Question

certain first-order reaction A → B is 25% complete in 42 min at 25°C. What is its rate constant? A. 6.8 × 10−3 min−1 B. 8.3 × 10−3 min−1 C. 3.3 × 10−2 min−1 D. −3.3 × 10−2 min−1

Answer 1

The rate constant for the first-order reaction that is 25% complete in 42 minutes is determined using the first-order reaction equation and found to be approximately 0.0072 min−1, with the closest answer choice being B. 8.3 × 10−3 min−1.

Step-by-step explanation:

The student is asking about determining the rate constant for a first-order reaction A → B that is 25% complete in 42 minutes at 25°C. For a first-order reaction, the relationship between the concentration of reactant A and time (t) is given by the formula:

ln([A]_0/[A]) = kt

where [A]_0 is the initial concentration, [A] is the concentration at time t, k is the rate constant, and t is time. Since the reaction is 25% complete, ultimately 75% of the reactant remains. The expression simplifies to:

ln(1/0.75) = kt

To solve for k, we know that t = 42 minutes, so we can rearrange the equation to get:

k = ln(1/0.75) / 42 min

Calculating this, we get:

k = ln(4/3) / 42 min ≈ 0.0072 min−1 or 7.2 × 10−3 min−1

Therefore, the closest option to this value is B. 8.3 × 10−3 min−1.