Comprehensive Notes: Energy Changes, Hess’ Law, Entropy and Gibbs Free Energy

Energy Changes in Chemical Reactions

Exothermic Reactions
  • Definition: Reactants -> Products + energy

  • Example: CH4 + 2O2 -> CO2(g) + 2H2O(g) + energy

  • Reactions that release energy

  • Products have less chemical energy than reactants

  • Excess energy is released into surroundings, usually as heat

Endothermic Reactions
  • Definition: Reactants + energy -> Products

  • Example: CaCO3(s) + energy -> CO2(g) + CaO(s)

  • Reactions that absorb energy

  • Products have more chemical energy than reactants

  • Energy is absorbed from the surroundings

Thermochemical Equations
  • A chemical reaction which also shows the enthalpy change of the reaction

  • Enthalpy: heat content of a system

  • Exothermic: ΔH = -ve

    • Example: H2(g) + 1/2 O2(g) -> H2O(l) ΔH = -286 kJ/mol

    • 286 kJ of energy released per mole of hydrogen reacted

  • Endothermic: ΔH = +ve

    • Example: Dissolution (solvation) of glucose C6H12O6(s) -> C6H12O6(aq) ΔH = +11 kJ/mol

    • Endothermic; absorbs 11 kJ per mole of glucose dissolved

  • Note: "Δ" represents ‘change in’

Dissociation of Ions in Aqueous Solution
  • When an ionic substance dissolves in water, both the ionic lattice and hydrogen bonds between water molecules are broken

  • These are replaced by ion–dipole attractions between the ions and water molecules, leading to hydrated ions

  • Concept: Lattice energy + hydration energy determine overall dissolution enthalpy

Combustion as an Exemplar of Exothermic Reactions
  • Releases heat from the reaction

  • Typical complete combustion releases a large amount of energy per mole of fuel

Enthalpy Changes and Calorimetry

Enthalpy Changes (ΔH)
  • Enthalpy means heat content of a system

  • We can’t measure total heat energy of the system, but we can measure the change in enthalpy

  • Notation: ΔH or q used to express change in enthalpy (change in heat energy, in joules)

  • Formula: ΔH = Hproducts - Hreactants

  • Sign conventions

    • Exothermic: ΔH < 0

    • Endothermic: ΔH > 0

Factors Affecting Heat Exchange
  • Amount of substance (mass)

  • Temperature change of the system

  • Specific heat capacity of the substance

  • Different materials absorb/retain heat at different rates

  • Example: Bitumen heats up faster than cement, making barefoot exposure uncomfortable on hot days

Heat Capacity and Specific Heat Capacity
  • Heat capacity: Ability of a substance to absorb heat energy

    • Depends on: type of particles and mass

  • Specific heat capacity, c: Amount of heat required to raise the temperature of 1 g of a substance by 1 K

    • Unit: J g-1 K-1

    • Example: Castor oil has c = 1.8 J g-1K-1

    • To raise 1 g by 5 K requires 1.8 x 5 = 9 J

Calorimetry
  • Purpose: Measures heat changes in chemical reactions and physical processes

  • Typical calorimeter: Nested Styrofoam cups to insulate the reaction

  • Monitoring tools: Thermometer and glass stirrer

Dissolution Energy Details (Revisited)
  • Breaking attractions within water (dispersion, dipole-dipole, hydrogen bonding) requires energy

  • Breaking attractions between solute particles requires energy (ionic: electrostatic; covalent: intermolecular forces)

  • Re-establishing attraction between solute and solvent particles releases energy (hydration/solvation)

Energy Profile Diagrams, Activation Energy, and Catalysts

Activation Energy (Ea)
  • The energy barrier that must be overcome for a reaction to proceed

  • Illustrated in energy profile diagrams

  • Y in diagrams often represents activation energy; Z may denote the enthalpy change Delta H

Catalysts
  • A substance that speeds up a chemical reaction and is not consumed (remains unchanged at the end)

  • Provides an alternative pathway with a lower activation energy

  • Does not lower the activation energy of the reactants directly; rather, provides a lower-energy route

Modelling Catalyst Action (Conceptual)
  • Reactants break apart and form products on the surface of the catalyst

  • Example: Haber process (ammonia synthesis) is catalysed by iron oxide

    • Reaction: N2(g) + 3H2(g) --Fe2O3--> 2NH3(g)

  • Analogy: Catalyst provides an alternate route (a tunnel) that lowers the energy barrier without lowering the hill itself

Industrial Examples of Catalysis
  • Manufacture of ammonia: Iron catalyst (Fe or Fe2O3 as cited) enables N2(g) + 3H2(g) -> 2NH3(g)

  • Manufacture of nitric oxide (NO): First step uses platinum–rhodium catalyst

    • Reaction: 4NH3(g) + 5O2(g) -> 4NO(g) + 6H2O(g)

Enthalpy and Hess’ Law

Enthalpy Change in Terms of Breaking and Reforming Bonds
  • Delta H can be viewed as the energy required to break bonds minus the energy released when bonds form

  • General expression: ΔH = (energy to break bonds) - (energy released in forming bonds)

  • Example numerical scaffold (thermochemical equation):

    • If given: ΔH = 600 - 800 = -200 kJ/mol and Ea = 100 kJ/mol

    • Then for the reaction: Reactants -> Products Delta H = -200 kJ/mol

Hess’ Law and Enthalpy Change
  • Key idea: The enthalpy of any reaction with the same reactants and products is the same, regardless of the path (multiple-step vs single-step)

  • This allows calculation of ΔH for reactions that don’t occur under standard conditions by combining known steps

