Question

For the hypothetical reaction \(3 A+2 B \rightarrow 2 C+3 D\) the rate was experimentally determined to be Rate \(=k[\mathrm{A}]^{1}[\mathrm{B}]^{1}\) What is the order of the reaction with respect to A? With respect to B? What is the overall order of the reaction? Suggest how many molecules each of \(\mathrm{A}\) and \(\mathrm{B}\) are likely to be involved in the detailed mechanism of the reaction.

Short answer

Order w.r.t A is 1; w.r.t B is 1; overall order is 2. Likely one molecule each of A and B involved.

Step-by-step solution

Determine the order with respect to A

The rate law provided is Rate = k[A]^{1}[B]^{1}. The exponent of [A] (which is 1) indicates the order of the reaction with respect to A. Therefore, the order with respect to A is 1.

Determine the order with respect to B

Similarly, the exponent of [B] in the rate law is 1. Therefore, the order of the reaction with respect to B is 1.

Determine the overall order of the reaction

The overall order of the reaction is the sum of the orders with respect to each reactant. In this case, it is 1 (order of A) + 1 (order of B) = 2. So the overall order of the reaction is 2.

Hypothesize the molecular involvement in the mechanism

The reaction's rate law, Rate = k[A]^1[B]^1, suggests that one molecule of A and one molecule of B are involved in the rate-determining step of the reaction. Therefore, it is likely that the detailed mechanism involves 1 molecule of A and 1 molecule of B.

Key concepts

rate law

The rate law of a reaction describes how the reaction rate depends on the concentration of the reactants. It's like a recipe for how fast a reaction goes. For the given reaction, the rate law is: Rate = k[A]^1[B]^1. Here, 'Rate' represents how fast the reaction occurs. The constant 'k' is called the rate constant and it varies with temperature.
The terms [A] and [B] represent the concentrations of reactants A and B, respectively. The exponents (which are 1 for both A and B in this case) determine the influence of each reactant's concentration on the rate. This relationship helps us understand how changes in concentration affect the reaction's speed.

reaction order

Reaction order indicates the power to which the concentration of a reactant is raised in the rate law. It shows the relationship between the reactants' concentrations and the reaction rate.
In the provided reaction's rate law, Rate = k[A]^1[B]^1, the exponents of [A] and [B] are both 1. This means the reaction is first order with respect to A and first order with respect to B. To find the overall order of the reaction, simply add these exponents together: 1 (for A) + 1 (for B) = 2. Hence, the overall reaction order is 2. Knowing the reaction order is crucial for predicting how the reaction rate will change with varying reactant concentrations.

molecular mechanism

The molecular mechanism of a reaction provides a step-by-step description of how reactants convert to products. It often involves several smaller steps, each representing a different chemical process.
From the given rate law, Rate = k[A]^1[B]^1, we can infer that the detailed mechanism likely involves one molecule of A and one molecule of B interacting in the rate-determining step. This means that these two molecules directly participate in the step that controls the overall reaction rate. Understanding the mechanism helps in explaining how reactants transform at the molecular level, which can guide further studies or applications of the reaction.

rate-determining step

The rate-determining step is the slowest step in a reaction mechanism, acting like a bottleneck that limits the reaction rate. Even if other steps are fast, the overall reaction can't proceed faster than this slowest step.
For our example reaction, the rate law Rate = k[A]^1[B]^1 tells us that one molecule of A and one molecule of B are involved in the slowest, rate-determining step. This indicates that the collision and interaction of these molecules are the primary factors slowing down the reaction. Knowing the rate-determining step is essential for enhancing reaction speed, as it highlights which part of the process to target for optimization.