Energetics — IAL Edexcel Modular (Chemistry) Revision Notes & Topical Questions

Section 1 of 27Enthalpy changes and level diagrams

Enthalpy change, ΔH

Enthalpy change, ΔH the heat energy change at constant pressure, measured in kJ mol^-1

• It can be positive or negative.
• The system is the reacting substances and the surroundings is everything else.

Exothermic reaction

• Exothermic reaction products have less enthalpy than reactants and heat passes to the surroundings
• The temperature of the surroundings rises and ΔH is negative.

Endothermic reaction

• Endothermic reaction products have more enthalpy than reactants and heat is absorbed from the surroundings
• The temperature of the surroundings falls and ΔH is positive.

State symbols

• State symbols must be given,
• because a change of state can alter enthalpy changes greatly,
  • as with NaCl(s) → Na⁺(aq) + Cl⁻(aq) at +4 kJ mol^-1 but NaCl(g) → Na⁺(g) + Cl⁻(g) at +500 kJ mol^-1

Section 2 of 27Reaction profile diagrams

Enthalpy level diagrams

• Enthalpy level diagrams show only the levels of the reactants and the products
• Activation energy is not shown.

Reaction profile diagrams

• Reaction profile diagrams also show the activation energy and the transition state
• Activation energy, E_a = the minimum energy needed for reactant molecules to collide successfully and start the reaction.
• The transition state is the peak, where bonds are partly broken and partly formed, and it cannot be isolated.

Exothermic profiles

• Exothermic profiles reactants are higher than products, so E_a is usually lower

Endothermic profiles

• Endothermic profiles reactants are further from the transition state, so E_a is usually higher

Feasibility

• Feasibility an exothermic reaction is thermodynamically possible, but if its rate is too slow it may not occur
• Such a reaction is kinetically controlled.

Section 3 of 27Standard enthalpy changes

• Standard conditions
  • a pressure of 100 kPa, a temperature of 298 K and each substance in its standard state
  • The symbol ⦵ shows standard conditions.

Enthalpy change	Definition
Reaction, ΔrH	The enthalpy change when the amounts shown in the balanced equation react
Formation, ΔfH	The enthalpy change when one mole of a compound forms from its elements in their standard states
Combustion, ΔcH	The enthalpy change when one mole of a substance burns completely in oxygen
Neutralisation, ΔneutH	The enthalpy change when one mole of water forms from the reaction of an acid with an alkali
Atomisation, ΔatH	The enthalpy change when one mole of gaseous atoms forms from an element in its standard state

Elements

• Elements the standard enthalpy of formation of an element in its standard state is zero

Scaling

• Scaling enthalpy changes are multiplied by the number of moles in the equation

Section 4 of 27Calorimetry for reactions in solution

• Principle
  • carry out the reaction with an excess of one reagent in an insulated vessel, such as a polystyrene cup, and record the temperature change

1

Measure a known volume of solution into the cup and record its temperature at regular intervals.

2

Add the second reagent at a precisely noted time without recording that reading, stirring throughout.

3

Continue recording the temperature at regular intervals.

4

Plot temperature against time and extrapolate the cooling section back to the time of mixing to find ΔT.

5Calculate q

Calculate q mcΔT, with m the mass of solution, c = 4.18 J g^-1 K^-1 and ΔT the temperature change.

6Convert q to kJ and divide by the moles of the limiting reagent to get ΔH

−q ÷ n.

Assumptions

• Assumptions the solution has the specific heat capacity and density of water
• The heat capacity of the container is ignored.
• The reaction is complete and heat losses are negligible.

Reason for extrapolation

• Reason for extrapolation the maximum temperature is never reached in a slow reaction because of heat loss

Sign

• Sign a temperature rise means the reaction is exothermic, so ΔH is negative, and a temperature fall gives a positive ΔH

Section 5 of 27Calorimetry for combustion

Heat a known mass of water in a metal (copper) calorimeter using a spirit burner.

Record the starting and final temperatures of the water.

Weigh the burner before and after to find the mass of fuel burned.

Calculate q

Calculate q mcΔT for the water and the moles of fuel burned from its mass and molar mass.

Divide q by the moles of fuel for Δ_cH, giving a negative value.

