A weak monobasic acid is 1% ionized in 0.1 M solution at `25^@`C. The percentage of ionization in its 0.025 M solution is :

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To solve the problem of finding the percentage of ionization of a weak monobasic acid in a 0.025 M solution, we can follow these steps:

### Step 1: Understand the given data
We know that:
- The concentration of the first solution (C1) = 0.1 M
- The percentage of ionization in the first solution = 1%
- The concentration of the second solution (C2) = 0.025 M
- We need to find the percentage of ionization in the second solution.

### Step 2: Define the degree of ionization
Let α1 be the degree of ionization in the first solution and α2 be the degree of ionization in the second solution. The degree of ionization can be expressed as:
- α1 = 1% = 0.01
- α2 = ? (to be determined)

### Step 3: Use the formula for dissociation constant
For weak acids, the dissociation constant (Ka) can be expressed using the degree of ionization (α) and concentration (C):
\[ K_a = C \cdot \alpha^2 \]
Since the dissociation constant (Ka) is the same for both solutions, we can equate the two expressions:
\[ C_1 \cdot \alpha_1^2 = C_2 \cdot \alpha_2^2 \]

### Step 4: Substitute the known values
Substituting the known values into the equation:
\[ 0.1 \cdot (0.01)^2 = 0.025 \cdot \alpha_2^2 \]

### Step 5: Simplify the equation
Calculating the left side:
\[ 0.1 \cdot 0.0001 = 0.00001 \]
So the equation becomes:
\[ 0.00001 = 0.025 \cdot \alpha_2^2 \]

### Step 6: Solve for α2
Now, we can solve for α2:
\[ \alpha_2^2 = \frac{0.00001}{0.025} \]
\[ \alpha_2^2 = 0.0004 \]
Taking the square root of both sides:
\[ \alpha_2 = \sqrt{0.0004} = 0.02 \]

### Step 7: Calculate the percentage of ionization
To find the percentage of ionization in the second solution:
\[ \text{Percentage of ionization} = \alpha_2 \times 100 = 0.02 \times 100 = 2\% \]

### Final Answer
The percentage of ionization in the 0.025 M solution is **2%**.

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