How to Calculate Non-Integer Number of Half Lifes

240221 question

Half life is the time taken for the concentration of reactants to decrease to half of its original amount.

For first order reactions, half life is constant.

For this question, half life is 3.47 seconds so we will expect the initial concentration x to decrease by 50% every 3.47 seconds.

240221 half life

1/3 of initial concentration does not correspond to integer number of half lifes hence we will need to use the following formula.

240221 formula

Ct is concentration of reactants at time t
C0 is initial concentration of reactants
n is number of half lifes which is also time divided by half life

We can calculate n to be 1.585.

240221 calculate n

Next time can be determined to be 5.5 seconds.

240221 calculate time

Hence the answer to this question is option C.

240221 answer

Topic: Kinetics, Physical Chemistry, A Level Chemistry, Singapore

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