Question

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

Short answer

Order with respect to A: 2; Order with respect to B: 1; Total order: 3.

Step-by-step solution

Understanding Reaction Order

Reaction order refers to the power to which the concentration term of a reactant is raised in the rate equation. For any reactant specified in a rate law, the reaction order indicates how the rate is affected by changes in the concentration of that reactant.

Identify Order with Respect to A

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

Identify Order with Respect to B

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

Calculate Total Order of the Reaction

The total order of the reaction is the sum of the orders with respect to all reactants involved. So, the total order is \(2 + 1 = 3\).

Key concepts

Rate Equation

A rate equation, often called the rate law, is an expression that quantifies the rate of a chemical reaction in relation to the concentration of its reactants. It helps us understand how different factors like concentration affect the speed of a reaction. For example, in our rate equation:

\[\text{Rate} = k[\mathrm{A}]^2[\mathrm{B}] \]

• The letter \( k \) is the rate constant. It provides a proportionality constant that makes the equation work out correctly, based on experimental data.
• The terms \( [\mathrm{A}] \) and \( [\mathrm{B}] \) represent the molar concentrations of reactants \( \mathrm{A} \) and \( \mathrm{B} \).
• The exponents \( 2 \) and \( 1 \) in this equation are crucial because they tell us the reaction order with respect to each reactant.

Understanding the components of a rate equation helps in predicting how changing one factor will change the rate of the reaction. This makes it a powerful tool in both academic studies and industrial applications.

Second Order Reaction

The term second order reaction specifically refers to the reaction order with respect to a given reactant. In the rate equation provided:

\[ \text{Rate} = k[\mathrm{A}]^{2}[\mathrm{B}] \]\( \mathrm{A} \) is raised to the power of \( 2 \), signifying that the reaction is second order with respect to \( \mathrm{A} \). This means the rate of reaction is highly sensitive to changes in the concentration of \( \mathrm{A} \). For example, if the concentration of \( \mathrm{A} \) is doubled, the reaction rate will increase by a factor of four.

• This squared relationship implies that any change in \( \mathrm{A} \) will have a pronounced effect on the reaction rate.
• Second order reactions are often observed in complex processes like enzyme kinetics and polymerization.
• Second order doesn't only mean the presence of a squared term; it indicates a deeper dependence on a particular reactant.

Knowing the second order nature of the reaction is crucial for figuring out how to effectively control the reaction rate in practical applications.

Total Order of Reaction

The total order of a reaction is determined by summing the exponents of all the reactants in the rate equation. It gives a holistic view of how the reaction rate is affected by the concentrations of all reactants involved. For our rate equation:

\[\text{Rate} = k[\mathrm{A}]^{2}[\mathrm{B}] \]

• The reaction is second order with respect to \( \mathrm{A} \) since the concentration of \( \mathrm{A} \) is raised to the power of 2.
• It is first order with respect to \( \mathrm{B} \), as its concentration is raised to the power of 1.

The total order of the reaction is calculated by adding these individual orders:
\[ 2 + 1 = 3 \]Understanding the total order is important because it guides you in understanding the overall behavior of the reaction. If you're considering a system where multiple reactants are interacting, knowing the total order of reaction aids in understanding how variations in concentrations influence overall reaction rates. This information is highly useful when designing experiments or industrial processes involving the reaction.