We tried a few of these but I can't seem to get this one

Question

A first order reaction initially contains 2.25 × 10²⁰ molecules. If the reaction has a half-life of 20.0 minutes, how many molecules remain unreacted after 80.0 minutes?

Answer 1

There are a couple of ways to do this. I find the simplest one (without a lot of math) is

FR = 0.5ⁿ

FR = fraction remaining = ?

n = number of half lives that have elapsed = 80 min x 1 half life / 20 min = 4 half lives

FR = fraction remaining = 0.5⁴ = 0.0625

Number of molecules remaining = 0.0625 x 2.25x10²⁰ = 1.41x10¹⁹