pH of `10^(-11)M HCl` is

Options

A. 11
B. 3
C. 6.8
D. 7

Answer

To find the pH of a `10^(-11) M HCl` solution, we need to consider both the contribution of HCl and the autoionization of water. Here’s a step-by-step solution:

### Step 1: Understand the Contribution of HCl
HCl is a strong acid and dissociates completely in water:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]
For a `10^(-11) M` solution of HCl, the concentration of hydrogen ions contributed by HCl is:
\[ [\text{H}^+] = 10^{-11} \, \text{M} \]

### Step 2: Consider the Contribution from Water
Pure water also contributes to the concentration of hydrogen ions due to its autoionization:
\[ \text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^- \]
At 25°C, the ion product of water (\( K_w \)) is:
\[ K_w = [\text{H}^+][\text{OH}^-] = 10^{-14} \]
In pure water, the concentration of hydrogen ions is:
\[ [\text{H}^+] = [\text{OH}^-] = 10^{-7} \, \text{M} \]

### Step 3: Calculate Total Hydrogen Ion Concentration
In the solution, the total concentration of hydrogen ions is the sum of the contributions from HCl and water:
\[ [\text{H}^+]_{\text{total}} = [\text{H}^+]_{\text{HCl}} + [\text{H}^+]_{\text{water}} \]
\[ [\text{H}^+]_{\text{total}} = 10^{-11} + 10^{-7} \]

Since \( 10^{-11} \) is much smaller than \( 10^{-7} \), we can approximate:
\[ [\text{H}^+]_{\text{total}} \approx 10^{-7} \]

### Step 4: Calculate pH
Now, we can calculate the pH using the total concentration of hydrogen ions:
\[ \text{pH} = -\log([\text{H}^+]_{\text{total}}) \]
Substituting the total concentration:
\[ \text{pH} = -\log(10^{-7}) = 7 \]

However, since we have a small contribution from HCl, we need to refine our calculation:
\[ [\text{H}^+]_{\text{total}} = 10^{-7} + 10^{-11} \approx 10^{-7} \, \text{(dominant term)} \]

To be more precise:
\[ [\text{H}^+]_{\text{total}} = 10^{-7} + 10^{-11} \approx 10^{-7}(1 + 10^{-4}) \]
Taking logarithm:
\[ \text{pH} = 7 - \log(1 + 10^{-4}) \]
Using the approximation \( \log(1+x) \approx x \) for small \( x \):
\[ \text{pH} \approx 7 - 10^{-4} \approx 6.999 \]

### Final Step: Approximate pH
Thus, the approximate pH of the solution is:
\[ \text{pH} \approx 6.95 \]

### Summary
The pH of a `10^(-11) M HCl` solution is approximately **6.95**.

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