Sodium hydroxide (NaOH), a strong base, dissociates fully in water. The concentration of hydroxide ions (\(\text{OH}^-\)) matches the NaOH concentration, which is 0.1 M.
Step 1: Dissociation Equation
\[
\text{NaOH} \to \text{Na}^+ + \text{OH}^-
\]
The concentration of \(\text{OH}^-\) is 0.1 M.
Step 2: pOH Calculation
The pOH formula is:
\[
\text{pOH} = -\log[\text{OH}^-]
\]
Substituting the \(\text{OH}^-\) concentration:
\[
\text{pOH} = -\log(0.1) = -\log(10^{-1}) = 1
\]
Step 3: pH Calculation
The pH and pOH are related by:
\[
\text{pH} + \text{pOH} = 14
\]
Therefore:
\[
\text{pH} = 14 - 1 = 13
\]
Answer: The solution's pH is 13, corresponding to option (2).