• Sources of error
  • heat loss to the surroundings and calorimeter, and incomplete combustion
  • Heat loss is reduced by placing the calorimeter close to the flame, using a lid and using draught shields.
  • Experimental values are less exothermic than data-book values.

Section 6 of 27Hess's law and energy cycles

1Hess's law

Hess's law the total enthalpy change of a reaction is independent of the route, provided the initial and final conditions are the same

• It follows from conservation of energy.
• It is used for enthalpy changes that cannot be measured directly, such as 3C(s) + 4H₂(g) → C₃H₈(g).

2Using formation data

• Δ_rH = ΣΔ_fH(products) − ΣΔ_fH(reactants)
• Draw the elements at the bottom with arrows up to the compounds, multiply by the moles,
  • and reverse the sign of any arrow followed against its direction.

3Using combustion data

• Δ_rH = ΣΔ_cH(reactants) − ΣΔ_cH(products)
• Draw arrows down from each substance to its combustion products and balance the atoms of each element.

4Elements

• Elements do not need arrows because Δ_fH of an element is zero

Section 7 of 27Bond enthalpies

Bond enthalpies

Bond enthalpy (bond dissociation enthalpy)

Bond enthalpy (bond dissociation enthalpy) the energy required to break a particular bond

• Breaking bonds is endothermic and forming bonds is exothermic, with the same magnitude but opposite sign.

Mean (average) bond enthalpy

Mean (average) bond enthalpy the energy needed to break one mole of bonds in a gaseous molecule, averaged over similar compounds

• Actual bond strengths vary with the environment of the bond.
• Values from mean bond enthalpies differ from accurate data, and the method assumes gaseous species.

Calculation

• Δ_rH = Σ(bonds broken) − Σ(bonds formed)
• Draw full displayed structures so that no bonds are missed.
• Multiply by the coefficients in the balanced equation.

Overall change

• Overall change if more energy is released forming bonds than is needed to break bonds, the reaction is exothermic
• The products are more stable than the reactants.

Reactivity

• Reactivity bonds with low bond enthalpy break more easily and are likely to break first

Section 8 of 27Born–Haber cycles (outline)

1Born–Haber cycle

Born–Haber cycle a Hess's law cycle for an ionic solid

• Δ_fH = Δ_atH(metal) + IE + Δ_atH(non-metal) + EA + lattice energy.

2Steps

• Steps atomise the elements, ionise the metal, add electrons to the non-metal, then form the lattice from gaseous ions
• First electron affinities are exothermic and second electron affinities are endothermic.
• Lattice energy (formation) is strongly exothermic.

3Use

• Use rearranging gives the lattice energy, and comparing it with the theoretical ionic value shows the covalent character caused by polarisation

4Lattice energy trend

• Lattice energy trend more exothermic for smaller ions and higher charges

Section 9 of 27More from the specification

Enthalpy level diagram

• Enthalpy level diagram shows reactants and products at different energy levels, with exothermic having a negative enthalpy change

Energy transferred

• Energy transferred calculated using q equals mass times specific heat capacity times temperature change

Calorimetry

• Calorimetry burning an organic liquid in a spirit burner to heat water;
  • take temperature readings every minute before and after,
• and use a temperature correction by extrapolating a cooling graph

Heat losses

• Heat losses transferred energy is less than the true value because of incomplete combustion and loss to surroundings

Temperature correction

• Extrapolating a temperature-time graph back to the mixing time to estimate the true temperature change.

Section 10 of 27More on this topic

Bond enthalpy

• Bond enthalpy breaking bonds absorbs energy and making bonds releases energy, so Δ_rH = Σ(bonds broken) − Σ(bonds formed)

Surroundings

• Everything other than the reacting chemicals.

Section 11 of 27Key enthalpy terms for Born–Haber cycles

1Lattice energy (formation)

Lattice energy (formation) the enthalpy change when one mole of an ionic compound forms from its gaseous ions

• Na⁺(g) + Cl⁻(g) → NaCl(s), ΔH = −776 kJ mol^-1.
• It is very exothermic, and the more exothermic it is, the stronger the ionic bonding.
• It cannot be measured directly, so an energy cycle is used.

2Enthalpy of atomisation

Enthalpy of atomisation the enthalpy change when one mole of gaseous atoms forms from an element in its standard state

• It is always endothermic, as in Na(s) → Na(g), ΔH = +108 kJ mol^-1.
• For mercury it is Hg(l) → Hg(g).

