To determine the pH of the solution, let's follow a step-by-step process:
1. Identify the given hydrogen ion concentration:
[tex]\[
\left[ H^+ \right] = 0.01 \, \text{M}
\][/tex]
2. State the formula for pH:
[tex]\[
\text{pH} = -\log \left[ H_3O^+ \right]
\][/tex]
Note that [tex]\( \left[ H_3O^+ \right] \)[/tex] and [tex]\( \left[ H^+ \right] \)[/tex] are used interchangeably here because they represent the concentration of hydrogen ions in the solution.
3. Substitute the given hydrogen ion concentration into the formula:
[tex]\[
\text{pH} = -\log \left( 0.01 \right)
\][/tex]
4. Recall the property of logarithms:
[tex]\[
\log(b^n) = n \cdot \log(b)
\][/tex]
Since [tex]\( \log(10) = 1 \)[/tex], we can use this property on [tex]\( 0.01 \)[/tex]:
5. Express [tex]\( 0.01 \)[/tex] as a power of 10:
[tex]\[
0.01 = 10^{-2}
\][/tex]
6. Apply the logarithm rule:
[tex]\[
\log(10^{-2}) = -2 \cdot \log(10) = -2 \cdot 1 = -2
\][/tex]
7. Substitute the log value into the pH formula:
[tex]\[
\text{pH} = -(-2)
\][/tex]
[tex]\[
\text{pH} = 2
\][/tex]
Therefore, the pH of the solution is:
[tex]\[
\boxed{2}
\][/tex]
