Question

For a first order reaction, if the rate constant is 1 min^-1 and the reaction time is 2 min, then the ratio of final to initial concentration is ____

(a) 0.167

(b) 0.135

(c) 0.198

(d) 0.764

The question was asked in an online quiz.

The origin of the question is Conversion and Reactor Sizing in portion Ideal Reactors for a Single Reaction, Conversion and Reactor Sizing of Chemical Reaction Engineering

Answer 1

Right choice is (b) 0.135

Best explanation: –\(\frac{dC_A}{dt}\) = kCA

Integrating between initial and final concentrations,

CA = CA0e^-kt

\(\frac{C_A}{C_{A0}} \) = e^-2

\(\frac{C_A}{C_{A0}} \) = 0.135.