3First electron affinity

First electron affinity the enthalpy change when one mole of gaseous atoms gains one electron each

• It is exothermic, as in Cl(g) + e^- → Cl⁻(g), ΔH = −364 kJ mol^-1.

4Second electron affinity

• Second electron affinity endothermic, as in O⁻(g) + e^- → O²⁻(g), ΔH = +844 kJ mol^-1
• A large repulsion between the negative ion and the electron must be overcome.

5Ionisation energy

• Ionisation energy always endothermic, as in Na(g) → Na⁺(g) + e^-

Section 12 of 27Constructing a Born–Haber cycle

• Principle
  • a Born–Haber cycle is Hess's law applied to an ionic compound, drawn with energy increasing up the diagram

1

Draw the elements in their standard states with state symbols as the starting level.

2

Draw upward arrows to gaseous atoms for the enthalpies of atomisation of the metal and the non-metal.

3

Draw an upward arrow for the ionisation energy of the metal and a downward arrow for the electron affinity of the non-metal.

4

Draw the enthalpy of formation from the elements to the solid compound, usually downward.

5

Draw the lattice formation arrow from the gaseous ions to the solid.

• Formation arrow
  • can be shown above the elements if the enthalpy of formation is endothermic

Section 13 of 27Calculating lattice energy

Calculating lattice energy

Hess's law relationship

• Δ_fH = Δ_atH(metal) + Δ_atH(non-metal) + IE + EA + Δ_lattH
• Simplified, Δ_fH = ΔH₁ + Δ_lattH, where ΔH₁ is the sum of the steps from elements to gaseous ions.

Rearranged

• Δ_lattH = Δ_fH − ΔH₁

Direct and indirect routes

• Direct and indirect routes the quantity being found is always the direct route
• The cycle can also find any other step, such as Δ_fH, if the lattice energy is given.

Stoichiometry

• Stoichiometry some values must be doubled or halved
• For MgCl₂, the electron affinity of chlorine is doubled because two moles of Cl⁻ form.
• For MgO, both ionisation energies of magnesium and both electron affinities of oxygen are included.

Presentation

• Presentation write the working with brackets so that signs are not lost, and check the arrows against the definitions

Section 14 of 27Polarisation and covalent character

Polarisation and covalent character

Theoretical lattice energy

• Theoretical lattice energy assumes 100% spherical ions with purely electrostatic attraction
• It assumes complete transfer of electrons and whole-number charges.

Experimental lattice energy

• Experimental lattice energy differs when the cation distorts the anion's electron density
• This introduces covalent character, and an experimental value more exothermic than the theoretical value indicates it.

Polarising power

• Polarising power high for cations with high charge density, which are small and highly charged
• Li⁺ polarises more than K⁺, and Mg²⁺ more than Na⁺.

Polarisability

• Polarisability high for large anions
• Br⁻ is more polarisable than Cl⁻.

Examples

• NaCl, with a large cation of low charge density, agrees closely with the ionic model,
• whereas MgCl₂ and compounds containing Br⁻ or I⁻ show larger differences

Section 15 of 27Enthalpy of solution and hydration

Enthalpy of solution

Enthalpy of solution the enthalpy change when one mole of an ionic substance dissolves in sufficient water to form an infinitely dilute solution

• (aq) means dissolved in sufficient water.
• It can be exothermic or endothermic.

Enthalpy of hydration

Enthalpy of hydration the enthalpy change when one mole of a specified gaseous ion dissolves in sufficient water to form an infinitely dilute solution

• Mg²⁺(g) + aq → Mg²⁺(aq).
• It is always exothermic.

Ion–dipole attractions

• Ion–dipole attractions the δ− oxygen of water is attracted to cations and the δ+ hydrogens to anions
• The ions become hydrated.

Section 16 of 27Energy cycles for solution

1

Two routes from gaseous ions to aqueous ions

• Route 1 goes through the lattice: gaseous ions to ionic solid, then to aqueous ions.
• Route 2 is the direct hydration of the gaseous ions.

2Relationship

• Σ Δ_hydH = Δ_lattH + Δ_solH, where Δ_lattH is the lattice formation enthalpy

3Solution enthalpy

• Δ_solH = −Δ_lattH + Δ_hydH(cation) + Δ_hydH(anion)
• Lattice breaking is endothermic, the reverse of lattice formation.
• Hydration of the ions is exothermic.

