Concentration Chemistry

Question

The initial concentration of a reactant in a first order reaction is 1.25 M. The rate constant k is 0.02 min^-1. How long will it take for the concentration to be reduced to 0.50 M?

Answer 1

For a first order reaction, the half life (t_1/2) = 0.693/k, so we can find t_1/2 from the data provided.

t_1/2 = 0.693/0.02 min^-1 = 34.65 min

We can then use FR = 0.5n

FR = fraction remaining = 0.5 M/1.25 M = 0.4

n = number of half lives that have elapsed = ?

0.4 = 0.5n

log 0.4 = n log 0.5

n = 1.32 half lives have elapsed

Time = 1.32 half lives x 34.65 min/half life = 45.8 minutes

It will take 45.8 minutes for the concentration to be reduced to 0.50 M