Chap 7: Energy, Rates, and Equilibrium: Study Notes for GOB Chemistry

Energy, Rates, and Equilibrium

Introduction

This chapter explores the energetic and kinetic aspects of chemical reactions, including how to predict spontaneity, understand reaction rates, and describe chemical equilibrium. Key concepts include enthalpy, entropy, free energy, activation energy, and Le Châtelier’s principle.

Energy Changes in Chemical Reactions

Bond Dissociation Energy

• Bond dissociation energy is the amount of energy required to break a specific chemical bond in an isolated gaseous molecule.

• Breaking bonds requires energy input; forming bonds releases energy.

• Bond dissociation energies indicate the strength of covalent bonds.

• Example: The triple bond in N2 has a bond dissociation energy of 226 kcal/mol, while the single bond in Cl2 is 58 kcal/mol.

Important Definitions

• Endothermic reaction: Absorbs heat; ΔH is positive.

• Exothermic reaction: Releases heat; ΔH is negative.

• Law of conservation of energy: Energy cannot be created or destroyed in any physical or chemical change.

• Heat of reaction (ΔH): The difference between energy absorbed in breaking bonds and energy released in forming bonds; also called enthalpy change.

• Enthalpy (H): A measure of energy in the form of heat.

Thermochemical Equations

• Thermochemical equations include energy changes in chemical equations.

• There are two ways to write them:

  • Include heat as a product or reactant.

  • Indicate ΔH value separately.

• Example (Exothermic):

  • $\mathrm{CH}_4(g) + 2\mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g) + 2\mathrm{H}_2\mathrm{O}(l) + 213\ \mathrm{kcal}$

  • $\Delta H = -213\ \mathrm{kcal/mol}$

• Example (Endothermic):

  • $\mathrm{N}_2(g) + \mathrm{O}_2(g) + 43\ \mathrm{kcal} \rightarrow 2\mathrm{NO}(g)$

  • $\Delta H = +43\ \mathrm{kcal/mol}$

Spontaneity and Free Energy

Free Energy Change (ΔG)

• Free energy change (ΔG): Determines whether a reaction is spontaneous.

• Spontaneous process: Proceeds without external influence; ΔG is negative (exergonic).

• Nonspontaneous process: Requires continuous external influence; ΔG is positive (endergonic).

• Equation:

  • $\Delta G = \Delta H - T\Delta S$

  • Where ΔH = enthalpy change, T = temperature in Kelvin, ΔS = entropy change.

• Be sure to use compatible units for ΔH and ΔS.

Entropy (ΔS)

• Entropy (S): A measure of molecular disorder; units are cal/(mol·K).

• Physical state and number of particles affect entropy.

• ΔS is positive when disorder increases (e.g., solid → liquid → gas, or fewer moles → more moles).

• ΔS is negative when disorder decreases.

Summary Table: Spontaneity Based on ΔH and ΔS

ΔH	ΔS	Spontaneity
− (favorable)	+ (favorable)	Always spontaneous
− (favorable)	− (unfavorable)	Spontaneous at low T
+ (unfavorable)	+ (favorable)	Spontaneous at high T
+ (unfavorable)	− (unfavorable)	Never spontaneous

Reaction Rates

Collision Theory and Activation Energy

• Reactant particles must collide with proper orientation and sufficient energy for a reaction to occur.

• Activation energy (Ea): Minimum energy required for productive collisions.

• Lower activation energy → faster reaction; higher activation energy → slower reaction.

Factors Affecting Reaction Rate

• Temperature: Higher temperature increases reaction rate (typically, a 10°C rise doubles the rate).

• Concentration: Higher reactant concentration increases collision frequency and reaction rate.

• Catalysts: Substances that speed up reactions by lowering activation energy without being consumed. Biological catalysts are called enzymes.

Summary Table: Effects on Reaction Rate

Condition	Change	Effect on Rate
Reactant concentration	Increase	Increases rate
Reactant concentration	Decrease	Decreases rate
Temperature	Increase	Increases rate
Temperature	Decrease	Decreases rate
Catalyst	Added	Increases rate

Chemical Equilibrium

Reversible Reactions and Equilibrium

• Reversible reactions can proceed in both forward and reverse directions.

• At equilibrium, the rates of forward and reverse reactions are equal, and concentrations of reactants and products remain constant.

Equilibrium Constant (K)

• For a general reaction: $aA + bB \rightleftharpoons mM + nN$

• The equilibrium constant is:

  • $K = \dfrac{[M]^m[N]^n}{[A]^a[B]^b}$

• K depends on temperature.

Interpreting K Values

K Value	Interpretation
> 1000	Reaction goes essentially to completion (mostly products)
1 – 1000	More products than reactants at equilibrium
0.001 – 1	More reactants than products at equilibrium
< 0.001	Essentially no reaction occurs (mostly reactants)

Le Châtelier’s Principle

Effect of Changing Conditions on Equilibrium

• When a stress (change in concentration, pressure, volume, or temperature) is applied to a system at equilibrium, the system shifts to relieve the stress.

• Concentration: Increasing reactant or product concentration shifts equilibrium to consume the added substance.

• Temperature: Increasing temperature favors the endothermic direction; decreasing temperature favors the exothermic direction.

• Pressure (for gases): Increasing pressure favors the side with fewer moles of gas; decreasing pressure favors the side with more moles of gas.

• Catalysts: Speed up attainment of equilibrium but do not affect the position of equilibrium or the value of K.

Summary Table: Effects on Equilibrium

Change	Effect on Equilibrium
Increase reactant concentration	Shifts toward products
Increase product concentration	Shifts toward reactants
Increase temperature	Favors endothermic reaction
Decrease temperature	Favors exothermic reaction
Increase pressure (gases)	Favors side with fewer moles of gas
Decrease pressure (gases)	Favors side with more moles of gas
Add catalyst	Equilibrium reached faster; K unchanged

Key Takeaways

• The strength of a covalent bond is measured by its bond dissociation energy.

• Exothermic reactions release heat (ΔH < 0); endothermic reactions absorb heat (ΔH > 0).

• Spontaneity depends on both enthalpy and entropy changes, as described by ΔG = ΔH – TΔS.

• Reaction rates depend on temperature, concentration, and catalysts.

• At equilibrium, forward and reverse reaction rates are equal; the equilibrium constant K indicates the favored direction.

• Le Châtelier’s principle predicts how changes in conditions affect equilibrium position.