Chemical Kinetics

Reaction Rates and Rate Laws

Chemical kinetics is the study of the speed at which chemical reactions occur and the factors that affect these rates. The rate of a reaction is defined as the change in concentration of a reactant or product per unit time.

• Rate Law: An equation that relates the reaction rate to the concentrations of reactants, often in the form where is the rate constant, and , are the reaction orders with respect to each reactant.

• Order of Reaction: The exponent of a reactant in the rate law; the overall order is the sum of all exponents.

• Example: For the reaction , the rate law might be .

Determining Reaction Order

The order of a reaction with respect to each reactant can be determined experimentally by measuring how the rate changes as the concentration of each reactant is varied.

• Zero order: Rate does not depend on the concentration of the reactant.

• First order: Rate is directly proportional to the concentration.

• Second order: Rate is proportional to the square of the concentration.

Integrated Rate Laws and Half-Life

Integrated rate laws relate the concentration of reactants to time. The half-life () is the time required for half of a reactant to be consumed.

• First-order: ,

• Second-order: ,

• Zero-order: ,

Arrhenius Equation and Activation Energy

The Arrhenius equation describes how the rate constant () depends on temperature and activation energy ():

• Where is the frequency factor, is the gas constant, and is temperature in Kelvin.

• Plotting vs yields a straight line with slope .

Reaction Mechanisms and Rate-Determining Step

A reaction mechanism is a sequence of elementary steps that describes the pathway from reactants to products. The slowest step is the rate-determining step.

• Mechanisms must be consistent with the observed rate law.

• Intermediates are species produced and consumed during the reaction.

Chemical Equilibrium

Equilibrium Constant Expressions

At equilibrium, the rates of the forward and reverse reactions are equal. The equilibrium constant () expresses the ratio of product to reactant concentrations at equilibrium.

• For a general reaction :

• is used for gases and relates to by , where is the change in moles of gas.

Le Châtelier's Principle

If a system at equilibrium is disturbed, it will shift to counteract the disturbance and restore equilibrium.

• Increasing concentration of reactants shifts equilibrium toward products.

• Increasing pressure (by decreasing volume) shifts equilibrium toward the side with fewer moles of gas.

• Increasing temperature favors the endothermic direction.

Calculating Equilibrium Concentrations

To find equilibrium concentrations, set up an ICE (Initial, Change, Equilibrium) table and solve for unknowns using the equilibrium constant expression.

Free Energy and Equilibrium

The relationship between free energy and equilibrium is given by:

• If , is negative (spontaneous forward reaction).

• If , is positive (non-spontaneous forward reaction).

Acids and Bases

Definitions of Acids and Bases

• Arrhenius: Acids produce in water; bases produce .

• Brønsted-Lowry: Acids are proton donors; bases are proton acceptors.

• Lewis: Acids accept an electron pair; bases donate an electron pair.

Strong Acids

There are seven common strong acids that completely ionize in water:

• Hydrochloric acid ()

• Hydrobromic acid ()

• Hydroiodic acid ()

• Nitric acid ()

• Perchloric acid ()

• Sulfuric acid ()

• Chloric acid ()

Conjugate Acids and Bases

When an acid donates a proton, it forms its conjugate base; when a base accepts a proton, it forms its conjugate acid.

• Example: (acid) (conjugate base)

• Example: (base) (conjugate acid)

Radioactive Decay and Half-Life Calculations

Radioactive Decay

Radioactive isotopes decay at a constant rate characterized by their half-life (). The amount remaining after time is given by:

• Example: Carbon-14 dating is used to estimate the age of organic materials.

Sample Table: Rate Law Determination

The following table summarizes how initial rates are used to determine reaction order:

Main Purpose: This table is used to determine the order of reaction with respect to each reactant by comparing how the rate changes as concentrations are varied.

Additional info:

• Some questions reference specific calculations (e.g., equilibrium concentrations, rate constants) that require ICE tables or use of the Arrhenius equation.

• For equilibrium problems, always check if the reaction is at equilibrium by comparing the reaction quotient to .

• For radioactive decay, logarithmic calculations may be needed to solve for time or remaining quantity.