To determine the pH of the given HCl solution with a concentration of [tex]\([ H^+ ] = 0.01 \, \text{M}\)[/tex], we use the following pH formula:
[tex]\[ pH = -\log [ H^+ ] \][/tex]
Step-by-Step Solution:
1. Identify the concentration of hydrogen ions [tex]\( [ H^+ ] \)[/tex]:
Given [tex]\( [ H^+ ] = 0.01 \, \text{M} \)[/tex].
2. Substitute the [tex]\( [ H^+ ] \)[/tex] value into the pH formula:
[tex]\[ pH = -\log (0.01) \][/tex]
3. Calculate the logarithm of 0.01:
[tex]\[ \log (0.01) \][/tex]
Recall the properties of logarithms: [tex]\(\log(10^{-2}) = -2\)[/tex].
4. Find the negative of the logarithm:
[tex]\[ -\log (0.01) = -(-2) = 2 \][/tex]
Thus, the pH of the solution is:
[tex]\[ pH = 2 \][/tex]
Therefore, the correct answer is [tex]\(2\)[/tex].
