Question

75 of a first order reaction is completed in 30 min the time required to 93.75 completion

Answer 1

50% of reaction will complete in 15 minutes, 75% will take 30 minutes, 87.5% will be completed in 45 minutes and 93.75% will be completed in 60 minutes.

Answer 2

Answer: 55.5 minutes

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant  

t = age of sample

a = let initial amount of the reactant  

a - x = amount left after decay process  

a) for completion of 75 % :

a = 100

a-x = 100-75 = 25

$t_{\frac{3}{4}}=\frac{2.303}{k}\log\frac{100}{25}$

$30=\frac{2.303}{k}\log\frac{100}{25}$

$k=0.05min^{-1}$

b) for completion of 93.75 % of reaction  

a = 100

a-x = 100- 93.75 = 6.25

$t=\frac{2.303}{0.05}\log\frac{100}{6.25}$

$t=55.5min$

Thus time required to 93.75 completion is 55.5 minutes.