What is the half-life of a first-order reaction with a rate constant of 9.00 Tim

Question

What is the half-life of a first-order reaction with a rate constant of 9.00 Times 10^-4 s^-1? Express your answer with the appropriate units. What is the rate constant of a first-ordor reaction that takes 155 seconds for the reactant concentration to drop to half of its initial value? Express your answer with the appropriate units. A certain first-order reaction has a rate constant of 6.30Times10^-3 s^-1. How long will it take for the reactant concentration to drop to 1/8 of its intial value? Express your answer with the appropriate units.

Explanation / Answer

for first order reaction there is a relatio between half life and rate constant

t1/2 = 0.693 /k

where k = rate constant

t1/2 = 0.693 / 9 x 10-4

t1/2 = 770 sec

Paer B

time required tyo consume half of its amount means half life

t1/2 = 155 sec

again

k = 0.693 / t1/2

k = 0.693 / 155

k = 4.5 x 10-3 s-1

PartC

k = 6.3 x 10-3 s-1

use the equation

k = 2.303 / t log [A0/A]

lets A0 = intial concentration = 100%

A = contentration after certain time = 12.5 %

6.3 x 10-3 s-1 = 2.303 / t    log[ 100 / 12.5]

6.3 x 10-3 s-1 = 2.08 / t

t = 2.08 / 6.3 x 10-3 = 444.4444 sec

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