What is the half-life of a compound if 78 percent of a given sample of the compound decomposes in 70. min? Assume first-order kinetics.?

For a first-order reaction, the half-life is independent of the initial temperature.

Let n be the number of half-lives.

Amount of the compound left after 70 min :
(1/2)ⁿ = (100 - 78)%
0.5ⁿ = 0.22
log(0.5ⁿ) = log(0.22)
n log(0.5) = log(0.22)
n = log(0.22)/log(0.5)

Half-life = (70 min) / [og(0.22)/log(0.5)] = 70 log(0.5)/ log(0.22) min = 32 min