The half-life of a first-order reaction is 13 min. If the initial concentration of reactant is 0.13 M, it takes min for it to decrease to 0.085 M. The half-life of a first-order reaction is 13 min. If the initial concentration of reactant is 0.13 M, it takes min for it to decrease to 0.085 M. 10. 11 7.0 12 8.0

The time taken is 8 minutes.

The rate of decay of a radioactive substance is given by:

      λN

here N is the concentraion, λ is the decay constant. If inially the concentration is  t time t = 0.

Then solving the above equation we get:

λ =

Now the half-life is defined as the time after which half of the initial concentration is left. The relation between half-life and decay constant is:

λ =  

Given that   = 13 min

λ = 0.693/13 = 0.0533

So, the time taken for a first-order reaction such that the concentration decreases from 0.13 M to 0.085M can be calculated by following equation:

λ =

t =  

t = 8 min

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Therefore it takes 8.0 mins for it to decrease to 0.085 M

Explanation:

First order reaction: The rate of reaction is proportional to the concentration of reactant of power one is called first order reaction.

A→ product

Let the concentration of A = [A]

[A₀] = initial concentration

[A]= final concentration

t= time

k= rate constant

Half life: Half life is time to reduce the concentration of reactant of its half.

Here

To find the time takes for it to decrease to 0.085 we use the below equation

Here ,   ,  [A₀] = 0.13 m and [ A] = 0.085 M

Therefore it takes 8.0 mins for it to decrease to 0.085 M

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