Question

A reaction is experimentally found to follow the rate law, rate = k[a]², where k = 0.355 m⁻¹min⁻¹. Starting with [a]₀ = 1.55 m, how many seconds will it take for [a]ₜ = 0.150m?

Answer 1

The question involves calculating the time it takes for a reactant's concentration to change in a second-order reaction, given the rate constant and initial/final concentrations.

Step-by-step explanation:

The student is asking about how long it will take for the concentration of a reactant [A] to decrease from 1.55 M to 0.150 M in a reaction that follows a second-order rate law, rate = k[A]², with a given rate constant (k). To solve this, we use the integrated rate law for a second-order reaction, which is 1/[A] - 1/[A]₀ = kt. Plugging in the given values and solving for time (t), we can find out how many seconds it takes for the concentration to reach the desired level.

Here is how the calculation would be set up:

1/[A]ₜ - 1/[A]₀ = kt
1/0.150 M - 1/1.55 M = (0.355 m⁻¹min⁻¹) × t

After solving the equation for t, convert the time from minutes to seconds.