Chemical Reaction Kinetics: Understanding First-Order Reactions

How does the given chemical reaction demonstrate first-order kinetics?

The following chemical reaction: A → products shows first order kinetics with respect to A; rate = k[A]. Assume k = 12.19 x 10^-5 s^-1. If the initial concentration of A is 0.42 mol L-1, what is the concentration of A (in mol L^-1) after 31.6 hours?

Explanation

The given reaction follows first-order kinetics, which means that the rate of the reaction is directly proportional to the concentration of reactant A raised to the power of 1. The rate equation is given as rate = k[A], where k is the rate constant.

To find the concentration of A after a certain time, we can use the integrated rate equation for a first-order reaction:

ln([A]t/[A]0) = -kt

Where [A]t is the concentration of A at time t, [A]0 is the initial concentration of A, k is the rate constant, and t is time.

Plugging in the values, we have:

ln([A]t/0.42 mol L^-1) = -(12.19 x 10^-5 s^-1) * (31.6 hours * 3600 s/hour)

Solving for [A]t gives:

[A]t = 0.42 mol L^-1 * e^(-(12.19 x 10^-5 s^-1) * (31.6 hours * 3600 s/hour))

Calculating this gives [A]t ≈ 0.098 mol L^-1.

Understanding reaction kinetics and the behavior of chemical reactions over time is crucial in chemistry. First-order reactions are a common type of reaction where the rate depends on the concentration of a single reactant. The integrated rate equation and the concept of half-life are important tools for studying reaction kinetics and determining reaction progress.