Problem 3 - Chemistry The Molecular Science

Question

Using the rate law, rate \(=k[\mathrm{~A}]^{2}[\mathrm{~B}],\) define the order of the reaction with respect to \(\mathrm{A}\) and \(\mathrm{B}\) and the overall reaction order.

Step-by-Step Solution

Answer

Second order with respect to A, first order with respect to B, overall reaction order is 3.

Step 1: Identify the Order with Respect to A

The order of the reaction with respect to a particular reactant is determined by the exponent of its concentration in the rate law. In the given rate law \( \text{rate} = k[\mathrm{A}]^{2}[\mathrm{B}] \), the concentration of \( \mathrm{A} \) is raised to the power of 2. Therefore, the reaction is second order with respect to \( \mathrm{A} \).

Step 2: Identify the Order with Respect to B

Similarly, the order of the reaction with respect to \( \mathrm{B} \) is determined by the exponent of its concentration in the rate law. Here, \( \mathrm{B} \) has an exponent of 1 in the rate law \( \text{rate} = k[\mathrm{A}]^{2}[\mathrm{B}] \). Thus, the reaction is first order with respect to \( \mathrm{B} \).

Step 3: Calculate the Overall Reaction Order

The overall reaction order is the sum of the exponents of all the reactants in the rate law. For \( \text{rate} = k[\mathrm{A}]^{2}[\mathrm{B}] \), the exponents are 2 for \( \mathrm{A} \) and 1 for \( \mathrm{B} \). Thus, the overall reaction order is \( 2 + 1 = 3 \).

Key Concepts

Reaction Order

In chemical kinetics, the reaction order is a crucial concept that relates to how the concentration of reactants affects the rate of a chemical reaction. Reaction order is determined by the exponents of the reactants' concentrations in the rate law equation. For example, in a given rate law \( \text{rate} = k[\mathrm{A}]^{2}[\mathrm{B}] \), the exponents indicate the reaction order for each reactant.

• Order with respect to \( \mathrm{A} \): The exponent for \( \mathrm{A} \) is 2, meaning the reaction is second order in \( \mathrm{A} \). Generally, this implies that if the concentration of \( \mathrm{A} \) doubles, the reaction rate increases by a factor of four \((2^2)\).
• Order with respect to \( \mathrm{B} \): The exponent for \( \mathrm{B} \) is 1, so it is first order in \( \mathrm{B} \). This means that doubling the concentration of \( \mathrm{B} \) will result in doubling the rate of reaction \((2^1)\).

The overall reaction order is the sum of the individual orders. For our example, it is \( 2 + 1 = 3 \), indicating a third-order reaction. This tells us how sensitive the reaction rate is to changes in the concentrations of all reactants.

Rate of Reaction

The rate of reaction is a measure of how quickly reactants are converted into products in a chemical process. It is expressed as a change in concentration of reactants or products per unit time. Understanding the rate of reaction helps us predict how fast a reaction will occur, which is essential for both laboratory and industrial applications. The rate law, which defines the rate of reaction, is an equation that combines the reaction rate constant \( k \) with the concentrations of reactants, each raised to their respective orders. In the rate law \( \text{rate} = k[\mathrm{A}]^{2}[\mathrm{B}] \), the reaction rate is influenced by how the concentrations of \( \mathrm{A} \) and \( \mathrm{B} \) affect this expression.

• Impact of Concentration: By increasing the concentration of a reactant with a higher reaction order, the overall rate of reaction increases significantly.
• Role of the Rate Constant \( k \): The rate constant depends on temperature and other conditions. It represents the proportionality factor that relates the concentration terms to the reaction rate.

These insights help chemists control reaction rates, essential in processes where precise timing is crucial.

Chemical Kinetics

Chemical kinetics is the area of chemistry that studies the speed or rate of chemical reactions and the factors affecting them. It sits at the crossroads of theoretical and applied chemistry, offering insights into how reactions proceed and how they can be manipulated. Chemical kinetics involves understanding:

• Reaction Mechanism: The detailed steps through which reactants transform into products. These steps can suggest intermediate compounds and help in optimizing reaction conditions.
• Factors Influencing Reactions: Temperature, concentration, pressure, and the presence of catalysts are among the factors that affect reaction rates. Higher temperatures typically increase the reaction rate by providing more energy for reactant molecules.
• Use of Models: Kinetic models help predict the outcome and efficiency of reactions under various conditions. These models are constructed using the rate law derived from experimental data.

By examining these aspects, chemical kinetics allows chemists to design reactions for maximum efficiency and desired outcomes.