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The half-life of a reaction, t1/2, is the time it takes for the reactant concent

ID: 562906 • 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.

1. A certain first-order reaction (Aproducts) has a rate constant of 9.60×103 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?

2. A certain second-order reaction (Bproducts) has a rate constant of 1.55×103 M1s1 at 27 C and an initial half-life of 274 s . What is the concentration of the reactant B after one half-life?

Explanation / Answer

1)

rate constant k = 9.60 x 10^-3 s-1

original concentration Ao = 100 %

final concentration At = 6.25 %

for first - order reaction :

k = 1/t ln (Ao / At)

9.60 x 10^-3 = 1/t ln (100 / 6.25)

t = 288.8 sec

time taken = 4.81 min

2)

rate constant k = 1.55×103 M1s1

half - life = 274 sec

t1/2 = 1 / k Ao

274 = 1 / 1.55 x 10^-3 x Ao

Ao = 2.355 M

concentration of B after one half - life = 1.18 M