In a first-order reaction, how does doubling the concentration affect the rate?

In a first-order reaction, the rate of the reaction is directly proportional to the concentration of one reactant. This means that if the concentration of the reactant is doubled, the rate of the reaction will also double. The mathematical representation of a first-order reaction rate can be written as:

[ \text{Rate} = k [A] ]

where ( k ) is the rate constant and ( [A] ) is the concentration of the reactant A. If the concentration ( [A] ) is increased from ( [A]_0 ) to ( 2[A]_0 ), the rate expression becomes:

[ \text{Rate}_{new} = k (2[A]_0) = 2k [A]_0 ]

This demonstrates that the new rate is twice the original rate, confirming that doubling the concentration of the reactant in a first-order reaction results in doubling the rate of the reaction. This direct relationship is characteristic of first-order kinetics, where changes in concentration lead proportionally to changes in the reaction rate.