145 \]

### Step 3: Use the formula for the ionization constant
The formula for the ionization constant (Ka) is given by:
\[ K_a = C \times \alpha^2 \]

### Step 4: Substitute the values into the formula
Now, substitute the values of C and α into the formula:
\[ K_a = 0.01 \, \text{M} \times (0.145)^2 \]

### Step 5: Calculate α squared
First, calculate \( (0.145)^2 \):
\[ (0.145)^2 = 0.021025 \]

### Step 6: Multiply by the concentration
Now, multiply this value by the concentration:
\[ K_a = 0.01 \times 0.021025 = 0.00021025 \]

### Step 7: Express in scientific notation
To express this in scientific notation:
\[ K_a = 2.1025 \times 10^{-4} \]

### Conclusion
Thus, the ionization constant (Ka) of formic acid is:
\[ K_a \approx 2.10 \times 10^{-4} \]