The pH value of `10^(-7)` M solution HCI is

Options

A. Equal to 1
B. Equal to 2
C. Less than 7
D. Equal to 0

Answer

To find the pH value of a `10^(-7)` M solution of HCl, we can follow these steps:

### Step 1: Understand the dissociation of HCl
HCl is a strong acid and dissociates completely in water:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]

### Step 2: Determine the concentration of H⁺ ions from HCl
Since the concentration of HCl is `10^(-7)` M, the concentration of H⁺ ions contributed by HCl will also be `10^(-7)` M.

### Step 3: Consider the contribution of H⁺ ions from water
At 25°C, pure water also contributes H⁺ ions due to its autoionization:
\[ \text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^- \]
The concentration of H⁺ ions from water is also `10^(-7)` M.

### Step 4: Calculate the total concentration of H⁺ ions
The total concentration of H⁺ ions in the solution will be the sum of the contributions from HCl and water:
\[ [\text{H}^+] = [\text{H}^+]_{\text{HCl}} + [\text{H}^+]_{\text{H}_2\text{O}} = 10^{-7} + 10^{-7} = 2 \times 10^{-7} \text{ M} \]

### Step 5: Calculate the pH
The pH is calculated using the formula:
\[ \text{pH} = -\log [\text{H}^+] \]
Substituting the total concentration of H⁺ ions:
\[ \text{pH} = -\log(2 \times 10^{-7}) = -\log(2) - \log(10^{-7}) = -\log(2) + 7 \]
Since \(-\log(2)\) is a positive number (approximately 0.301), we can conclude:
\[ \text{pH} = 7 - \log(2) \]

### Step 6: Determine the value of pH
Since \(-\log(2)\) is approximately 0.301, we find:
\[ \text{pH} \approx 7 - 0.301 = 6.699 \]
Thus, the pH value is less than 7.

### Final Answer
The pH value of a `10^(-7)` M solution of HCl is **less than 7**.

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