In the context of half-life, k represents the rate constant for a reaction. The rate constant is a crucial factor in determining the half-life, t½, which is the time required for the initial concentration of a reactant to be reduced to one-half its initial value. According to the reference text: Determining a Half Life, to determine a half life we need to know the order of the reaction and the rate constant, k.
The relationship between k and t½ depends on the order of the reaction. Here's a breakdown:
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First-Order Reactions: For a first-order reaction, the half-life is inversely proportional to the rate constant k. The equation is:
t½ = 0.693 / k
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Other Reaction Orders: The relationship is different for other reaction orders. For example, for a second-order reaction, the half-life also depends on the initial concentration of the reactant.
Determining Half-Life
To calculate or understand half-life, you need to know:
- The order of the reaction: This tells you how the rate of reaction depends on the concentration of the reactants.
- The rate constant, k: This value quantifies the rate of the reaction at a given temperature.
Examples
Here are examples of calculating k:
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Given a first-order reaction with t½ = 10 seconds, calculate k:
- k = 0.693 / t½
- k = 0.693 / 10 s
- k = 0.0693 s⁻¹
