Question

A compound decomposes by a first-order process. if 25.0% of the compound decomposes in 60.0 minutes, the half-life of the compound is _________.

a. 65 minutes
b. 198 minutes
c. 120 minutes
d. 145 minutes
e. 180 minutes

Answer 1

Answer:d. 145 minutes

Half-life is the time needed for a radioactive to decay half of its weight. The formula to find the half-life would be:

Nt= N0 (1/2)^ t/h

Nt= the final mass
N0= the initial mass
t= time passed
h= half-life

If 25.0% of the compound decomposes that means the final mass would be 75% of initial mass. Then the half-live for the compound would be:
Nt= N0 (1/2)^ t/h
75%= 100% * (1/2)^ (60min/h)
3/4= 1/2^(60min/h)
log2 3/4 = log2 1/2^(60min/h)
0.41503749928 = -60min/h
h= -60 min / 0.41503749928= 144.6min