Question

The half-life of a reaction of compound A to give compounds D and E is 8.50 min when the initial concentration of A is 0.150 M. What is the rate constant (k) for the reaction?

a) 0.0816 min^−1
b) 0.0408 min^−1
c) 0.0204 min^−1
d) 0.0102 min^−1

Answer 1

The rate constant (k) for the first-order reaction with a half-life of 8.50 minutes is calculated using the formula k = 0.693 / t1/2, which results in k = 0.0816 min⁻¹.

Step-by-step explanation:

The student has asked about the rate constant (k) for the reaction where compound A gives compounds D and E with a given half-life. The half-life formula for a first-order reaction is t1/2 = 0.693/k. Since the half-life is given as 8.50 minutes, we can rearrange the formula to k = 0.693 / t1/2 and substitute the half-life to find the rate constant.

Step-by-step calculation:

Use the half-life formula for a first-order reaction: t1/2 = 0.693/k.

Rearrange the formula to solve for k: k = 0.693 / t1/2.

Substitute the given half-life (8.50 min) into the equation: k = 0.693 / 8.50 min.

Perform the calculation to find k.

Calculation:

k = 0.693 / 8.50 min = 0.0816 min−1

Thus, the rate constant for the reaction is 0.0816 min−1, which corresponds to option a.