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
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