4Typical question

• Typical question find one hydration enthalpy from the lattice enthalpy, the enthalpy of solution and the hydration enthalpy of the other ion
• Number of ions matters, so the hydration enthalpy of the anion is doubled for MCl₂.

5

Either a Hess cycle or a Born–Haber style diagram works, provided the labels and directions are correct

Section 17 of 27More from the specification

1Ionic bonding in metal oxide compounds

• Ionic bonding in metal oxide compounds strong attractive electrostatic forces between cations and oxide anions account for high ceramic melting points.

2Electrostatic force

• Force of attraction between opposite charges.

3Born-Haber cycle

• A Hess's law cycle linking formation enthalpy, lattice energy and other steps for an ionic compound.

4Sodium chloride

• Compound of sodium and chlorine; common salt.

5Ionic radius

• Distance from the nucleus to the outermost electrons of an ion.

Section 18 of 27Factors affecting lattice enthalpy

Factors affecting lattice enthalpy

Two key factors

• Two key factors the charge and the radius of the ions in the lattice

Ionic radius

• Ionic radius lattice enthalpy becomes less exothermic as ionic radius increases
• The charge is spread over a larger ion.
• The ion centres are further apart, so the electrostatic attraction is weaker.
• CsF is less exothermic than KF because Cs⁺ is larger than K⁺.

Ionic charge

• Ionic charge lattice enthalpy becomes more exothermic as ionic charge increases
• Higher charge gives higher charge density and stronger attraction.
• CaO is much more exothermic than KCl because Ca²⁺ and O²⁻ have double charges and are also smaller ions.

Down a group

• Down a group the cation gets larger, so the lattice enthalpy becomes less exothermic

Section 19 of 27Factors affecting hydration enthalpy

Factors affecting hydration enthalpy

Hydration is exothermic

• Hydration is exothermic energy is released as water molecules bond to the ions
• Negative ions attract the δ+ hydrogens and positive ions attract the δ− oxygen.

Higher charge density gives a more exothermic hydration enthalpy

• Higher charge density gives a more exothermic hydration enthalpy ions that are smaller or more highly charged attract water more strongly
• F⁻ is more exothermic than I⁻.
• Mg²⁺ is more exothermic than Na⁺, and Mg²⁺ more than Ba²⁺.

Common control

• Common control charge and radius control both the energy needed to break the lattice and the energy released on hydration

Section 20 of 27Enthalpy of solution as a balance

Enthalpy of solution as a balance

Dissolving needs two changes

• Dissolving needs two changes the lattice is broken and the ions are hydrated
• Breaking the lattice is endothermic and is the reverse of lattice formation.
• Hydration is exothermic.

Result

• Result the enthalpy of solution is a small difference between two large numbers, so trends are not always simple

Summary

• Summary both lattice enthalpy and hydration enthalpy are more exothermic with higher charge and smaller ions, so both terms must be considered

Section 21 of 27Entropy changes on dissolving

Breaking the lattice

• Breaking the lattice increases the number of moles of particles, so entropy increases

Hydrating the ions

• Hydrating the ions water molecules become more ordered around the ions, so entropy of the water decreases
• This partly offsets the increase from the lattice breaking.

Conclusion

• Conclusion both entropy and enthalpy changes must be considered to explain why some compounds are soluble and others insoluble

Section 22 of 27Total entropy and feasibility

Total entropy and feasibility

Total entropy change

• ΔS_total = ΔS_system + ΔS_surroundings
• ΔS_surroundings = −ΔH ÷ T, with T in kelvin and ΔH converted to J mol^-1.
• ΔS_total = ΔS_system − Δ_solH ÷ T.

Feasible

• Feasible a process is thermodynamically spontaneous when ΔS_total is positive
• An endothermic dissolving (positive Δ_solH) can still be feasible if ΔS_system is large enough to outweigh the negative ΔS_surroundings.
• For ammonium nitrate at 298 K, a positive total entropy shows it is soluble.

Solubility depends on three factors

• ΔS_system, the enthalpy of solution and the temperature in kelvin

Section 23 of 27Solubility trends of Group 2 compounds

Solubility trends of Group 2 compounds

Group 2 sulfates

• Group 2 sulfates lattice enthalpy changes little down the group while hydration becomes less exothermic with larger cations
• Solubility therefore decreases down the group.

