To find the pH of the solution of HCl, we start by noting the given concentration of hydrogen ions [tex]\(\left[ H^+ \right] = 0.01 \, M\)[/tex].
The formula to calculate pH is:
[tex]\[ \text{pH} = -\log \left[ H^+ \right] \][/tex]
Substitute the given concentration into the formula:
[tex]\[ \text{pH} = -\log (0.01) \][/tex]
Next, recall that [tex]\(0.01\)[/tex] can be expressed as [tex]\(10^{-2}\)[/tex]. Thus, we have:
[tex]\[ \text{pH} = -\log (10^{-2}) \][/tex]
Using the properties of logarithms, specifically [tex]\(\log (10^x) = x\)[/tex], we find:
[tex]\[ \text{pH} = -(-2) \][/tex]
[tex]\[ \text{pH} = 2 \][/tex]
Therefore, the pH of the solution is:
[tex]\[ \boxed{2} \][/tex]
