Question

Based on the data given and a rate constant of 0.031 M−1⋅min−1, calculate the time at which the concentration of reactant A will be 0.150 M .

t (min) [A]t(M)
0.00 0.500
20.0 0.382
40.0 0.310
60.0 0.260
80.0 0.224

Answer 1

The time at which the concentration of reactant A will be 0.150 M is 20 minutes.

Step-by-step explanation:

The given data shows the concentration of reactant A at different time intervals. To calculate the time at which the concentration of reactant A will be 0.150 M, we can use the integrated rate law for a second-order reaction, which is: [A] = [A]0 / (1 + k[A]0t). Rearrange the equation to solve for time: t = ([A]0 / [A] - 1) / (k[A]0). Plugging in the values where [A]0 = 0.500 M, [A] = 0.150 M, and k = 0.031 M−1⋅min−1, we get:

t = (0.500 / 0.150 - 1) / (0.031 * 0.500) = 20 minutes

Answer 2

Known :

[A]₀ = 0.500 M

[A] = 0.150 M

Based on units of rate constant :

k = 0.031 M⁻¹ · min⁻¹

We know it's a second order of reaction, so

1 / [A] = k • t + 1 / [A]₀

Plug in the value :

1 / (0.150) = 0.031 • t + 1 / (0.500)

t = 150.5 min