A first order reaction initially contains 3.25 × 10²⁰ molecules. If the reaction has a half-life of 20.0 minutes, how many molecules remain unreacted after 80.0 minutes?

Answer 1

For a first order reaction, FR = 0.5ⁿ

FR = fraction remaining = ?

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

FR = 0.5⁴ = 0.0625 ... this is the fraction of 3.25x10²⁰ molecules that REMAIN

Number of molecules remaining = 0.0625 x 3.25x10²⁰ = 2.03x10¹⁹ molecules remain