Reaction Kinetics

Factors Affecting Reaction Rates

Reaction rates describe how quickly reactants are converted into products in a chemical reaction. Several factors influence the rate at which reactions occur:

• Temperature: Increasing temperature generally increases reaction rates by providing more kinetic energy to the reacting molecules, leading to more frequent and energetic collisions.

• Concentration: Higher concentrations of reactants lead to more collisions per unit time, thus increasing the reaction rate.

• Surface Area: For reactions involving solids, increasing the surface area (e.g., by grinding a solid into a powder) exposes more particles to react, increasing the rate.

• Catalyst: Catalysts speed up reactions by providing an alternative pathway with a lower activation energy, without being consumed in the reaction.

Expressing and Calculating Reaction Rates

The rate of a chemical reaction can be expressed as the change in concentration of a reactant or product per unit time:

• Average Rate: (for reactant A)

• Instantaneous Rate: The rate at a specific moment, found by taking the derivative of concentration with respect to time.

Example: If [A] decreases from 0.50 M to 0.30 M in 20 seconds, the average rate is:

Rate Laws and Reaction Order

A rate law expresses the relationship between the rate of a reaction and the concentration of its reactants. The general form is:

where k is the rate constant, and m and n are the orders with respect to reactants A and B, respectively.

• Overall Order: The sum of the exponents (m + n).

Example: If doubling [A] doubles the rate, and doubling [B] quadruples the rate, the rate law is (first order in A, second order in B, third order overall).

Determining Rate Laws and Orders

• Use experimental data to see how changes in concentration affect the rate.

• Compare rates from different experiments to deduce the order with respect to each reactant.

Integrated Rate Laws and Calculations

Integrated rate laws relate concentration and time for reactions of different orders:

• Zero Order:

• First Order:

• Second Order:

Half-life (t1/2):

• First Order:

• Second Order:

• Zero Order:

Reaction Mechanisms and Rate Laws

A reaction mechanism is a sequence of elementary steps that describes how a reaction occurs at the molecular level. Key terms include:

• Elementary Step: A single step in a mechanism, with its own molecularity.

• Intermediate: A species produced in one step and consumed in another.

• Rate-Determining Step: The slowest step, which controls the overall rate.

The rate law for the overall reaction is determined by the rate-determining step.

Chemical Equilibrium

Equilibrium Expressions

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal. The equilibrium constant expression for a reaction:

• For :

Only gases and aqueous species are included; pure solids and liquids are omitted.

Calculations Using ICE Tables

ICE (Initial-Change-Equilibrium) tables help organize data for equilibrium calculations:

• Initial: Initial concentrations of reactants and products.

• Change: The change in concentrations as the system moves toward equilibrium.

• Equilibrium: The concentrations at equilibrium.

Example: For , if [A]0 = 1.0 M, [B]0 = 0, and x mol/L reacts:

Reaction Quotient (Q) and Direction of Reaction

The reaction quotient (Q) is calculated like K but with initial (not equilibrium) concentrations. Comparing Q and K predicts the direction the reaction will proceed:

• If Q < K: Reaction proceeds forward (toward products).

• If Q > K: Reaction proceeds in reverse (toward reactants).

• If Q = K: System is at equilibrium.

Le Chatelier’s Principle

Le Chatelier’s Principle states that if a system at equilibrium is disturbed, it will shift to counteract the disturbance and restore equilibrium. Disturbances include changes in concentration, pressure, or temperature.

• Adding Reactant: Shifts equilibrium toward products.

• Removing Product: Shifts equilibrium toward products.

• Increasing Pressure (for gases): Shifts toward the side with fewer moles of gas.

• Changing Temperature: For endothermic reactions, increasing temperature shifts toward products; for exothermic, toward reactants.

Common Equations Provided

Additional info: The quadratic formula is often used in equilibrium calculations when the equilibrium expression leads to a quadratic equation in terms of concentration.