In a first-order batch reaction, what characterizes the concentration over time?

In a first-order batch reaction, the concentration of reactants changes over time according to an exponential decay function. This behavior is governed by the first-order kinetics, where the rate of reaction is directly proportional to the concentration of the reactant present. Mathematically, this can be expressed using the equation:

[ C(t) = C_0 e^{-kt} ]

where ( C(t) ) is the concentration at time ( t ), ( C_0 ) is the initial concentration, ( k ) is the rate constant, and ( e ) is the base of natural logarithms. As time progresses, the exponential function shows that the concentration decreases rapidly initially and then more slowly as it approaches zero, which is a hallmark of first-order kinetics.

This characteristic is crucial for understanding reaction dynamics in various contexts, such as chemical reaction engineering and environmental engineering processes, where predicting how pollutants degrade over time is essential for designing effective mitigation strategies.