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Integrated Rate Laws for AP Chemistry (page 2)

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By — McGraw-Hill Professional
Updated on Feb 9, 2011

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.

Answer: 1.4 × 1010 yr.

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?

Answer: 2.08° × 1021 s.

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.

If you are unsure about your work in either of these problems, just follow your units. You are asked for time, so your answer must have time units only and no other units.

Practice problems for these concepts can be found at:

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