The pH of `10^(-11)` M HCI at `25^@C` is

Options

A. 11
B. 3
C. Slightly greater than 7
D. Slightly less than 7

Answer

To find the pH of a `10^(-11)` M HCl solution at `25°C`, we need to consider the contribution of both the HCl and the water ionization to the concentration of hydrogen ions (H⁺).

### Step-by-Step Solution:

1. **Identify the concentration of H⁺ from HCl:**
- The concentration of H⁺ ions from the HCl solution is `10^(-11)` M because HCl is a strong acid and dissociates completely in water.
- \[ [H^+]_{HCl} = 10^{-11} \, \text{M} \]

2. **Consider the contribution from water:**
- At `25°C`, pure water also contributes H⁺ ions due to its autoionization, which gives a concentration of `10^(-7)` M for H⁺ ions.
- \[ [H^+]_{water} = 10^{-7} \, \text{M} \]

3. **Calculate the total concentration of H⁺ ions:**
- The total concentration of H⁺ ions in the solution is the sum of the H⁺ ions from HCl and the H⁺ ions from water:
- \[ [H^+]_{total} = [H^+]_{HCl} + [H^+]_{water} = 10^{-11} + 10^{-7} \]

4. **Approximate the total concentration:**
- Since `10^(-11)` is much smaller than `10^(-7)`, we can approximate:
- \[ [H^+]_{total} \approx 10^{-7} \, \text{M} \]

5. **Refine the calculation:**
- To be more precise, we can factor out `10^(-7)`:
- \[ [H^+]_{total} = 10^{-7} \left(1 + \frac{10^{-11}}{10^{-7}}\right) = 10^{-7} \left(1 + 10^{-4}\right) \]
- \[ [H^+]_{total} = 10^{-7} \times 1.0001 \]

6. **Calculate the pH:**
- The pH is calculated using the formula:
- \[ \text{pH} = -\log[H^+] \]
- Substituting the total concentration:
- \[ \text{pH} = -\log(10^{-7} \times 1.0001) \]
- Using the logarithmic property: \(-\log(ab) = -\log a - \log b\):
- \[ \text{pH} = -\log(10^{-7}) - \log(1.0001) \]
- \[ \text{pH} = 7 - \log(1.0001) \]

7. **Calculate \(\log(1.0001)\):**
- Using a calculator, we find:
- \[ \log(1.0001) \approx 0.000043 \]
- Therefore:
- \[ \text{pH} \approx 7 - 0.000043 \]
- \[ \text{pH} \approx 6.99996 \]

8. **Final Result:**
- The pH of the solution is slightly less than 7, which can be rounded to:
- \[ \text{pH} \approx 6.99996 \]

### Conclusion:
The pH of `10^(-11)` M HCl at `25°C` is approximately **6.99996**, which is slightly less than 7.