Half-Life of Reaction Calculator

Simulate radioactive decay and chemical kinetics by calculating the half-life for zero, first, and second-order reactions.

Reaction Order

Rate Constant (k)

Initial Concentration [A]₀

Calculated Half-Life (t₁/₂)

6.9300e+1 s

Concentration DependenceIndependent of [A]₀ (Constant)

Dimensional Analysis1 / (1/s) = s

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The Concept of Half-Life

The Half-Life ( $t_{1/2}$ ) of a reaction is the precise amount of time it takes for the concentration of a reactant to drop to exactly half of its initial value.

While half-life is most famous for describing the decay of radioactive isotopes (like Carbon-14 dating), it is also a fundamental concept in chemical kinetics and pharmacology (describing how long it takes for your body to clear half of a drug from your system).

The Order of the Reaction

The mathematical formula for half-life changes entirely depending on the "Order" of the reaction. The order dictates how the reaction rate responds to changes in concentration.

First-Order Kinetics (The Most Common)

In a first-order reaction (like radioactive decay), the half-life is perfectly constant. It does not matter if you start with 100 grams or 1 gram; it will always take the exact same amount of time to lose half the material.

\begin{aligned} t_{1/2} = \frac{\ln(2)}{k} \approx \frac{0.693}{k} \end{aligned}

Where:

t_{1/2}

Half-Life

First-Order Rate Constant

Zero and Second-Order Kinetics

Zero-Order: The reaction proceeds at a fixed, constant speed regardless of concentration. Because the speed doesn't slow down, the half-life gets shorter as the concentration drops.
Second-Order: The reaction rate depends heavily on the concentration. As the concentration drops, the reaction slows down massively, meaning the half-life gets longer over time.

Frequently Asked Questions

In perfect first-order kinetics, theoretically no. You keep dividing the remainder by half infinitely (1/2, 1/4, 1/8, 1/16...). However, in reality, after about 10 half-lives, the remaining amount (0.1%) is usually considered negligible.

The rate constant is a proportionality value specific to that exact reaction at that exact temperature. A larger 'k' means a faster reaction, which naturally results in a shorter half-life.

Because their half-life formulas include the initial concentration ( $[A]_0$ ). As the reaction proceeds, the 'initial' concentration for the next half-life is smaller, causing the resulting half-life time to physically change.

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