For a first-order reaction, the half-life is constant. It depends only on the ra

Question

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=1/(k[A]0)

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

A certain second-order reaction (Bproducts) has a rate constant of 1.20×103 M1s1 at 27 C and an initial half-life of 232 s . What is the concentration of the reactant B after one half-life?

Explanation / Answer

1)

k = 9.00×10^3 s-1

Ao = 100

At = 6.25 = remaining

t = 1/k * ln (Ao/At)

t = 1/ 9.00×103 * ln (100/6.25)

t = 308.06 sec

t = 5.13 min

2)

k = 1.20×103 M1s1

t1/2 = 232 s

t1/2 = Ao / 2k

232 = Ao / 2 x 1.20×103

Ao = 0.5568 M

initial concentration = 0.5568 M

after one halflife concentration = 0.2784 M

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