HalfLife Expressions 
Previous Page: SecondOrder Reactions
Next Page:

In ALL cases, you can use the rate law to calculate the expression for halflife. When I was in first year, I didn't memorize the halflife 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 zeroorder, firstorder and secondorder reactions (OR skip to the last line of each)...
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 zeroorder, firstorder and secondorder reactions (OR skip to the last line of each)...
ZeroOrderHalf life DECREASES with time, since the reactant concentration is going down. The less you have (the lower [A]o), the lower the halflife.


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.