Question

A first order decomposition reaction takes 40 minutes for 30% decomposition. Calculate its $t_{1/2}$ value.

Answer 1

For a first order reaction,

t = 2.303/k Log [R]º / [R]

k = 2.303/40min  Log 100 / 100-30

= 2.303/40min  Log 10 / 7

= 8.918 x 10-3 min-1

Therefore, t1/2 of the decomposition reaction is

t1/2 = 0.693/k

=  0.693 / 8.918 x 10-3  min

= 77.7 min (approximately)