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

Options

A. `2.1xx10^(-4)`
B. `14.5`
C. `0.145`
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: Understand the given data
We have:
- Concentration of formic acid (C) = 0.01 M
- Percentage ionization = 14.5%

### Step 2: Convert percentage ionization to fraction
To find the fraction of the acid that is ionized (α), we convert the percentage to a decimal:
\[ \alpha = \frac{14.5}{100} = 0.145 \]

### Step 3: Calculate the concentration of ionized acid
The concentration of the ionized formic acid can be calculated using:
\[ \text{Concentration of ionized acid} = \alpha \times C \]
Substituting the values:
\[ \text{Concentration of ionized acid} = 0.145 \times 0.01 = 0.00145 \, \text{M} \]

### Step 4: Calculate the concentration of undissociated acid
The concentration of the undissociated formic acid can be calculated as:
\[ \text{Concentration of undissociated acid} = C - \text{Concentration of ionized acid} \]
Substituting the values:
\[ \text{Concentration of undissociated acid} = 0.01 - 0.00145 = 0.00855 \, \text{M} \]

### Step 5: Write the expression for the ionization constant (Ka)
The ionization of formic acid (HCOOH) can be represented as:
\[ \text{HCOOH} \rightleftharpoons \text{H}^+ + \text{HCOO}^- \]
The expression for the ionization constant (Ka) is given by:
\[ K_a = \frac{[\text{H}^+][\text{HCOO}^-]}{[\text{HCOOH}]} \]
Since the concentration of \(\text{H}^+\) and \(\text{HCOO}^-\) are equal to the concentration of ionized acid (0.00145 M), we can write:
\[ K_a = \frac{(0.00145)(0.00145)}{0.00855} \]

### Step 6: Calculate Ka
Now we can calculate Ka:
\[ K_a = \frac{(0.00145)^2}{0.00855} \]
Calculating \((0.00145)^2\):
\[ (0.00145)^2 = 0.0000021025 \]
Now substituting this value into the Ka equation:
\[ K_a = \frac{0.0000021025}{0.00855} \approx 0.000245 \]
This can be expressed in scientific notation:
\[ K_a \approx 2.45 \times 10^{-4} \]

### Final Answer
Thus, the ionization constant (Ka) of formic acid is approximately:
\[ K_a \approx 2.45 \times 10^{-4} \]