Half-life equation for first-order reactions: t 1/2=0.693 k where t 1/2 is the h

Question

Half-life equation for first-order reactions:
t1/2=0.693k
where t1/2 is the half-life in seconds (s), and k is the rate constant in inverse seconds (s1).

The half-life of a first-order reaction with a rate constant of 6.20×104  s1 is 1120 seconds.

a) What is the rate constant of a first-order reaction that takes 7.10 minutes for the reactant concentration to drop to half of its initial value?

b) A certain first-order reaction has a rate constant of 3.80×103 s1. How long will it take for the reactant concentration to drop to 18 of its initial value?

Explanation / Answer

a) k = 0.693/t1/2 = (0.693/7.1) = 0.0976 min-1.

b) k = (1/t)ln(a/x)

   3.8*10^-3 = (1/t)ln(18/1)

t = 760.62 min

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