Given pH of a solution A is 3 and it is mixed with another solution B having pH 2. If both mixed, then resultant pH of the solution will be

Options

A. 3.2
B. 1.9
C. 3.4
D. 3.5

Answer

To find the resultant pH when mixing two solutions with known pH values, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the pH values of the solutions**:
- Solution A has a pH of 3.
- Solution B has a pH of 2.

2. **Calculate the concentration of H⁺ ions for each solution**:
- The concentration of H⁺ ions can be calculated using the formula:
\[ [H^+] = 10^{-\text{pH}} \]
- For Solution A (pH = 3):
\[ [H^+]_A = 10^{-3} \text{ M} = 0.001 \text{ M} \]
- For Solution B (pH = 2):
\[ [H^+]_B = 10^{-2} \text{ M} = 0.01 \text{ M} \]

3. **Assume equal volumes for both solutions**:
- Let the volume of each solution be \( V \). Therefore, the total volume after mixing will be \( 2V \).

4. **Calculate the total moles of H⁺ ions in each solution**:
- Moles of H⁺ in Solution A:
\[ n_1 = [H^+]_A \times V = 0.001 \times V = 0.001V \]
- Moles of H⁺ in Solution B:
\[ n_2 = [H^+]_B \times V = 0.01 \times V = 0.01V \]

5. **Find the total moles of H⁺ ions after mixing**:
- Total moles of H⁺ ions:
\[ n_{\text{total}} = n_1 + n_2 = 0.001V + 0.01V = 0.011V \]

6. **Calculate the concentration of H⁺ ions in the resultant solution**:
- The concentration of H⁺ ions in the mixed solution is:
\[ [H^+]_{\text{total}} = \frac{n_{\text{total}}}{\text{Total Volume}} = \frac{0.011V}{2V} = \frac{0.011}{2} = 0.0055 \text{ M} \]

7. **Calculate the resultant pH**:
- Using the concentration of H⁺ ions to find the pH:
\[ \text{pH} = -\log([H^+]_{\text{total}}) = -\log(0.0055) \]
- Calculating this gives:
\[ \text{pH} \approx 2.26 \]

### Final Result:
The resultant pH of the mixed solution is approximately **2.26**.

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