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Chapter 17 | Kinetics
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If we set the time t equal to the half-life, the corresponding concentration of A at this time is equal to one-half of its initial concentration. Hence, when
Therefore:
Thus:
We can see that the half-life of a first-order reaction is inversely proportional to the rate constant k. A fast reaction (shorter half-life) will have a larger k; a slow reaction (longer half-life) will have a smaller k.
Example 17.10
Calculation of a First-order Rate Constant using Half-Life
Calculate the rate constant for the first-order decomposition of hydrogen peroxide in water at 40 °C, using the data given in Figure 17.13.
Figure 17.13 The decomposition of H2O2 at 40 °C is illustrated. The intensity of the color symbolizes the concentration of H2O2 at the indicated times; H2O2 is actually colorless.
Solution
The half-life for the decomposition of H2O2 is 2.16 104 s:
Check Your Learning
The first-order radioactive decay of iodine-131 exhibits a rate constant of 0.138 d−1. What is the half-life for this decay?
Answer: 5.02 d.
