Let's solve the problem step-by-step.
We are given the concentration of hydrogen ions in the solution, [tex]\(\left[ H^{+} \right] = 0.01 \, \text{M}\)[/tex]. We are asked to find the pH of this solution using the formula:
[tex]\[ pH = -\log \left[ H_3 O^{+} \right] \][/tex]
or equivalently,
[tex]\[ pH = -\log \left[ H^{+} \right] \][/tex]
1. Substitute the given concentration into the pH formula:
[tex]\[ pH = -\log \left( 0.01 \right) \][/tex]
2. Recall that [tex]\( \log \left( 0.01 \right) \)[/tex] can be rewritten as [tex]\( \log \left( 10^{-2} \right) \)[/tex].
3. Using the properties of logarithms, [tex]\(\log \left( 10^{-2} \right) = -2 \)[/tex].
4. Now, substitute this back into the pH calculation:
[tex]\[ pH = -(-2) \][/tex]
5. Simplify the expression:
[tex]\[ pH = 2 \][/tex]
Therefore, the pH of the solution is [tex]\(2\)[/tex]. This matches the given information and the correct answer from the choices is [tex]\(2\)[/tex].
