Step 1: Recall the pH formula
pH is determined by the formula:\[\text{pH} = -\log[\text{H}^+]\]where \( [\text{H}^+] \) denotes the hydrogen ion concentration.
Step 2: Utilize the HCl concentration
Hydrochloric acid (\( \text{HCl} \)) is a strong acid that fully dissociates in water:\[\text{HCl} \rightarrow \text{H}^+ + \text{Cl}^-\]Consequently, the \( \text{H}^+ \) ion concentration equals the \( \text{HCl} \) concentration, which is \( 0.01 \, \text{M} \).
Step 3: Calculate the pH
Insert the \( \text{H}^+ \) concentration into the pH formula:\[\text{pH} = -\log(0.01) = 2\]
Answer:
The pH of the 0.01 M \( \text{HCl} \) solution is \( 2 \). Thus, option (1) is the correct answer.