± Half-life (kinetics) for First Order Reactions Half-life equation for first-or

Question

± Half-life (kinetics) for First Order Reactions

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 (s?1).

Part A

What is the half-life of a first-order reaction with a rate constant of 2.40×10?4 s?1?

Express your answer with the appropriate units.

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Part B

What is the rate constant of a first-order reaction that takes 484 seconds for the reactant concentration to drop to half of its initial value?

Express your answer with the appropriate units.

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Part C

A certain first-order reaction has a rate constant of 5.80×10?3 s?1. 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

t1/2 = 0.693k

here given, k = 2.40×10-4

t ½ = 0.693 x ( 2.40 x 10-4)

= 0.693 x 0.00024

=0.00016632 sec

k = (t1/2) / 0.693

= 484/0.693

=698.4126

ln A0/A =kt

Ao intial concentration

A final concentration

k = equilibrium constant

ln (18/1) = 5.80×10-3 x t

2.8903 = 5.80×10-3 t

t = 2.8903 / ( 5.80×10-3)

=498.3275 sec

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