Question

A first order reaction is 75
complete in 20 minutes how long will it take to be 60 complete

Answer 1

Answer: 13.1 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 = time taken for completion  = 20 minutes

a = let initial amount of the reactant  = 100 g

x = amount decayed = $\frac{75}{100}\times 100=75 g$

a - x = amount left after decay process  = 100 - 75 = 25 g  

Now put all the given values in above equation, we get

$20=\frac{2.303}{k}\log\frac{100}{25}$

$k=0.07min^{-1}$

For calculating the time taken for the reaction to be 60% complete:

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

where,

k = rate constant  = $0.07min^{-1}$

t = time taken for completion  = ? minutes

a = let initial amount of the reactant  = 100 g

x = amount decayed = $\frac{60}{100}\times 100=6g$

a - x = amount left after decay process = 100-60 = 40 g  

$t=\frac{2.303}{0.07}\log\frac{100}{40}=13.1minutes$

Thus it will take 13.1 minutes to be 60% complete.