Final answer:
The half-life of a first-order reaction can be calculated using the formula t₁₂ = 0.693 / k, where k is the rate constant. To find the half-life of the compound given that 25% has decomposed in 52 minutes, we need to first determine k from this data point. Without the rate constant, we cannot calculate the half-life.
Step-by-step explanation:
The student wants to calculate the half-life of a reaction assuming first-order kinetics after being given that 25% of a compound decomposes in 52 minutes. The half-life of a reaction is the time required for half of the reactant to be consumed. For first-order reactions, half-life is calculated using the formula t₁₂ = 0.693 / k, where k is the rate constant of the reaction.
We can find the rate constant k from the given information, using the first-order kinetics formula ln([A]0 /[A]t) = kt, where [A]0 is the initial concentration, and [A]t is the concentration at time t. Since 25% has decomposed, 75% remains, and we have ln(1/0.75) = k(52 minutes), from which k can be determined. Once k is known, we can substitute it back into the half-life equation to find the half-life of the reaction.
However, we cannot directly calculate the half-life in this scenario without the specific rate constant k. Since it is not provided, and the half-life formula for first-order reactions requires the rate constant, we need additional information or data points to determine the half-life.