Question

The reaction 2A → B is first order in A with a rate constant of 2.8 x 10^-2 s^-1 at 80°C. How long (in seconds) will it take for A to decrease from 0.700 M to 0.110 M?

(a) 189 seconds
(b) 176 seconds
(c) 193 seconds
(d) 204 seconds

Answer 1

The time it takes for the concentration of A to decrease from 0.700 M to 0.110 M in a first-order reaction is approximately c) 193 seconds.

Step-by-step explanation:

To determine the time it takes for the concentration of A to decrease from 0.700 M to 0.110 M in a first-order reaction, we can use the integrated rate law for a first-order reaction:

[A] = [A]₀ * e^(-kt)

Where [A] is the concentration of A at a given time, [A]₀ is the initial concentration of A, k is the rate constant, t is the time, and e is the base of the natural logarithm.

By rearranging the equation, we can solve for t:

t = -ln([A]/[A]₀) / k

Substituting the given values:

t = -ln(0.110/0.700) / (2.8 x 10^-2 s^-1)

t ≈ 193 seconds