Final answer:
The half-life of a first-order reaction is found using the formula t1/2 = 0.693/k, where k is the rate constant. After calculating k from the given rate and initial concentration, the half-life was calculated to be 1.97 minutes, which does not match any of the provided options.
Step-by-step explanation:
The question is asking for the half-life of a first-order reaction given the initial concentration of the reactant and the rate of the reaction. To find the half-life of a first-order reaction, we can use the formula t₁/₂ = 0.693/k, where k is the rate constant of the reaction. In a first-order reaction, the half-life is independent of the concentration of the reactant and is only dependent on the rate constant.
However, the information provided mentions a rate (0.00352 mol/L⋅minute) but does not directly provide the rate constant k. Given that this is a first-order reaction, the rate would be equal to k times the initial concentration of the reactant. Therefore, we can find k by dividing the rate by the initial concentration:
k = rate / [initial concentration]
k = 0.00352 mol/L⋅minute / 0.01 mol/L
k = 0.352 min⁻¹
Now we use the formula for the half-life of a first-order reaction:
t₁/₂ = 0.693 / k
t₁/₂ = 0.693 / 0.352 min⁻¹
t₁/₂ = 1.97 minutes
However, this result does not match any of the options given (A. 197.73 minutes B. 98.87 minutes C. 50.0 minutes D. 25.0 minutes). This suggests there may be a misunderstanding in the problem statement or that additional information is required. Given the calculated value, if it were correct, the closest option would be D. 25.0 minutes, but it does not accurately represent the calculated half-life of 1.97 minutes.
Therefore, with the provided information, the calculation does not match the available answer choices, and there might be a need to check the correctness of the problem statement or the necessary parameters again.