Write the reaction rate expressions for the following reactions in terms of the disappearance of the reactants and the appearance of products: (a) \(2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)\) (b) \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)

Understanding chemical kinetics is crucial for grasping how reaction rates are influenced by various factors. Chemical kinetics delves into the speed or rate at which chemical reactions occur and the mechanisms by which reactions proceed.

Within this field, it's vital to consider the energy needed to initiate a reaction, known as activation energy, and how temperature, catalysts, and concentration of reactants can affect the reaction rate. The rate of a reaction can tell us a lot about the mechanism, allowing chemists to optimize conditions for industrial processes or to understand natural phenomena. To quantify these rates, we use the concept of the reaction rate expression, which involves calculus to measure the change in concentration of reactants or products over time.

Stoichiometry is the mathematical relationship between the amounts of reactants and products in a chemical reaction. It's based on the law of conservation of mass, which states that in a chemical reaction, the total mass of the reactants must equal the total mass of the products.

Balancing Equations

At the core of stoichiometry is the balanced chemical equation, which serves as a recipe for the reaction. To balance an equation, we must ensure that the same number of atoms of each element are present on both sides of the reaction. This balance is reflected in the stoichiometric coefficients, which are the numbers placed in front of the chemical formulas.

Relation to Reaction Rates

These coefficients also play a central role in the calculation of reaction rates, as seen in the given exercise. They tell us the proportional rates at which compounds react and form products. For instance, the coefficient '2' in front of \( \mathrm{H}_{2} \) in reaction (a) means that two moles of hydrogen gas are consumed for every mole of oxygen gas used to form water.

Reaction rates are a fundamental part of understanding chemical reactions. They indicate how quickly reactants are transformed into products over a certain period.

A reaction's rate can be expressed in terms of the rate of disappearance of reactants or the rate of appearance of products. This rate is generally given as a negative value for reactants because they are being consumed, and as a positive value for products because they are being created.

When determining the reaction rate expression, the stoichiometric coefficients must be taken into account to ensure the rate is consistent with the reaction stoichiometry. In the solutions provided for reactions (a) and (b), the reaction rate expressions illustrate how the coefficients from the balanced equations are inverted and applied to each reactant and product, normalizing the rates of change. This approach highlights the stoichiometrically balanced view of the reaction, linking the disappearance of reactants to the appearance of products in a quantitative manner.