A first order reaction takes 20 minutes for 25% decomposition.

Calculate the time when 75% of the reaction will be completed.

(Given : log 2 = 0.3010, log 3 = 0.4771, log 4 = 0.6021)

Given:

Time for 25% decomposition = 20 minutes

First we need to calculate the value of rate constant. To calculate rate constant, we apply the formula for the first order reaction:

K = log

Where t is time,

a is the no. of moles per litre,

(a-x) is the concentration of a after time t

As, t = 20 minutes (given)

a = 100, x = 25

∴ k = log

⇒ k = log

⇒ k = 0.0143 min^-1

Now, t= ?, when reaction is 75% complete, i.e., x= 75

To calculate the time, we apply the same formula

K = log

Using formula, we write

t = log

As, k = 0.0143 min^-1 (calculated above)

∴ t = log

⇒ t = log

⇒ t = 96.96 minute

Thus, the time when 75% of the reaction will be completed is 96.96 minutes.