Item 6 The half-life of a reaction, t1/2, is the time it takes for the reactant

Question

Item 6

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 6.30×10^3 s^1 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 1.75×10^3 M1s^1 at 27 C and an initial half-life of 208 s . What is the concentration of the reactant B after one half-life?

Express your answer with the appropriate units.

Explanation / Answer

A)

for a first order reaction

t1/2 = 0.693 /k

given

k = 6.3 x 10-3

so

t1/2 = 0.693 / 6.3 x 10-3

t1/2 = 110 s

now

consider 100% of reactant initillay

after 110 s it beomces half of it

so

after 110 s , it becomes 50%

and

after another half life , 110 + 110 = 220 s , it becomes 25%

after 220 +110 = 330 , it becomes 12.5 %

after 330 + 110 = 440 , it becomes 6.25%

so

time taken to reach 6.25% = 440 s = 7.33 min

so

the answer is 7.33 min

B)

for a second order reaction

t1/2 = 1 / k[Ao]

given

k = 1.75 x 10-3

and

initial half lfie =208 s

so

208 = 1 / k[Ao]

k [Ao] = 1/ 208

1.75 x 10-3 [Ao] = 1/208

[Ao] = 2.75 M

so

concentration of one half life = 2.75 / 2 = 1.375

so

the concentration of the reactant B after one half life is 1.375 M

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.