The pH of solution obtained by mixing equal volumes of two aqueous solutions of pH 5 and pH 3 of the same substance is

Options

A. 3.5
B. 4
C. 3.3
D. 4.5

Answer

To find the pH of the solution obtained by mixing equal volumes of two aqueous solutions with pH 5 and pH 3, we can follow these steps:

### Step-by-Step Solution:

1. **Understand pH and H⁺ Concentration**:
- The pH of a solution is defined as:
\[ \text{pH} = -\log[H^+] \]
- To find the concentration of hydrogen ions \([H^+]\) from pH, we use:
\[ [H^+] = 10^{-\text{pH}} \]

2. **Calculate [H⁺] for Each Solution**:
- For the solution with pH 5:
\[ [H^+]_1 = 10^{-5} \, \text{M} \]
- For the solution with pH 3:
\[ [H^+]_2 = 10^{-3} \, \text{M} \]

3. **Calculate Moles of H⁺ in Each Solution**:
- Assume we mix equal volumes \(V\) of each solution.
- Moles of H⁺ from the first solution:
\[ \text{Moles}_1 = [H^+]_1 \times V = 10^{-5} \times V \]
- Moles of H⁺ from the second solution:
\[ \text{Moles}_2 = [H^+]_2 \times V = 10^{-3} \times V \]

4. **Total Moles of H⁺**:
- Total moles of H⁺ after mixing:
\[ \text{Total Moles} = \text{Moles}_1 + \text{Moles}_2 = 10^{-5}V + 10^{-3}V \]
- Factor out \(V\):
\[ \text{Total Moles} = V(10^{-5} + 10^{-3}) \]

5. **Calculate Total Volume**:
- The total volume after mixing is:
\[ \text{Total Volume} = V + V = 2V \]

6. **Calculate Final Concentration of H⁺**:
- The concentration of H⁺ in the mixed solution is:
\[ [H^+]_{\text{final}} = \frac{\text{Total Moles}}{\text{Total Volume}} = \frac{V(10^{-5} + 10^{-3})}{2V} \]
- Simplifying gives:
\[ [H^+]_{\text{final}} = \frac{10^{-5} + 10^{-3}}{2} \]

7. **Calculate pH of the Mixed Solution**:
- Now, we need to calculate the pH:
\[ \text{pH}_{\text{final}} = -\log\left(\frac{10^{-5} + 10^{-3}}{2}\right) \]

8. **Calculate the Final Value**:
- First, calculate \(10^{-5} + 10^{-3}\):
\[ 10^{-5} + 10^{-3} = 0.00001 + 0.001 = 0.00101 \]
- Now divide by 2:
\[ \frac{0.00101}{2} = 0.000505 \]
- Finally, calculate the pH:
\[ \text{pH}_{\text{final}} = -\log(0.000505) \approx 3.296 \]

### Final Answer:
The pH of the solution obtained by mixing equal volumes of two aqueous solutions of pH 5 and pH 3 is approximately **3.296**.