Question

75% of a first-order reaction is completed in 32 minutes.the t 1/2 of the reaction is

Answer 1

Let initial amount = A
after 32 minutes = 75% of A completed = 0.75A

we know , formula for 1st order reaction ,
K = 2.303/t log[ initial ]/[final]

= 2.303/32 log{ A/(A - 0.75A)}

={2.303/32}× log4 --------(1)

for half life , formula is
T½ = 2.303/K log2

put K ={2.303/32} × log4

T½ = 2.303/[{2.303/32} × log4 ] × log2

= 32 log2/log4

= 32log2/2log2

= 16 min

hence, half life of given reaction is 16 minutes .