Problem 7 - Chemistry and Chemical Reactivity

Question

Using the rate equation Rate \(=k[\mathrm{A}]^{2}[\mathrm{B}],\) define the order of the reaction with respect to A and B. What is the total order of the reaction?

Step-by-Step Solution

Answer

Second-order with respect to A, first-order with respect to B, total order is 3.

Step 1: Identify the Reaction Order with Respect to A

The given rate equation is \( \text{Rate} = k[\mathrm{A}]^{2}[\mathrm{B}] \). The concentration of \( [\mathrm{A}] \) is raised to the power of 2, which means the reaction is second-order with respect to A.

Step 2: Identify the Reaction Order with Respect to B

In the given rate equation \( \text{Rate} = k[\mathrm{A}]^{2}[\mathrm{B}] \), the concentration of \( [\mathrm{B}] \) is raised to the power of 1. This means the reaction is first-order with respect to B.

Step 3: Calculate the Total Order of Reaction

The total order of a reaction is the sum of the orders with respect to all reactants. For our rate equation \( \text{Rate} = k[\mathrm{A}]^{2}[\mathrm{B}] \), the reaction is second-order with respect to A and first-order with respect to B. Therefore, the total order is \( 2 + 1 = 3 \).

Key Concepts

Rate Equation

The rate equation is a fundamental concept in chemistry that helps you understand how the rate of a reaction depends on the concentration of its reactants. The specific form of a rate equation provides insight into the reaction order with respect to each reactant. Let's break down the given rate equation:

• Rate = k[ A]^{2}[ B]

The rate equation displays how the rate of reaction changes with the concentration of reactants, A and B. The letter k represents the rate constant, which is unique for each reaction at a given temperature. The powers to which the concentrations of A and B are raised indicate the orders of the reaction relative to each reactant.

In this instance, the reaction is second-order with respect to A because A is squared, and it is first-order with respect to B since B is raised to the first power. Understanding this structure is crucial because it reflects the relationship between reactant concentrations and the speed of the chemical reaction.

Chemical Kinetics

Chemical kinetics involves the study of the rate at which chemical processes occur. It focuses on how different conditions, such as concentration and temperature, impact the speed of a chemical reaction. By analyzing the rate equation, we can gather information about the mechanism of the reaction and how several factors influence it. Reaction rates can be affected by:

• Concentration of reactants: Higher concentrations generally increase the rate of reaction by raising the number of reactant particles available to collide.
• Temperature: Increasing temperature usually speeds up reactions by providing more energy, enabling more effective collisions.
• Catalysts: Substances that increase reaction rates without being consumed in the reaction.
• Surface area: More surface area offers more space for collisions to occur.

Chemical kinetics is vital not only for understanding the dynamics of existing chemical reactions but also for designing and optimizing new processes, especially in industrial applications. By understanding these principles, chemists can develop more efficient methods for producing substances and energy.

Total Order of Reaction

The total order of a reaction is an important concept, representing the sum of the orders with respect to each reactant in the rate equation. For the given equation Rate = k[ A]^{2}[ B], A contributes a second-order, while B adds a first-order. Thus, the total order of the reaction is the sum:

• Total Order = Second-order (from A) + First-order (from B) = 3

This total order provides insight into how sensitive the reaction rate is to changes in concentration. A higher total order suggests that more significant changes in rate can occur with small changes in reactant concentrations. The total order is a key concept since it indicates the overall proportionality between the reaction rate and reactant concentrations, giving important hints into the reaction's dynamics and mechanisms.