Practice: Decomposition of a certain substance Y at 45°C was found to be zero order. What is the half-life of substance Y if it took 15.5 minutes to decompose 67% of this substance? [Y]_{0} = 0.25 M.

**Half-Life** is the time it takes for *half *of a reactant to *decay* in a certain time period.

Concept #1: Zero-Order Half-Life

Example #1: The reverse Haber reaction: 2 NH_{4} (g) → 3 H_{2} (g) + N_{2} (g), has a rate constant of 1.45 x 10-6 M•s^{-1} at 25ºC. Calculate the half-life for the reaction where [NH_{4}]_{0} = 2.47 x 10^{-2 }mol/L.

Practice: Decomposition of a certain substance Y at 45°C was found to be zero order. What is the half-life of substance Y if it took 15.5 minutes to decompose 67% of this substance? [Y]_{0} = 0.25 M.

Concept #2: First-Order Half-Life

Example #2: Rate constant for the following reaction was found to be** **2.3 x 10^{-3 }s^{-1 }at 35ºC:

2 NO_{2 }→ N_{2}O_{4}

If the initial concentration of NO_{2} was 1.4 x 10^{-1}, what is the half-life on this reaction?

Practice: Radioactive plutonium-239 (t_{1/2} = 2.41 × 10^{5} yr) is used in nuclear reactors and atomic bombs. If there are 5.70 × 10^{2} g of plutonium isotope in a small atomic bomb, how long will it take for the substance to decay to 3.00 × 10^{2} g?

Concept #3: Second-Order Half-Life

Example #3: The half-life of a certain reaction with 2^{nd} order was found to be 0.45 seconds. What was the initial concentration of a reactant if the slope of the straight line for this reaction is 3.5 x 10^{-3}?

Practice: Use the data below to determine the half-life of decomposition of NOCl reaction which follows 2nd order kinetics.