Problem 128 - Introductory Chemistry Atoms First

Question

Write the general rate law for each reaction, using \(x\) and \(y\) exponents as orders: (a) \(2 \mathrm{NO}+\mathrm{O}_{2} \rightarrow 2 \mathrm{NO}_{2}\) (b) \(2 \mathrm{H}_{2} \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}\)

Step-by-Step Solution

Answer

(a) \(Rate = k [NO]^x [O_2]^y\) (b) \(Rate = k [H_2O_2]^x\)

Step 1: a) Writing the rate law for 2 NO + O2 → 2 NO2

For the given reaction, we will be using the concentration of reactants: NO and O2. The rate law for a reaction involves the rate constant k multiplied by the concentrations of reactants, raised to the power of their respective orders in the reaction. Using x and y as the exponents, we have: \(Rate = k [NO]^x [O_2]^y\)

Step 2: b) Writing the rate law for 2 H2O2 → 2 H2O + O2

For this reaction, we will be using the concentration of the reactant H2O2. Following the same process as before and using x as the exponent for the concentration of H2O2, we have the rate law as: \(Rate = k [H_2O_2]^x\)

Key Concepts

Reaction Order

Understanding the reaction order is crucial in chemical kinetics, as it determines how the concentration of a reactant affects the rate of the reaction. In a chemical reaction, the reaction order is typically represented by the exponents in the rate law. For instance, in the reaction between NO and O₂, the order with respect to NO is denoted by the exponent \(x\) while the order with respect to O₂ is denoted by \(y\).

• The overall reaction order is the sum of these exponents.
• Individual orders provide insight into each reactant's influence on the rate.

Since the reaction order is determined experimentally, it is not necessarily directly related to the stoichiometric coefficients.
Identifying the reaction order helps predict how changes in concentration affect the rate, which is essential for controlling industrial and laboratory reactions.

Chemical Kinetics

Chemical kinetics is the field of chemistry concerned with the speed, or rate, at which chemical reactions occur. It not only involves the study of how different conditions like concentration and temperature affect reaction rates but also provides insights into the reaction mechanisms.

• Kinetics helps chemists understand how fast reactions proceed.
• It explores factors such as pressure, temperature, and reactant concentration, which all play roles in affecting the rate.

Studying kinetics can shed light on the steps, or the mechanism, a reaction undergoes from reactants to products, which is fundamental for developing new chemical processes.
This domain is vast and applies to various fields, from pharmaceuticals to environmental science, aiding in the design and analysis of reactions.

Rate Constant

The rate constant, represented as \(k\) in the rate law, is a crucial factor in chemical kinetics that mathematically ties the rate of a reaction to the concentration of reactants. It is a unique value for each reaction at a given temperature, influenced by catalysts and environmental factors.

• The rate constant is specific to the temperature and must be determined experimentally.
• Large rate constants indicate faster reactions under given conditions.

In the reaction laws provided for NO and H₂O₂, \(k\) serves as a multiplier in the rate equation.
It quantitively connects how concentration changes translate into reaction rate changes, allowing predictions on how quickly a reaction might proceed under specific conditions.

Reactant Concentration

Reactant concentration plays a pivotal role in defining the reaction rate, as elucidated by the rate law. The term '[reactant]' signifies the concentration of the reactant, which is raised to an exponent that symbolizes its order in the reaction. This relationship exemplifies how kinetic studies delve into the impact of concentration on rate dynamics.

• Higher concentrations of reactants typically increase reaction rates.
• Changes in concentration can dramatically affect the overall speed of the reaction.

In the reactions given, changes in NO or H₂O₂ concentration would directly influence how fast the product is formed.
This principle is integral in processes such as designing reactors where precise control over reactant concentrations can optimize the efficiency and yield of chemical reactions.