교과서 질문
This reaction was monitored as a function of time: A → B + C A plot of ln[A] versus time yields a straight line with slope -0.0045/s. c. What is the half-life?
15. Chemical Kinetics
Half-Life
객관식
For the hypothetical second-order reaction: A → products, the general rate law is: rate = k[A]². How long is the third half-life of the reaction if [A]₀ is 0.080 M and the first half-life is 22 minutes?
A
110 minutes
B
66 minutes
C
88 minutes
D
44 minutes
검증된 단계별 안내1
Understand that for a second-order reaction, the half-life is not constant and depends on the initial concentration. The formula for the half-life of a second-order reaction is: .
Given that the first half-life is 22 minutes, use the formula for the first half-life to find the rate constant k. Substitute the values: . Solve for k.
Once you have the value of k, use the second-order half-life formula to find the third half-life. The concentration of A after each half-life is halved, so after the first half-life, [A] = 0.040 M, and after the second half-life, [A] = 0.020 M.
Calculate the third half-life using the concentration after the second half-life: . Substitute the value of k obtained from step 2.
Solve the equation from step 4 to find the duration of the third half-life. This will give you the time in minutes for the third half-life of the reaction.
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