Reaction Order Equations

[Layla Qumsieh 3C]

Hi! I understand how to find reaction order, and I know which equation correlates with which reaction order, but I'm not understanding exactly why each reaction order calls for a different equation? What about the reaction order influences the equations so drastically?

[Andre Contreras 1I]

This is because the Equations are derived differently. They are derived from the differential rate laws which are governed by the reaction order. Dr. Lavelle shows how they are derived in his lecture recordings.

[Joshua Chandran 2D]

Reaction orders determine the power to which each single compound is raised to, and this power makes a big difference when integrating to find the integrated rate law for each reaction order. For example, if we have a reactant A is which is in first order with respect to the reaction rate, the instantaneous rate of change of [A] is -d[A]/dt = k[A]. Integrating this to find the integrated rate law, we get d[A]/[A] = -kdt, which yields ln[A] = -kt + ln[A]initial.

However, if A was in second order with respect to the reaction rate, the instantaneous rate of change would be -d[A]/dt = k[A]^2. Integrating this to find the integrated rate law, we get -d[A]/d[A]^2 = kdt, which yields 1/[A] = kt + 1/[A]initial. Thus, the order of the reaction drastically affects the rate equations when considering the derivations for each reaction order.

[405773279]

this is because in each reaction, the speed/rate of the reaction could depend on different reactants. for instance lets say that in reaction A + B -> C + D, the rate only depends on [A], then there would be no need to involve B into the equation because it essentially acts as a constant that does not affect the rate of the reaction. For example 2, lets say we have reaction F + G -> H + I where the reaction depends on F and G, this would mean that we would have to account for changes in both. The number number of reactants the rate depends on is the order (for rate = k[A], order would be 1, rate = [A][B], order would be 2)
This is why we have different equations for each order because once we have these equations for each order, they can be generalised