`HCOOH` and `CH_(3)COOH` solutions have equal `pH.` If `K_(1)//K_(2)` is `4`, the ratio of their molar concentration will be

Options

A. `0.25`
B. `0.5`
C. `2`
D. `4`

Explanation

To solve the problem, we need to find the ratio of the molar concentrations of formic acid (HCOOH) and acetic acid (CH₃COOH) given that their pH values are equal and the ratio of their acid dissociation constants \( K_1/K_2 \) is 4.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We have two weak acids: formic acid (HCOOH) with dissociation constant \( K_1 \) and acetic acid (CH₃COOH) with dissociation constant \( K_2 \).
- The ratio \( K_1/K_2 = 4 \) implies that \( K_1 = 4K_2 \).
- The pH of both solutions is equal.

2. **Relate pH to H⁺ Ion Concentration**:
- Since the pH is the same for both solutions, the concentration of hydrogen ions \( [H^+] \) must also be equal for both acids.
- For a weak acid, the concentration of hydrogen ions can be expressed as:
\[ [H^+] = \sqrt{K_a \cdot C} \]
- Therefore, for formic acid:
\[ [H^+]_1 = \sqrt{K_1 \cdot C_1} \]
- And for acetic acid:
\[ [H^+]_2 = \sqrt{K_2 \cdot C_2} \]

3. **Set the Equations Equal**:
- Since \( [H^+]_1 = [H^+]_2 \), we can equate the two expressions:
\[ \sqrt{K_1 \cdot C_1} = \sqrt{K_2 \cdot C_2} \]

4. **Square Both Sides**:
- Squaring both sides gives:
\[ K_1 \cdot C_1 = K_2 \cdot C_2 \]

5. **Rearrange to Find the Ratio of Concentrations**:
- Rearranging the equation gives us:
\[ \frac{C_1}{C_2} = \frac{K_2}{K_1} \]

6. **Substitute the Known Ratio**:
- Since \( K_1/K_2 = 4 \), we have \( K_2 = K_1/4 \).
- Therefore,
\[ \frac{C_1}{C_2} = \frac{K_2}{K_1} = \frac{1}{4} \]

7. **Final Result**:
- The ratio of the molar concentrations \( C_1 : C_2 \) is \( 1 : 4 \) or \( 0.25 \).

### Conclusion:
The ratio of their molar concentrations is \( 0.25 \).