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Multiple Choice
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
66 minutes
B
110 minutes
C
88 minutes
D
44 minutes
Verified step by step guidance
1
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. Rearrange the formula to solve for k: .
Substitute the values for the first half-life and initial concentration into the equation to calculate k: .
For the third half-life, recognize that the concentration of A will be halved twice. Therefore, the concentration at the start of the third half-life is M.
Use the second-order half-life formula again with the new concentration to find the third half-life: .