Question

Compound A reacts by 1st order kinetics at 25°C with a rate constant of 0.45 sec^-1. What is the half-life of A at 25°C? What is the time required to have 12.5% unreacted A for a 1st order reaction?

A) Half-life of A at 25°C is 1.54 seconds; time required for 12.5% unreacted A is 1.61 seconds.
B) Half-life of A at 25°C is 1.54 seconds; time required for 12.5% unreacted A is 3.22 seconds.
C) Half-life of A at 25°C is 0.693 seconds; time required for 12.5% unreacted A is 1.61 seconds.
D) Half-life of A at 25°C is 0.693 seconds; time required for 12.5% unreacted A is 3.22 seconds.

Answer 1

The half-life of compound A at 25°C for a first-order reaction with a rate constant of 0.45 sec^-1 is 1.54 seconds, and the time required for 12.5% of compound A to remain unreacted is 3.22 seconds.

Step-by-step explanation:

To find the half-life of compound A at 25°C for a first-order reaction with a rate constant (k) of 0.45 sec-1, we use the formula for the half-life of a first-order reaction: t₁₂ = 0.693/k. By plugging in the given rate constant, we find the half-life:

t₁₂ = 0.693 / 0.45 sec-1 ≈ 1.54 seconds.

For the time required to have 12.5% unreacted A, we utilize the first-order kinetics formula where the concentration of A at time t (Ct) is related to the initial concentration of A (C0) by Ct = C0 × e-kt. We want the time (t) when Ct/C0 = 0.125 (12.5%), which translates to ln(0.125) = -kt, and solving for t gives:

t = ln(0.125) / -k ≈ 3.22 seconds.

Therefore, the correct answer is B) Half-life of A at 25°C is 1.54 seconds; the time required for 12.5% unreacted A is 3.22 seconds.