Problem 129 - Chemistry: An Atoms-Focused Approach

Question

Why can't an elementary step in a mechanism have a rate law that is zero order in a reactant?

Step-by-Step Solution

Answer

Answer: An elementary step in a reaction mechanism cannot have a rate law that is zero order in a reactant because it contradicts the fundamental idea that the rate of an elementary step is directly influenced by the concentrations of the reactants involved. In an elementary step, reactants collide directly to form products, so the reaction rate should be intrinsically linked to their concentrations. A zero-order dependence would imply that the reactant with zero order would not contribute to the reaction rate at all, even though it is involved in the elementary step. This is not consistent with the concept of direct collisions and the influence of reactant concentrations on the rate of an elementary step.

Step 1: Understanding elementary steps

In a reaction mechanism, an elementary step represents a single molecular event. These steps combine in a consecutive or concurrent manner to form the overall reaction. The rate of an elementary step can be influenced by the concentration of the reactants involved and the rate constant of the step.

Step 2: Rate laws and order of reaction

A rate law expresses the relationship between the rate of a reaction and the concentration of the reactants. The order of reaction for a specific reactant represents the power to which its concentration is raised in the rate law and determines the sensitivity of the reaction rate to changes in that reactant's concentration. A zero-order reaction means the rate of the reaction is independent of the concentration of that reactant.

Step 3: Elementary steps and stoichiometry

The rate law for an elementary step is derived from its stoichiometry, as it involves a direct collision of the reactants. For example, consider the following elementary step: A + B -> C. Its rate law can be expressed as: rate = k[A]^[m]*[B]^[n] where k is the rate constant, [A] and [B] are the concentrations of the reactants A and B, and m and n represent the orders of reaction for A and B, respectively.

Step 4: Contradiction of zero-order dependence in an elementary step

Now, let's consider a reactant with a zero-order dependence in an elementary step, which means m=0 or n=0 in the rate law. If m=0, the rate law simplifies to rate = k*[B]^n, and similarly for n=0, rate = k*[A]^m. This means that the rate of the reaction is completely independent of the concentration of one of the reactants. In an elementary reaction, the reactants collide directly to form products, so the rate of the reaction should be intrinsically linked to the concentrations of the reactants. A zero-order dependence in the rate law for an elementary step contradicts this, as the reactant with a zero-order would not contribute to the reaction rate at all, even though it is involved in the elementary step. Therefore, an elementary step in a mechanism cannot have a rate law that is zero order in a reactant because this would contradict the fundamental idea that the rate of an elementary step is directly influenced by the concentrations of the reactants involved. The rate should depend on the collision frequency of the reactants, which is directly proportional to their concentrations.