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