I can't seem to get this one, could I get some help please?

Question

The half-life for the first-order conversion of A to B is 56.5 hours. How long does it take for the concentration of A to decrease to 10.0% of its original concentration?

Answer 1

FR = 0.5ⁿ

FR = fraction remaining = 10% = 0.10

n = number of half lives that have elapsed = ?

0.10 = 0.5ⁿ

log 0.10 = n log 0.5

-1 = -0.301n

n = 3.32 half lives

Since each half life = 5.6 hours...

56.5 hours / half life x 3.32 half lives = 188 hours