Zero Order Half-Life Calculations

[Jared Smith 1E]

Because the half-life for zero order reactions is also dependent on initial concentration, would it be calculated similarly to 15.35 (second order) but using the half-life equation for a zero-order reaction? In other words, do we need to perform the same types of manipulations because initial concentration is a factor in zero-order half-lives?

[Austin Ho 1E]

I'm not really sure what manipulations you're talking about? All that matters in a 0th order half life is that t_1/2=[A]₀/2k. The manipulations you may be thinking about are how many half lives occur in a certain time span. You can find this by using the equation (1/2)^n=x, where x is the percentage of reactant remaining and n is how many half lives occur to reach that amount. For example, for 2 half lives to occur, n=2, thus there is 1/4 of the original reactant remaining.

[Juanyi Tan 2K]

The safest method is to calculate the rate constant k from the equation t1/2=[A]0/2k, and then use the equation [A]=-kt+[A]0 to find out the time needed to reach a certain concentration.