The Integrated Rate Law for 2nd Order Reactions is a mathematical expression that describes the relationship between the concentration of a reactant and time for a second-order reaction. It is derived from the rate law for a second-order reaction and allows for the determination of the rate constant and half-life of the reaction.
The Integrated Rate Law for 2nd Order Reactions is derived by integrating the rate law for a second-order reaction, which is rate = k[A]². The integration process involves separating the variables, integrating both sides of the equation, and solving for the concentration of the reactant as a function of time.
The general form of the Integrated Rate Law for 2nd Order Reactions is: 1/[A]t = kt + 1/[A]0, where [A]t is the concentration of the reactant at time t, k is the rate constant, and [A]0 is the initial concentration of the reactant.
The Integrated Rate Law for 2nd Order Reactions can be rearranged to the form ln([A]t/[A]0) = -kt, which is a linear equation with a slope of -k and a y-intercept of ln([A]0/[A]t). By plotting ln([A]t/[A]0) against time, the rate constant can be determined from the slope of the line. The half-life can be calculated by using the equation t1/2 = 1/(k[A]0), where t1/2 is the half-life and [A]0 is the initial concentration of the reactant.
The units of the rate constant in the Integrated Rate Law for 2nd Order Reactions depend on the overall order of the reaction. For a second-order reaction, the units of the rate constant are M⁻¹s⁻¹, where M is the unit for concentration and s is the unit for time.