Step 1: Recognize that HCl is a strong acid that dissociates completely in water: \[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^-. \] Thus, the concentration of H\(^+\) ions equals the concentration of HCl, which is 0.01 M.
Step 2: Calculate the pH using the formula \( \text{pH} = -\log_{10}[\text{H}^+] \). Substitute the H\(^+\) concentration: \[ \text{pH} = -\log_{10}(0.01) = -\log_{10}(10^{-2}) = -(-2) = 2. \]
Step 3: Verify the result. For a 0.01 M solution of a strong acid, the pH should be 2, which matches the calculation.