Question

$1.0 \times 10^{-4} \text{ M } \text{HCl}$ is diluted 10 times. The $\text{pH}$ of the final solution is:

• A. between 3 and 4
• B. between 4 and 5
• C. between 6 and 7
• D. equal to 7

Hint:

Dilution reduces the concentration proportionally. A 10-fold dilution increases the $\text{pH}$ by $\log(10) = 1$ unit for strong acids and bases, provided the resulting concentration is significantly greater than $10^{-7} \text{ M}$.

Answer 1

The Correct Option is B

The initial concentration of the strong acid $\text{HCl}$ is $[\text{H}^+]_{\text{initial}} = 1.0 \times 10^{-4} \text{ M}$.
When diluted 10 times, the final concentration $[\text{H}^+]_{\text{final}}$ is:
$[\text{H}^+]_{\text{final}} = \frac{10^{-4}}{10} = 1.0 \times 10^{-5} \text{ M}$.
The $\text{pH}$ is calculated as $\text{pH} = -\log[\text{H}^+]$.
$\text{pH} = -\log(10^{-5}) = 5$.
The $\text{pH}$ of the final solution is 5, which falls between 4 and 5.