Question

A first-order reaction, where [A]₀ = 1.00 M, is 73.3% complete in 397 s. How long does it take for the same reaction to go from 1.00 M to 89.5% completion?

Option 1: 448 s
Option 2: 505 s
Option 3: 573 s
Option 4: 625 s

Answer 1

The question involves calculating the time required for a first-order reaction to reach 89.5% completion, knowing it reaches 73.3% completion in 397 seconds. The time can be found using the first-order kinetic model, but the exact answer requires more information or the application of integrated rate laws.

Step-by-step explanation:

The question asks how long it will take for a first-order reaction with an initial concentration of 1.00 M to reach 89.5% completion, given that it reaches 73.3% completion in 397 seconds. A first-order reaction follows the first-order kinetic model, where the rate is proportional to the concentration of the reactant.

For a first-order reaction, the relationship between time, t, the rate constant, k, and the concentration of the reactant, [A], is given by the following equation: ln([A]₀/ [A]t) = kt. To find the time required to reach 89.5% completion, we can apply this model, assuming that k is a constant throughout the reaction course and an appropriate equation is used.

Since 89.5% completion is greater than 73.3% completion, the reaction will take longer to reach 89.5% completion compared to 397 s required for 73.3%. Without the exact rate constant, k, or more data, the exact time cannot be calculated here; the problem seems to require additional information or the application of integrated rate laws.