Problem 11 - Chemistry: Principles and Reactions

Question

A reaction has two reactants \(\mathrm{A}\) and \(\mathrm{B}\). What is the order with respect to each reactant and the overall order of the reaction described by each of the following rate expressions? (a) rate \(=k_{1}[\mathrm{~A}]^{3}\) (b) rate \(=k_{2}[\mathrm{~A}] \times[\mathrm{B}]\) (c) rate \(=k_{3}[\mathrm{~A}] \times[\mathrm{B}]^{2}\) (d) rate \(=k_{4}[\mathrm{~B}]\)

Step-by-Step Solution

Answer

Question: Determine the order of the reaction with respect to each reactant (A and B) as well as the overall order for the following rate expressions: a) rate=k1[A]^3 b) rate=k2[A][B] c) rate=k3[A][B]^2 d) rate=k4[B] Answer: a) Order with respect to A: 3, Order with respect to B: 0, Overall order: 3 b) Order with respect to A: 1, Order with respect to B: 1, Overall order: 2 c) Order with respect to A: 1, Order with respect to B: 2, Overall order: 3 d) Order with respect to A: 0, Order with respect to B: 1, Overall order: 1

Step 1: (a) Reaction order from rate=k1[A]^3

In this case, the rate expression is given by rate \(= k_{1}[\mathrm{~A}]^{3}\). Since the concentration of reactant A is raised to the power of 3, the order of the reaction with respect to A is 3. B is not present in this rate expression, so the order with respect to B is 0. Adding the orders of each reactant together, the overall order of this reaction is 3.

Step 2: (b) Reaction order from rate=k2[A][B]

In this case, the rate expression is given by rate \(=k_{2}[\mathrm{~A}] \times [\mathrm{B}]\). The order of the reaction with respect to A is 1, as the concentration of A is raised to the power of 1. Similarly, the order with respect to B is also 1. Adding the orders together, the overall order of this reaction is 2.

Step 3: (c) Reaction order from rate=k3[A][B]^2

In this case, the rate expression is given by rate \(=k_{3}[\mathrm{~A}] \times [\mathrm{B}]^{2}\). The order with respect to A is 1, as the concentration of A is raised to the power of 1. The order with respect to B is 2 since the concentration of B is raised to the power of 2. Adding the orders together, the overall order of this reaction is 3.

Step 4: (d) Reaction order from rate=k4[B]

In this case, the rate expression is given by rate \(=k_{4}[\mathrm{~B}]\). Since the concentration of reactant B is raised to the power of 1, the order of the reaction with respect to B is 1. A is not present in this rate expression, so the order with respect to A is 0. Adding the orders of each reactant together, the overall order of this reaction is 1.

Key Concepts

Rate Law

In chemical kinetics, the rate law is a mathematical expression that links the rate of a chemical reaction to the concentration of its reactants. It is always crucial to understand the rate law because it helps in determining how changes in concentration affect the speed of the reaction.
For a given reaction with two reactants, A and B, the rate law can be expressed as follows:

• rate = k × [A]^x
• [B]^y

The terms in the brackets represent the concentrations of reactants, and the exponents (x and y) represent the reaction orders with respect to each reactant. The rate constant, denoted by "k," is a factor that incorporates the effects of temperature and other environmental conditions to the reaction speed.
Each exponent in the rate law indicates how sensitive the reaction rate is to the concentration of each reactant. The sum of these exponents gives the overall reaction order. Understanding the rate law is fundamental for predicting how fast a reaction proceeds and for deriving potential methods to control the reaction.

Chemical Kinetics

Chemical kinetics is the branch of chemistry that concerns itself with the speed, or rate, at which chemical reactions occur. It connects the path of reaction, known as the reaction mechanism, with the rate at which transformations happen. This field is fundamental for predicting and controlling how fast a chemical process should complete. Key factors influencing reaction rates include:

• Concentration: As concentration increases, the number of collisions between reactant molecules also increases, generally speeding up the reaction.
• Temperature: Higher temperatures usually result in faster reactions because molecules move more energetically.
• Catalysts: These substances lower the activation energy needed, significantly increasing the rate of reaction without being consumed themselves.

Understanding chemical kinetics allows scientists and engineers to design more efficient chemical processes and reactors. It equips them with the insights necessary to optimize conditions for favorable product yields and energy consumption.

Reaction Mechanisms

A reaction mechanism describes how reactants transform into products through a series of elementary steps. Each of these steps represents a simple reaction that contributes to the overall reaction process. Recognizing the reaction mechanism provides insights into the molecular changes occurring during the reaction pathway. Mechanisms are determined through experimental data combined with theoretical models. Key points in understanding mechanisms include:

• Intermediates: These are transient species that are formed and consumed during the mechanism.
• Rate-determining step: This is the slowest step in the process and it controls the overall rate of the reaction.
• Stoichiometric coefficients: These play a crucial role in establishing the connection between elementary steps and the observed reaction rate law.

By understanding the mechanism of a reaction, chemists can often predict the conditions under which a reaction will occur most promptly and efficiently, and potentially identify any side reactions that may interfere with the desired product formation.