Question

For certain first order reaction 75% of the reaction complete in 30 minutes how much time is required to complete 99.9% of the reaction

Answer 1

it will take two half lives for completion of 75%
please mark it as brainliest

Answer 2

Answer: Time required to complete 99.9 % reaction is 149.5 mins.

Explanation: For first order reactions, rate is written as:

$k=\frac{2.303}{t}log\left(\frac{a}{a-x}\right)$

where, k = rate constant

t = time required

a = product formed

a - x = reactant left in the reaction

When the reaction is 75 % completed

a = 100

a - x = 100 - 75 = 25

Putting the values in rate equation, we get

$k=\frac{2.303}{30\times 60}log\left(\frac{100}{25}\right)$

$k=7.703\times 10^{-4}sec^{-1}$

As the rate constant for the reaction remains same. Now, when the reaction is 99.9% completed

a = 100

a - x = 100 - 99.9 = 0.1

Putting the values in the above rate equation, we get

$7.703\times 10^{-4}=\frac{2.303}{t}log\left(\frac{100}{0.1}\right)$

t = 8969.92 sec or     (Conversion factor: 1 min = 60 sec)

t = 149.5 mins