Step 1: Understanding the Question:
The question asks us to identify the reducing agent in the given redox reaction. A reducing agent is a substance that reduces another reactant by losing electrons, thereby causing its own oxidation state to increase.
Step 2: Key Formula or Approach:
We can determine the reducing agent by assigning oxidation numbers to the atoms involved in the reaction and locating the species whose oxidation number increases (undergoes oxidation).
Step 3: Detailed Explanation:
Let's analyze the changes in oxidation states for the elements in the reaction:
In hydrogen peroxide ($\text{H}_2\text{O}_2$), oxygen is in a special peroxide state and carries an oxidation number of $-1$.
In the product elemental oxygen gas ($\text{O}_2$), the oxidation number of oxygen is $0$.
Since the oxidation number of oxygen increases from $-1$ to $0$, $\text{H}_2\text{O}_2$ undergoes oxidation.
Conversely, the chlorine atom in the perchlorate ion ($\text{ClO}_4^-$) goes from an oxidation state of $+7$ to $+3$ in the chlorite ion ($\text{ClO}_2^-$), meaning it undergoes reduction.
Because $\text{H}_2\text{O}_2$ is the reactant that gets oxidized, it acts as the reducing agent for the perchlorate ion.
Step 4: Final Answer:
The reducing agent in the reaction is $\text{H}_2\text{O}_{2(aq)}$, which corresponds to option (B).