Question

Assume that the rate law for a generic chemical reaction is rate \(=[\mathrm{A}][\mathrm{B}]^{3}\) . What is the reaction order in \(\mathrm{A}\) , the reaction order in \(\mathrm{B}\) , and the overall reaction order?

Short answer

The reaction order in A is 1, the reaction order in B is 3, and the overall reaction order is 4.

Step-by-step solution

Understanding Reaction Order

A reaction order is a term which describes how the concentration of a reactant affects the rate of a chemical reaction. In this case, we have two reactants A and B. The reaction order with respect to A or B gives information about their influence on the reaction rate. The overall reaction order is the sum of the reaction orders with respect to each individual reactant.

Determine the Reaction Order in A

From the given rate law: rate = [A][B]^3. The concentration of A is raised to the power of 1, as it's not explicitly written. So, the reaction order in A is 1.

Determine the Reaction Order in B

The concentration of B is raised to the power of 3, so the reaction order in B is 3.

Determine the Overall Reaction Order

The overall reaction order is the sum of the reaction orders with respect to each individual reactant. Overall reaction order = Reaction order in A + Reaction order in B = 1 + 3 = 4. So, the reaction order in A is 1, the reaction order in B is 3, and the overall reaction order is 4.

Key concepts

Rate Law

The rate law of a reaction expresses the relationship between the rate of a chemical reaction and the concentration of its reactants.
The rate law is often determined from experimental data and can be used to predict how changes in concentration will affect the reaction rate.
In a typical rate law expression, such as rate = \([A]^m[B]^n\), each concentration term is raised to a power known as its order.

• The exponents (m and n) are the reaction orders corresponding to reactants A and B,.
• The rate constant (k) is a proportionality factor that remains constant throughout the reaction.

Understanding the rate law allows chemists to control and optimize reactions by adjusting concentrations of reactants.
It also assists in uncovering the mechanism behind the reaction, revealing insights into the way molecules interact during the process.

Chemical Reaction Kinetics

Chemical reaction kinetics studies the rates of chemical processes and helps understand how different conditions affect the speed of reactions.
Key factors influencing reaction rates include concentrations, temperature, and presence of a catalyst.

• Concentration: Increasing the concentration of reactants generally increases the rate of reaction as more molecules or atoms are available to collide and thus react.
• Temperature: Higher temperatures usually lead to higher reaction rates as heat increases molecule speeds, boosting collision frequency and energy.
• Catalyst: Catalysts speed up reactions without being consumed, offering an alternative pathway with a lower activation energy.

Kinetics is essential for industrial processes, environmental studies, and developing new materials, providing a framework for predicting how systems behave under different conditions.
By mastering this concept, students can gain insights into real-world applications such as drug manufacturing, pollution control, and energy production.

Overall Reaction Order

The overall reaction order of a chemical reaction is the sum of the orders of all reactants present in the rate law.
This value gives a complete picture of how the reaction rate is influenced by the concentrations of all species involved.
For example, in the rate law rate = \([A]^1[B]^3\), the overall reaction order is calculated as 1 + 3 = 4.

• A reaction order of 0 signifies that the reaction rate is independent of the concentration of that reactant.
• A first-order reaction means that the rate changes linearly with the concentration of that reactant.
• Higher orders indicate a stronger influence on the rate by changes in concentration.

Understanding the overall reaction order is crucial for predicting how a reaction will respond to changes in concentrations and for designing experiments to test hypotheses about reaction mechanisms.
This knowledge enables the effective scaling of reactions from the laboratory to industrial production, ensuring efficient and safe chemical processes.