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).

Part A

What is the half-life of a first-order reaction with a rate constant of 5.30×104  s1?

Express your answer with the appropriate units.

Part B
What is the rate constant of a first-order reaction that takes 348 seconds for the reactant concentration to drop to half of its initial value?

Express your answer with the appropriate units.

Part C

A certain first-order reaction has a rate constant of 9.00×103 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)

t1/2  = 0.693 / K

t1/2  = 0.693 / 5.30 x 10-4

t1/2   = 1307.5 s-1

B) K = 0.693 / t1/2

K = 0.693 / 348

K = 2.0 x 10-3 s-1

C) assume [A0] = 1.0

[A] = 0.05 (18 of 1 )

K = (2.303 / t) log [A0] / [A]

t = (2.303 / 0.009) log [1] / [0.05]

t = 332.92 s

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