Question

In a first-order decomposition reaction. 58.6% of a compound decomposes in 11.7 min. How long (in min) does it take for 80.2% of the compound to decompose

Answer 1

t = 21.5 min.

Step-by-step explanation:

Hello!

In this case, since the kinetics of a first-order reaction is:

`([A])/([A]_0)=exp(-kt)`

Thus, since we are given the 11.7 min for a 58.6-% consumption, we can compute the rate constant, k:

`ln(1-0.586)=-kt\\\\k=(ln(0.414))/(-t)=(-0.882)/(11.7min)=0.0754min^(-1)`

Now, for the second problem, as the new consumption is 80.2%, we can compute the required time as shown below:

`ln(1-0.802)=-kt\\\\t=(ln(198))/(k) \\\\t=(-1.62)/(0.0754min^(-1))\\\\t=21.5min`

Best regards!