At certain temperature, dissociation constant of formic acid and acetic acid are `1.8xx10^(-4)` and `1.8xx10^(-5)` respectively. At what concentration of acetic solution, the `H_93)O^(+)` ion concentration is same as that in 0.001 M formic acid solution

Options

A. `0.01 M`
B. `1xx10^(-3)M`
C. `1xx10^(-1)M`
D. `1xx10^(-4)M`.

Explanation

To solve the problem, we need to find the concentration of acetic acid such that the concentration of \( H_3O^+ \) ions is the same as that in a 0.001 M formic acid solution.

### Step-by-Step Solution:

1. **Identify the dissociation constants**:
- For formic acid (\( HCOOH \)): \( K_a = 1.8 \times 10^{-4} \)
- For acetic acid (\( CH_3COOH \)): \( K_a = 1.8 \times 10^{-5} \)

2. **Set up the equation for \( H_3O^+ \) concentration**:
- The concentration of \( H_3O^+ \) ions produced from a weak acid can be expressed as:
\[ [H_3O^+] = \sqrt{K_a \times C} \]
- Where \( C \) is the concentration of the acid.

3. **Calculate \( [H_3O^+] \) for formic acid**:
- For 0.001 M formic acid:
\[ [H_3O^+]_{HCOOH} = \sqrt{K_{a1} \times C_1} = \sqrt{(1.8 \times 10^{-4}) \times (0.001)} \]
- Simplifying this:
\[ [H_3O^+]_{HCOOH} = \sqrt{1.8 \times 10^{-7}} = 1.34 \times 10^{-4} \, \text{M} \]

4. **Set up the equation for acetic acid**:
- Let \( C_2 \) be the concentration of acetic acid. We want:
\[ [H_3O^+]_{CH_3COOH} = \sqrt{K_{a2} \times C_2} \]
- Setting the two concentrations equal:
\[ \sqrt{K_{a1} \times C_1} = \sqrt{K_{a2} \times C_2} \]
- Squaring both sides gives:
\[ K_{a1} \times C_1 = K_{a2} \times C_2 \]

5. **Substituting known values**:
- Substitute \( K_{a1} = 1.8 \times 10^{-4} \), \( C_1 = 0.001 \), and \( K_{a2} = 1.8 \times 10^{-5} \):
\[ (1.8 \times 10^{-4}) \times (0.001) = (1.8 \times 10^{-5}) \times C_2 \]

6. **Solve for \( C_2 \)**:
- Rearranging gives:
\[ C_2 = \frac{(1.8 \times 10^{-4}) \times (0.001)}{1.8 \times 10^{-5}} \]
- Simplifying:
\[ C_2 = \frac{1.8 \times 10^{-7}}{1.8 \times 10^{-5}} = 0.01 \, \text{M} \]

### Final Answer:
The concentration of acetic acid required is **0.01 M**.