A first order reaction takes 40 min for 30% decomposition. Calculate $t _{ 1/2 }$

a = 100, a - x = 100 - 30 = 70, t = 40 min

k = 2.303/t log a/(a-x) = 2.303/40 min log 100/70

= 2.303/40 log 10/7 = 2.303/40 log 1.428 = 2.303 /40 x 0 1548

k = 8.91 x ${{10}^{-3}}$ ${{min}^{-1}}$

$t _{ 1/2 }$ = 0.693/k = 0.693/8.91 x ${{10}^{-3}}$ ${{min}^{-1}}$ = 77.78 min

$t _{ 1/2 }$ = 77.78 min