Question

for a first order reaction the time taken to reduce the initial concentration by a factor of 1 by 4 is 10 minute if the reduction in concentration is carried out by a factor of 1 by 16 then time required in minutes will be​

Answer 1

Answer:

Explanation:

For first order reaction t1/2 doesn't depend on concentration

Answer 2

Time required if the reduction in concentration is carried out by a factor of 1 by 16 in  minutes will be​ 20

Explanation:

Rate law expression for first order kinetics is given by:

[tex]t=\frac{2.303}{k}\log\frac{a}{a-x} [/tex]

where,

k = rate constant

t = time taken for decay process

a = initial amount of the reactant

a - x = amount left after decay process

Given :

$t_\frac{1}{4} = 10 min$

$a-x =\frac{1}{4}\times a$

Thus [tex]t_\frac{1}{4}=\frac{2.303}{k}\log\frac{a}{a/4} [/tex]

Thus [tex]10 min=\frac{2.303}{k}\log\frac{a}{a/4} [/tex]

$k=0.14min^{-1}$

Thus [tex]t_\frac{1}{16}=\frac{2.303}{0.14}\log\frac{a}{a/16} [/tex]

[tex]t_\frac{1}{16}=\frac{2.303}{0.14}\log{16} [/tex]

[tex] t_\frac{1}{16}=20min[/tex]

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