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Half-life equation for first-order reactions: t1/2=0.693k where t1/2 is the half

ID: 968640 • Letter: 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)

What is the half-life of a first-order reaction with a rate constant of 6.20×104  s1?

1120

s

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?

9.76×102

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?

1120

s

Explanation / Answer

1) t1/2 = 0.693/k

           = 0.693/6.20*10^-4

           = 1117.7 s

2) K = 2.303/t *log(a/a-x)

        = 2.303/7.10*log(1/0.5)

        = 9.76*10^-2 min-1

3) 3.8*10^-3 = 2.303/t*log(100/18)

     t = 451.3 s