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For a given first order reaction the reactant reduced to 1/4th its initial value in 10 minutes. The rate constant of the reaction is?
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For a given first order reaction the reactant reduced to 1/4th its ini...
First Order Reaction:
A first-order reaction is a chemical reaction in which the rate of conversion of reactants into products is proportional to the concentration of only one reactant.

Given:
The reactant reduced to 1/4th its initial value in 10 minutes.

Formula:
The rate of a first-order reaction can be expressed as:

rate = k[A]

where,
k = rate constant
[A] = concentration of reactant

Calculation:
Let the initial concentration of the reactant be [A]₀.

After 10 minutes, the concentration of the reactant becomes [A]/4.

The rate equation can be written as:

rate = k[A]₀

At t = 10 min, the concentration of the reactant is [A]/4.

rate = k[A]/4

Substituting the values in the equation above, we get:

k[A]₀ = k[A]/4

Simplifying the equation, we get:

k = 2.303/t log ([A]₀/[A])

where,
t = time taken for the concentration of the reactant to reduce to 1/4th of its initial value.

Substituting the values, we get:

k = 2.303/10 log ([A]₀/[A]/4)

k = 2.303/10 log ([A]₀/[A]) + 2.303/10 log 4

k = 0.2303 log ([A]₀/[A]) + 0.09212

Answer:
The rate constant of the reaction is 0.2303 log ([A]₀/[A]) + 0.09212.
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For a given first order reaction the reactant reduced to 1/4th its initial value in 10 minutes. The rate constant of the reaction is?
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