Bond Energy (Bond Enthalpy)
  • Bond energy: Energy needed to break 1 mol of a specified bond into gaseous atoms under standard conditions

  • Application: Enthalpy change via bond energies

  • Calculating enthalpy change from bond energies: Delta H = (sum of bond energies for bonds broken) - (sum of bond energies for bonds formed)

Hess’ Law Applications: Heat of Combustion and Bond Energies
  • Many combustion reactions do not occur under standard conditions; Hess’ law allows their enthalpies to be computed via formation enthalpies or bond energies

  • Standard enthalpy of combustion, Delta H°c: The enthalpy change when 1 mole of a compound is burned completely in O2 under standard conditions; it is always negative (exothermic)

  • Enthalpy of reaction can be calculated from heats of formation: Delta H° = sum Delta Hf°(products) - sum Delta Hf°(reactants)

Enthalpy and Hess’ Law in Biological and Industrial Processes
  • Respiration and photosynthesis (illustrative applications)

    • Enthalpy and bond energy considerations underpin biological energy transfers

    • Balanced accounts show how energy is captured and stored in chemical bonds

  • Standard enthalpy change of combustion (Delta H°c)

    • Definition: Enthalpy change when one mole of a substance is combusted in excess O2 under standard conditions

    • Always exothermic; Delta H°c is negative

  • Enthalpy of formation (Delta_f H°)

    • Enthalpy change when 1 mole of a compound is formed from its elements in their standard states

    • Delta_f H° data used to compute reaction enthalpies via formation enthalpies

Entropy and Gibbs’ Free Energy

Differences between Entropy and Enthalpy
  • Enthalpy of formation of an element is zero in its standard state

  • Enthalpy of formation of a compound is the energy change when 1 mole of the compound is formed from its elements in their standard state

  • A highly negative Delta_f H indicates a stable compound (requires a lot of energy to decompose)

  • A highly positive Delta_f H indicates a less stable compound (easily decomposed)

  • Entropy: Measures randomness or dispersion of energy/motion; higher disorder corresponds to higher S

  • Entropy is denoted by S

  • Entropy of solids < liquids < gases

  • Exact entropy of a system cannot be measured; changes in entropy (Delta S) can be measured

  • Typical expression: Delta S = Delta Q / T

  • In spontaneous processes, the universe's entropy increases

  • Examples of spontaneous processes: Melting of ice, cooling coffee

Third Law of Thermodynamics
  • A gas in a container: as temperature approaches 0 K, molecule motion slows

  • At 0 K, kinetic energy is zero

  • At absolute zero, a perfectly crystalline system has zero disorder; entropy is zero

Enthalpy vs. Entropy: Two Energy Considerations
  • Enthalpy relates to bonds and bond energies

  • Entropy relates to molecular arrangement and configurational possibilities

Predicting Entropy Changes from Balanced Equations
  • Entropy changes can be predicted when products are more disordered than reactants, when the number of product particles increases, and with higher temperatures or dissolution of solids into ions

  • Volume expansion in gases increases entropy; concentration effects can also influence Delta S

Standard Entropies (S°) and Standard Conditions
  • S° is defined for substances in their standard states

  • Example standard entropies (selected values):

    • S°(s) = 71 J mol-1 K-1 (solid S)

    • S°(l) = 114 J mol-1 K-1 (liquid S)

    • S°(g) = 257 J mol-1 K-1 (gas S) [for sulfur trioxide data, illustrative]

Example: Determining Delta S° for a Reaction from Standard Entropies
  • Reaction: C(s) + O2(g) -> CO2(g)

  • Given:

    • S°(C) = 158.2 J mol-1 K-1

    • S°(O2) = 205.0 J mol-1 K-1

    • S°(CO2) = 213.8 J mol-1 K-1

  • Calculation: Delta S° = sum S°products - sum S°reactants = (1 x S°(CO2)) - [1 x S°(C) + 1 x S°(O2)]

    • = 213.8 - (158.2 + 205.0) = -149.4 J mol-1 K-1

Gibbs Energy and Spontaneity
  • Gibbs energy change: Delta G° = Delta H° - T Delta S°

  • If Delta G° < 0: spontaneous

  • If Delta G° = 0: at equilibrium

  • If Delta G° > 0: non-spontaneous

Temperature Effects on Spontaneity
  • Increasing temperature can increase spontaneity if the reaction is endothermic (Delta H° > 0) and Delta S° > 0

  • Decreasing temperature can increase spontaneity if the reaction is exothermic (Delta H° < 0) and Delta S° < 0

  • The balance between enthalpy and entropy drivers determines the overall spontaneity at a given temperature

Qualitative and Quantitative Problem Snapshots
  • Qualitative: Determine whether entropy change Delta S° is positive, negative, or zero for given reactions

  • Quantitative: Use standard entropies to compute Delta S° and then apply Delta G° = Delta H° - TDelta S° to discuss spontaneity at a given T

Notation Recap
  • Delta H°: Standard enthalpy change

  • Delta S°: Standard entropy change

  • Delta G°: Standard Gibbs free energy change

  • S°: Standard molar entropy; units J mol-1 K-1

Applications and Worked Examples

Worked Example: Standard Entropy Change From Formation of CO2
  • Reaction: C(s) + O2(g) -> CO2(g)

  • Given: S°(C) = 158.2 J mol-1 K-1; S°(O2) = 205.0 J mol-1 K-1; S°(CO2) = 213.8 J mol-1 K-1

  • Calculation: Delta S° = S°products - S°reactants = (1 x 213.8) - (1 x 158.2 + 1 x 205.0) = -149.4 J mol-1 K-1

Conceptual Reminder
  • Standard reference values and tables underpin enthalpy and entropy calculations; many real problems require combining