Rate Law (Simplified): Videos & Practice Problems

Rate law expresses the reaction rate as a function of reactant concentrations, rate constant, and reaction orders, focusing solely on reactants. The rate constant (k) links rate to concentration, while reaction orders (exponents) indicate how concentration changes affect rate. Concentrations are measured in molarity (M), and changes are denoted by Δ (final minus initial). The general rate law formula is rate=kAxBy, where A and B are reactants, and x and y are their respective orders. This concept is fundamental in understanding reaction kinetics and activation energy.

Rate Law (Simplified) Concept 1

Rate law is a fundamental concept in chemical kinetics that describes how the rate of a reaction depends on the concentration of its reactants. It is expressed as an equation relating the reaction rate to the concentrations of reactants, a rate constant, and the reaction order for each reactant. The change in concentration is denoted by the symbol Δ, which represents the difference between the final and initial concentrations, typically measured in molarity (M).

The rate constant, represented by k, is a proportionality constant that connects the reaction rate to the concentrations of the reactants. Reaction orders, indicated as exponents in the rate law expression, show how sensitively the rate depends on each reactant’s concentration. These orders are determined experimentally and are not necessarily related to the stoichiometric coefficients in the balanced chemical equation.

Importantly, the rate law focuses exclusively on reactants and does not include products. For a reaction involving two reactants, A and B, the rate law can be written as:

\[ \text{rate} = k [A]^x [B]^y \]

Here, [A] and [B] represent the molar concentrations of reactants A and B, while x and y are their respective reaction orders. If there is only one reactant, the rate law simplifies to:

\[ \text{rate} = k [A]^x \]

For reactions with more reactants, additional terms such as [C]^z can be included, where z is the reaction order for reactant C. Understanding the rate law allows prediction of how changes in reactant concentrations affect the speed of a chemical reaction, which is essential for controlling reaction conditions in both laboratory and industrial settings.

Rate Law (Simplified) Example 1

The rate law for a chemical reaction expresses how the reaction rate depends on the concentration of reactants. For the reaction where two moles of nitrogen monoxide (NO) react with one mole of oxygen gas (O₂) to form nitrogen dioxide (NO₂), the rate law focuses solely on the reactants' concentrations. It is generally written as:

\[ \text{Rate} = k[\text{NO}]^x[\text{O}_2]^y \]

Here, k is the rate constant, which is specific to the reaction at a given temperature. The exponents x and y represent the reaction orders with respect to NO and O₂, respectively. These orders indicate how changes in the concentration of each reactant affect the overall reaction rate. Importantly, the reaction orders are not necessarily equal to the stoichiometric coefficients from the balanced chemical equation and must be determined experimentally.

In summary, the rate law for this reaction depends on the concentrations of nitrogen monoxide and oxygen gas raised to their respective reaction orders, multiplied by the rate constant. Products do not appear in the rate law expression because the rate is determined by the reactants' concentrations.

Rate law for the given reaction is Rate = k[NO₂]²[Cl₂].
NO₂(g) + Cl₂(g) ⟶ NOCl(g) + ClO(g)
What effect would tripling the concentration of NO₂ have on the rate, if k = 7.2 × 10^-3 M^-2s^-1, at 35º C?

• A. Increase by 3
• B. Increase by 6
• C. Increase by 9
• D. No change

Answer: (C)

Here’s what students ask on this topic:

What is the rate law and how does it relate to reactant concentrations?

The rate law is an expression that relates the rate of a chemical reaction to the concentrations of its reactants. It shows how the reaction rate depends on the change in concentration of reactants, a rate constant, and the reaction order for each reactant. The general form for a reaction with reactants A and B is given by the equation: $\mathrm{rate}=k{A}_x{B}_y$, where $k$ is the rate constant, and $x$ and $y$ are the reaction orders determined experimentally. These exponents indicate how changes in reactant concentrations affect the rate. Importantly, the rate law only considers reactants, ignoring products.

How is the rate constant (k) different from reaction orders in the rate law?

The rate constant, denoted as $k$, is a proportionality constant that links the reaction rate to the concentrations of reactants in the rate law. It is specific to a particular reaction at a given temperature and does not change with reactant concentration. On the other hand, reaction orders (exponents like $x$ and $y$) indicate how sensitive the reaction rate is to changes in the concentration of each reactant. These orders are determined experimentally and can be zero, fractional, or whole numbers. While $k$ affects the overall speed of the reaction, reaction orders describe the relationship between concentration changes and rate changes.

Why does the rate law only include reactants and not products?

The rate law focuses exclusively on reactants because the rate of a chemical reaction depends on how quickly reactants are consumed to form products. The concentrations of reactants directly influence the frequency of effective collisions that lead to product formation. Products, however, do not affect the initial rate of the forward reaction and are therefore excluded from the rate law expression. This simplification helps in analyzing reaction kinetics by concentrating on the factors that control the reaction rate at the start.

How are reaction orders determined experimentally?

Reaction orders are determined through a series of experiments where the concentrations of reactants are varied systematically, and the resulting reaction rates are measured. By analyzing how changes in concentration affect the rate, scientists can deduce the exponents (reaction orders) in the rate law. For example, if doubling the concentration of reactant A doubles the rate, the order with respect to A is one. If the rate quadruples, the order is two. These experiments are essential because reaction orders cannot be predicted solely from the balanced chemical equation; they must be found experimentally.

What does the general rate law expression look like for a reaction with multiple reactants?

For a reaction involving multiple reactants, the general rate law expression is written as: $\mathrm{rate}=k{A}_x{B}_y{C}_z$, where $A$, $B$, and $C$ represent the concentrations of the reactants, $k$ is the rate constant, and $x$, $y$, and $z$ are the reaction orders for each reactant. These orders indicate how each reactant's concentration affects the overall reaction rate. This expression can be extended to any number of reactants by including additional terms with their respective reaction orders.