pH of `10^(-6)` M HCl (aq.) is :

Options

A. just less then 6
B. exactly equal to 6
C. just greater than 6
D. just less than 7

Answer

To find the pH of a `10^(-6)` M HCl solution, we can follow these steps:

### Step 1: Understand the definition of pH
The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration \([H^+]\):
\[ \text{pH} = -\log[H^+] \]

### Step 2: Identify the concentration of hydrogen ions
In a strong acid like HCl, it completely dissociates in water. Therefore, the concentration of hydrogen ions \([H^+]\) in a `10^(-6)` M HCl solution is:
\[ [H^+] = 10^{-6} \text{ M} \]

### Step 3: Calculate the pH
Now, we can substitute the value of \([H^+]\) into the pH formula:
\[ \text{pH} = -\log(10^{-6}) \]

### Step 4: Simplify the logarithm
Using the properties of logarithms, we can simplify:
\[ \text{pH} = -(-6) \cdot \log(10) = 6 \cdot 1 = 6 \]

### Step 5: Consider the contribution of water
In a solution where the concentration of HCl is `10^(-6)` M, we also have a contribution of hydrogen ions from the water itself, which is `10^(-7)` M. Therefore, the total concentration of hydrogen ions becomes:
\[ [H^+]_{\text{total}} = 10^{-6} + 10^{-7} = 1.1 \times 10^{-6} \text{ M} \]

### Step 6: Recalculate the pH with the total concentration
Now, we recalculate the pH using the total concentration:
\[ \text{pH} = -\log(1.1 \times 10^{-6}) \]
This can be approximated as:
\[ \text{pH} \approx 6 - \log(1.1) \approx 6 - 0.041 = 5.96 \]

### Final Answer
Thus, the pH of `10^(-6)` M HCl is approximately:
\[ \text{pH} \approx 5.96 \]