Half-Life Expressions

In ALL cases, you can use the rate law to calculate the expression for half-life. When I was in first year, I didn't memorize the half-life expressions, I just remembered how to derive them like you see below. BUT, if you're not strong with math, it might seem challenging. AND, you might be given an equation sheet that has these expressions on it. Nonetheless, I want to show you HOW we derive these expressions...

We simply replace [A] with [A]o/2 and solve for t. That value of t is the amount of time that passes before the reactant concentration is HALF its initial amount. Look below as we derive it for zero-order, first-order and second-order reactions (OR skip to the last line of each)...

Zero-Order

Half life DECREASES with time, since the reactant concentration is going down. The less you have (the lower [A]o), the lower the half-life.

First-Order

Half-life STAYS CONSTANT over time, since reactant concentration isn't in this expression at all.

Second-Order

Half-life INCREASES over time, since reactant concentration is going down. This makes sense, since fewer molecules of A means fewer collisions, and so it takes longer for half of the reactant to disappear.

REPEAT: You don't have to memorize the above derivations. You have two options:

Memorize the LAST formula in each derivation. These are the expressions you'll need to use.
Find out if the expressions are on the formula sheet, if you're given one.