Question

Explain how the exponents in the rate equation for a chemical reaction relate to the coefficients in the chemical equation.

Short answer

The exponents in the rate equation represent the reaction orders, which show the dependence of the reaction rate on the concentrations of the reactants. These exponents are determined experimentally and may not always match the stoichiometric coefficients in the chemical equation. However, in the case of elementary reactions (single-step reactions), the exponents usually correlate with the stoichiometric coefficients. For example, considering an elementary reaction \(2A + B \rightarrow C\), the rate equation would be \(Rate = k [A]^2[B]^1\), where the exponents match the stoichiometric coefficients.

Step-by-step solution

Definition of Rate Equation

A rate equation is a mathematical expression that describes the rate of a chemical reaction as a function of the concentrations of reactants (and sometimes products). It is usually in the form: Rate = k \([A]^m[B]^n...\), where 'Rate' represents the rate of the reaction, 'k' is the reaction rate constant, '[A]' and '[B]' are the concentrations of the reactants A and B respectively, and 'm' and 'n' are the exponents, also known as the reaction orders with respect to A and B.

Definition of Chemical Equation

A chemical equation is a symbolic representation of a chemical reaction showing the reactants and products involved, as well as their relative proportions. It is usually written as: aA + bB → cC + dD, where 'A' and 'B' are the reactants, 'C' and 'D' are the products, and 'a', 'b', 'c', and 'd' are the stoichiometric coefficients representing the number of molecules or moles of each species participating in the reaction.

Relating Exponents in the Rate Equation to the Coefficients in the Chemical Equation

It's essential to note that the exponents (reaction orders) in the rate equation are not always equal to the stoichiometric coefficients in the chemical equation. They are determined experimentally and represent the dependence of the reaction rate on the concentrations of reactants, while the stoichiometric coefficients are determined by the chemical equation's balanced form. However, in the case of elementary reactions (single-step reactions that occur in one collision or interaction), the exponents in the rate equation often match the stoichiometric coefficients in the chemical equation. In these cases, the reaction orders represent the molecularity (the number of reactant molecules involved) of the elementary reaction. For example, let's look at the elementary reaction: \(2A + B \rightarrow C\) The reaction order with respect to A would be 2 (since there are two molecules of A involved), and the reaction order concerning B would be 1 (since there is only one molecule of B involved). Therefore, the rate equation for this elementary reaction would be: Rate = k \([A]^2[B]^1\) In summary, the exponents in the rate equation may sometimes correlate with the stoichiometric coefficients in the chemical equation for elementary reactions, but the reaction orders are experimentally determined and may not always match the stoichiometric coefficients for multi-step reactions.

Key concepts

Understanding the Rate of Chemical Reactions

The rate of a chemical reaction is a measure of how quickly reactants are transformed into products. It is influenced by several factors, including reactant concentrations, temperature, presence of a catalyst, and the physical state of the reactants.

At its core, the rate of a reaction tells us the speed at which a chemical change occurs. This is typically measured in terms of a change in concentration per unit time, such as moles per liter per second (mol/L/s). A higher rate means the reaction proceeds more quickly, while a lower rate indicates a slower process.

Generally, the rate of a reaction increases with higher concentrations of reactants. This is because more reactant molecules are available to collide and form products. However, this relationship is not necessarily direct or simple. It depends on the reaction order with respect to each reactant, which is expressed as an exponent in the rate equation. It's important for students to grasp that these exponents can only be determined experimentally and do not simply reflect the stoichiometric coefficients from the chemical equation.

The Significance of Stoichiometric Coefficients

Stoichiometric coefficients are numbers used in a balanced chemical equation to represent the relative amounts of reactants and products involved in the reaction. They are essential for understanding the proportions in which substances react and form products.

To apply this concept, consider the equation aA + bB → cC + dD. The lowercase letters (a, b, c, d) are the stoichiometric coefficients, and they indicate, for example, that 'a' moles of substance A react with 'b' moles of substance B to form 'c' moles of substance C and 'd' moles of substance D.

The key takeaway here is that stoichiometric coefficients are fundamental for quantitative analysis in chemistry, allowing chemists to calculate the amounts of reactants needed and products formed. They stem from the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Thus, balancing equations is a critical skill for anyone studying chemistry.

Deciphering Reaction Order

Reaction order is a term used to describe the power to which the concentration of a reactant is raised in the rate equation, reflecting how the rate depends on the concentration of that reactant. This is pivotal in determining the relationship between the rate and the concentrations of individual reactants.

The overall reaction order is the sum of the exponents of the concentrations of the reactants in the rate equation. If the reaction is first-order with respect to a reactant A, it means that the rate is directly proportional to the concentration of A. A second-order reaction implies that the rate is proportional to the square of the concentration of A.

Why does reaction order matter?

Knowing the reaction order is crucial for predicting how a change in concentration will affect the reaction rate. For instance, doubling the concentration of a reactant in a first-order reaction doubles the rate, while in a second-order reaction, the rate would quadruple. It is vital to emphasize that the reaction order is not necessarily related to the stoichiometric coefficients in the chemical equation; it must be determined through experimental observation and analysis.