Step 1: Plan:
Find hydroxide ion concentration first, then take its negative logarithm.
Step 2: Hydroxide concentration:
Complete dissociation gives $[\text{H}^+] = 10^{-2}$ M. At 298 K, $K_w = [\text{H}^+][\text{OH}^-] = 10^{-14}$.
\[ [\text{OH}^-] = \frac{10^{-14}}{10^{-2}} = 10^{-12} \text{ M} \]
Step 3: Take the logarithm:
$\text{pOH} = -\log 10^{-12} = 12$.
Step 4: Check:
An acid solution has high pOH, so a value of 12 (not 2) makes sense.
Final Answer:
The pOH is 12, option (B).
\[ \boxed{\text{pOH} = 12} \]