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?
15. Chemical Kinetics
Half-Life
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How much of a radioactive parent isotope will remain after three half-lives have passed?
A
1/16 of the original amount
B
1/4 of the original amount
C
1/8 of the original amount
D
1/2 of the original amount
Verified step by step guidance1
Understand the concept of half-life: A half-life is the time required for half of the radioactive parent isotope to decay into its daughter isotopes. After each half-life, the amount of the parent isotope is reduced by half.
Start with the original amount of the parent isotope. Let's denote this original amount as \( A_0 \).
After one half-life, the amount of the parent isotope remaining is \( \frac{A_0}{2} \).
After two half-lives, the amount remaining is \( \frac{A_0}{4} \), because \( \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \).
After three half-lives, the amount remaining is \( \frac{A_0}{8} \), because \( \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8} \).
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