Question

After 77.0 min, 44.0% of a compound has decomposed. What is the half‑life of this reaction assuming first‑order kinetics?

Answer 1

The question involves determining the half-life of a first-order reaction based on the percentage of a compound that has decomposed over a period of time. However, additional information or data points are necessary to calculate the rate constant and, consequently, the half-life of the reaction.

Step-by-step explanation:

The student has asked about determining the half-life of a reaction given that after 77.0 minutes, 44.0% of a compound has decomposed, and the reaction follows first-order kinetics. The half-life of a first-order reaction can be calculated using the formula t1/2 = (ln(2))/k, where k is the rate constant. However, to find the rate constant k, we need to use the provided information about the percentage of decomposition and time elapsed. We can apply the first-order kinetics equation ln([A]0/[A]) = kt, where [A0] is the initial concentration, [A] is the concentration at time t, and k is the rate constant. Solving this equation for the rate constant k, and subsequently for the half-life, would provide the answer to the question. However, without knowing the rate constant or being able to derive it from additional information given in the question, we cannot complete the calculation. To successfully determine the half-life for the first-order reaction, additional information or data points are needed to calculate the rate constant or directly compute the half-life.

Answer 2

The half-life of a first-order reaction can be calculated using the integrated rate law for first-order kinetics; however, without the rate constant, it is not possible to determine the half-life based on the given information that 44.0% of a compound has decomposed after 77.0 minutes.

Step-by-step explanation:

When we consider that 44.0% of a compound has decomposed after 77.0 minutes, and we assume first-order kinetics for the reaction, we need to calculate its half-life. The half-life (t1/2) of a first-order reaction is the time required for the concentration of the reactant to decrease by half its initial amount. The special property of first-order reactions is that their half-life is independent of the initial concentration. Given this information, we can use the integrated rate law for a first-order reaction, which is ln([A]0/[A]) = kt, where [A]0 is the initial concentration, [A] is the remaining concentration after time t, k is the rate constant, and t is time.

To find the half-life, we need to use the fact that at half-life, only 50% of the reactant remains. As 44.0% has decomposed, 56.0% remains, so we are not at the half-life yet. However, if we know the rate constant, we could use the equation ln(2)/k to calculate the half-life. Without the specific value of k, we cannot calculate an exact number for the half-life from the given information alone. More information or data is needed to solve for the half-life under these conditions.