NaOH is a strong base and dissociates completely in water. The concentration of hydroxide ions (\(\text{OH}^-\)) is equal to the concentration of NaOH, which is 0.1 M.
Step 1: Write the dissociation equation
\[
\text{NaOH} \to \text{Na}^+ + \text{OH}^-
\]
The concentration of \(\text{OH}^-\) is 0.1 M.
Step 2: Calculate the pOH
The formula for pOH is:
\[
\text{pOH} = -\log[\text{OH}^-]
\]
Substituting the concentration of \(\text{OH}^-\):
\[
\text{pOH} = -\log(0.1) = -\log(10^{-1}) = 1
\]
Step 3: Calculate the pH
The relationship between pH and pOH is:
\[
\text{pH} + \text{pOH} = 14
\]
Thus:
\[
\text{pH} = 14 - 1 = 13
\]
Answer: The pH of the solution is 13, so the correct answer is option (2).