Final answer:
In the reaction Fe(OH)₂ + Mn²⁺ → MnO₂ + Fe²⁺, Mn²⁺ is the oxidizing agent as it gains electrons and is reduced, and Fe(OH)₂ is the reducing agent as it loses electrons and is oxidized.
Step-by-step explanation:
To identify the oxidizing agent and the reducing agent in a redox reaction, you need to determine which substance gains electrons and which one loses them. In the reaction Fe(OH)₂ + Mn²⁺ → MnO₂ + Fe²⁺, we assign oxidation numbers to see that iron (Fe) goes from a +2 oxidation state in Fe(OH)₂ to a +3 oxidation state in Fe²⁺. Manganese (Mn) goes from a +2 oxidation state in Mn²⁺ to a +4 oxidation state in MnO₂. Thus, Fe is oxidized and Mn is reduced.
The oxidizing agent is the substance that gets reduced by gaining electrons and the reducing agent is the substance that gets oxidized by losing electrons. In this reaction, Mn²⁺ is the oxidizing agent because it gains electrons (reduces), and Fe(OH)₂ is the reducing agent because it loses electrons (oxidizes).