We are given a 0.01 M solution of hydrochloric acid (HCl). Hydrochloric acid is a strong acid, which means it dissociates completely in water.
Step 1: Write the dissociation equation
\[
\text{HCl} \to \text{H}^+ + \text{Cl}^-
\]
Since HCl is a strong acid, the concentration of hydrogen ions (\(\text{H}^+\)) is equal to the concentration of HCl, which is 0.01 M.
Step 2: Calculate the pH
The formula for pH is:
\[
\text{pH} = -\log[\text{H}^+]
\]
Substituting the concentration of hydrogen ions:
\[
\text{pH} = -\log(0.01) = -\log(10^{-2}) = 2
\]
Answer: The pH of the solution is 2, so the correct answer is option (2).