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# Integrated Rate Laws for AP Chemistry (page 2)

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Consider the following problem: The rate constant for the radioactive decay of thorium–232 is 5.0 × 10–11/year. Determine the half–life of thorium–232.

This is a radioactive decay process. Radioactive decay follows first–order kinetics. The solution to the problem simply requires the substitution of the k–value into the appropriate equation:

tl/2 = 0.693/k = 0.693/5.0 × 10–11 yr–1 = 1.386 × 1010yr

which rounds (correct significant figures) to the answer reported.

Consider another case: Hydrogen iodide, HI, decomposes through a second–order process to the elements. The rate constant is 2.40° × 10–21/M s at 25°C. What is the halflife for this decomposition for a 0.200 M of HI at 25°C?

The problem specifies that this is a second–order process. Thus, you must simply enter the appropriate values into the second–order half–life equation:

t1/2 = 1/k[A]0 = 1/(2.40 × 10–21/M s)(0.200 M) = 2.08333 × 1021 seconds

which rounds to the answer reported.

Practice problems for these concepts can be found at:

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