Chemical Kinetics

Reaction Rates and Rate Laws

Chemical kinetics is the study of the speed (rate) at which chemical reactions occur and the factors that affect these rates. The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants.

• Rate of Reaction: The change in concentration of a reactant or product per unit time, usually expressed in M/s (moles per liter per second).

• General Rate Law: For a reaction aA + bB → products, the rate law is , where k is the rate constant, and m and n are the reaction orders with respect to A and B.

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

• Example: For 2NO(g) + Cl2(g) → 2NOCl(g), if the rate law is , the reaction is second order in NO and first order in Cl2, third order overall.

Determining Rate Laws from Experimental Data

• Compare initial rates from experiments where only one reactant concentration changes to determine the order with respect to each reactant.

• Use the method of initial rates to solve for the rate constant k.

• Example Table:

• From the table, doubling [A] doubles the rate (first order in A), doubling [B] quadruples the rate (second order in B).

Integrated Rate Laws and Half-Life

• First-Order Reactions: or

• Half-life (t1/2): For first-order,

• Second-Order Reactions:

• Zero-Order Reactions:

• Example: If a first-order reaction has k = 7.02 × 10-3 s-1, the half-life is s.

Arrhenius Equation and Activation Energy

• The Arrhenius equation relates the rate constant k to temperature T and activation energy Ea:

• Where A is the frequency factor, R is the gas constant (8.314 J/mol·K), and T is temperature in Kelvin.

• Taking the natural log:

• Plotting vs gives a straight line with slope .

• Example: If the slope of the Arrhenius plot is -10759, then J/mol = 89.5 kJ/mol.

Chemical Equilibrium

Equilibrium Constant Expressions

At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. The equilibrium constant (K) quantifies the ratio of product and reactant concentrations at equilibrium.

• For a general reaction: aA + bB ⇌ cC + dD

• Kp is used for gases, relating partial pressures.

• Example: For 2NO2(g) ⇌ 2NO(g) + O2(g):

Le Châtelier’s Principle

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

• Changes in concentration, pressure, or temperature can shift the equilibrium position.

• Example: Increasing the concentration of a reactant shifts equilibrium toward products.

Calculating Equilibrium Concentrations

• Set up an ICE (Initial, Change, Equilibrium) table to track concentrations.

• Solve for unknowns using the equilibrium constant expression.

• Example Table:

Predicting Direction of Shift

• Compare the reaction quotient Q to K:

• If Q < K, the reaction proceeds forward (toward products).

• If Q > K, the reaction proceeds in reverse (toward reactants).

Acids and Bases

Definitions of Acids and Bases

• Arrhenius: Acids produce H+ in water; bases produce OH-.

• 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:

• HCl, HBr, HI, HNO3, HClO3, HClO4, H2SO4

• They ionize completely in aqueous solution.

Conjugate Acid-Base Pairs

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

• Example: H2SO4 (acid) → HSO4- (conjugate base)

Naming Acids

• Acids containing -ate anions become -ic acids (e.g., HNO3 is nitric acid).

• Acids containing -ite anions become -ous acids (e.g., HNO2 is nitrous acid).

Radioactive Decay and Half-Life

Carbon-14 Dating

• Radioactive isotopes decay at a constant rate, characterized by their half-life.

• The age of ancient objects can be estimated by measuring the remaining fraction of carbon-14.

• Decay Formula: , where k is the decay constant.

• Half-life:

Additional info:

• Some questions reference specific calculations or require ICE tables, which are standard tools in equilibrium problems.

• Arrhenius plots are used to determine activation energy graphically.

• Mechanisms and rate-determining steps are important in understanding how reactions proceed at the molecular level.