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The half-life of a reaction, t 1/2, is the time it takes for the reactant concen

ID: 484509 • Letter: T

Question

The half-life of a reaction, t1/2, is the time it takes for the reactant concentration [A] to decrease by half. For example, after one half-life the concentration falls from the initial concentration [A]0 to [A]0/2, after a second half-life to [A]0/4, after a third half-life to [A]0/8, and so on. on.

For a first-order reaction, the half-life is constant. It depends only on the rate constant k and not on the reactant concentration. It is expressed as

t1/2=0.693k

For a second-order reaction, the half-life depends on the rate constant and the concentration of the reactant and so is expressed as

t1/2=1k[A]0

Part A

A certain first-order reaction (Aproducts) has a rate constant of 9.30×103 s1 at 45 C. How many minutes does it take for the concentration of the reactant, [A], to drop to 6.25% of the original concentration?

Express your answer with the appropriate units.

Part B

A certain second-order reaction (Bproducts) has a rate constant of 1.45×103M1s1 at 27 C and an initial half-life of 212 s . What is the concentration of the reactant B after one half-life?

Express your answer with the appropriate units.

Explanation / Answer

A)
[A] = 6.25% of [A]o
       = 6.25/100 * [A]o
        =(1/16) [A]o

concentration will become [A]o/16 after 4 half lifes

half life = 0.693/k
= 0.693/(9.30*10^-3)
= 74.52 s

time = 4 half life
= 4*74.52 s
= 298 s
Answer: 298 s

B)
half life = 1/{k[A]o}
212 = 1/(1.45*10^-3 * [A]o)
[A]o = 3.25 M

After one half life concentration will be halfed
concentration = 3.25/2 = 1.63 M

Answer: 1.63 M