Step 1: Understanding the Concept:
The order of a reaction is the sum of the powers to which the concentration terms are raised in the experimentally found rate law. It does not come from the stoichiometric coefficients.
Step 2: Read the rate law:
The given rate law is \(\text{rate} = k[\text{H}_2\text{O}_2]^1\). The power of \([\text{H}_2\text{O}_2]\) is 1.
Step 3: Find the order:
The order is 1, so the reaction is first order.
Step 4: Why the other options are wrong.
The coefficient 2 in the balanced equation does not set the order, so option C is a trap. Zero order would mean rate = k with no concentration term. Order 3 has no basis here.
Final Answer:
The reaction is first order.
\[ \boxed{\text{(B) }1} \]