A. What is the half-life of a first-order reaction with a rate constant of 5.90×

Question

A. What is the half-life of a first-order reaction with a rate constant of 5.90×104  s1?

Express your answer with the appropriate units.

B. What is the rate constant of a first-order reaction that takes 268 seconds for the reactant concentration to drop to half of its initial value?

Express your answer with the appropriate units.

C.

A certain first-order reaction has a rate constant of 2.70×103 s1. How long will it take for the reactant concentration to drop to 18 of its initial value?

Express your answer with the appropriate units.

Explanation / Answer

A. What is the half-life of a first-order reaction with a rate constant of 5.90×104  s1?

If this is 1st order, then:

Half life = ln(2) / rate constant

Half life = ln(2)/(5.9*10^-4) = 1,174.82 seconds

the half life then is 1,174.82 seconds

B. What is the rate constant of a first-order reaction that takes 268 seconds for the reactant concentration to drop to half of its initial value?

this is giving you the half life, since 50% of reactant is achieved

so

HL = 268

apply equation

Half life = ln(2) / rate constant

rate constant = ln(2) / 268 s = 0.00258637 1/s

C. A certain first-order reaction has a rate constant of 2.70×103 s1. How long will it take for the reactant concentration to drop to 18 of its initial value?

Apply 1st order equations

lnCfinal = lnCinitial - k*t

ln(Cfinal/Cinitial) = -k*t

t = ln(Cfinal/Cinitial) / -(2.7*10^-3)

ln Cfinal/Cinitial = 1/18

t = ln(1/18) / (2.7*10^-3)

t = 1,070.50 seconds

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