srry to bring up an old thread but im doing this one and a bit confused on the formulas that were listed ^^

Where did the ln2 come from? Whats [Ao]? and where is time(t) in the formulas for 1st and 2nd order?

Are you guys understanding this conceptually or just plugging stuff into the formula?

Also, what if the question asked for anything other than a 50% decomposition, ie 40%?

Ln 2 comes from the half-life formula for a first-order reaction. Mathematically, Ln 2 = .693 so the formula for half-life of a first order reaction is often abbreviated to .693/k rather than writing out (Ln 2)/k.

[Ao] represents initial concentration. The "t½" (half-life) time is what you are solving for with these equations. For half-life times I think knowing the formulas is sufficient:

Zero order: t½ = [Ao] / 2k

First order: t½ = 0.693 / k

Second order: t½ = 1 / k [Ao]

In other words this formula is not used to give you the amount of a substance at a given half-life, it is used to determine what the length of the half-life is. Notice that for zero and second order reactions, the half-life time changes as the concentration remaining changes (since radioactive decay is first order which means the half-life is constant, we usually don't have to worry about it). I don't think they would ask you for anything other than 50% decomposition if they only gave you half-life information. In the event they did you'd have to estimate it between the amounts known at certain half-lives.