📘 IB Understanding
The half-life of a first-order reaction is constant and independent of the initial concentration. It is related to the rate constant by \(t_{1/2} = \frac{\ln 2}{k}\).
What Is Half-Life?
The half-life (t½) is the time required for the concentration of a reactant to decrease to exactly half of its current value.
The Key Equation
This equation applies only to first-order reactions. Notice that t½ depends only on k, not on [A]₀. This means every successive half-life has the same duration.
First-Order Decay with Constant Half-Life
Worked Example
Problem: The radioactive decay of I-131 (first-order) has k = 0.138 days⁻¹. Find t½.
\(t_{1/2} = \frac{0.693}{0.138} = 5.02\text{ days}\)
📋 Exam Tip
To prove a reaction is first order from a graph: measure the time for [A] to go from 1.0 to 0.5 M, then from 0.5 to 0.25 M. If the two time intervals are equal, it is first order.
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