Group 2 hydroxides

• Group 2 hydroxides solubility increases down the group

Section 24 of 27Tackling energy cycle problems

1

Draw the cycle with arrows matching the definitions (lattice formation, hydration, solution).

2

Label each arrow with its value and sign.

3

Apply Hess's law, so route 1 equals route 2.

4

Use brackets to separate operations and show the working.

5

Check units and the number of moles of each ion.

Section 25 of 27More from the specification

1

Born-Haber cycles for ionic lattices

• Born-Haber cycles for ionic lattices summing formation enthalpy terms in Born-Haber cycles quantifies attractive electrostatic forces holding crystalline lattice structures.

2

Born-Haber cycle

• A Hess's law cycle linking formation enthalpy, lattice energy and other steps for an ionic compound.

3

Sodium chloride

• Compound of sodium and chlorine; common salt.

4

Electron affinity

• Enthalpy change when electrons are added to gaseous atoms or ions.

5

Ionic solid

• Lattice of alternating cations and anions.

6

Electrostatic force

• Force of attraction between opposite charges.

7

Covalent character

• The degree to which electron density is shared in an ionic bond.

8

Chloride

• Salt of hydrochloric acid.

9

Atomisation

• Formation of gaseous atoms from an element in its standard state.

10

Element

• A substance made of only one type of atom.

Section 26 of 27Key terms

Term	Meaning
Enthalpy change (ΔH)	The heat energy change at constant pressure.
Standard enthalpy of formation	The enthalpy change when one mole of a compound forms from its elements in their standard states.
Standard enthalpy of combustion	The enthalpy change when one mole of a substance burns completely in oxygen.
Hess's law	The total enthalpy change is independent of the route taken.
Mean bond enthalpy	The energy to break one mole of a bond averaged over similar compounds in the gas phase.
Activation energy	The minimum energy needed for a successful collision that starts a reaction.
Specific heat capacity	The energy needed to raise the temperature of 1 g of a substance by 1 K.

Term	Meaning
Born–Haber cycle	A Hess's law cycle relating the enthalpy of formation of an ionic compound to its lattice enthalpy and other steps.
Lattice enthalpy	The enthalpy change when one mole of an ionic lattice forms from its gaseous ions.
Enthalpy of hydration	The enthalpy change when one mole of gaseous ions dissolves in water.
Enthalpy of solution	The enthalpy change when one mole of solute dissolves in water to infinite dilution.
Electron affinity	The enthalpy change when one mole of gaseous atoms gains one electron each.
Enthalpy of atomisation	The enthalpy change when one mole of gaseous atoms forms from an element.
Polarisation	Distortion of an anion's electron cloud by a cation.

Term	Meaning
Charge density	The ratio of an ion's charge to its size.
Entropy	A measure of the dispersal of energy and the disorder of particles.
Total entropy change	The sum of the entropy changes of the system and the surroundings.
Hydration	The surrounding of ions by water molecules.
Lattice enthalpy	The enthalpy change when one mole of an ionic lattice forms from its gaseous ions.

Section 27 of 27Exam technique

1

Using bonds formed minus bonds broken — Δ_rH = Σ(bonds broken) − Σ(bonds formed)

2

Forgetting to multiply by the number of moles in the balanced equation

3

Using the wrong sign for ΔH after a temperature rise — a temperature rise means ΔH is negative

4

Using the mass of water as the mass of the reactants in q = mcΔT — use the mass of the solution being heated

5

Reversing the combustion cycle rule — formation data uses products minus reactants and combustion data uses reactants minus products

1

Forgetting to double or halve values for compounds such as MgCl₂

2

Using the wrong sign for the second electron affinity — it is endothermic

3

Subtracting the sum of steps without brackets, which loses signs

4

Confusing lattice enthalpy of formation with lattice enthalpy of dissociation, which have opposite signs

5

Taking the experimental lattice energy as purely ionic — a difference from the theoretical value indicates covalent character

1

Saying that large ions have more exothermic lattice enthalpies — larger ions give less exothermic values

2

Treating a positive enthalpy of solution as meaning the salt cannot dissolve

3

Using T in °C in entropy equations — T must be in kelvin

4

Mixing up the signs of lattice formation and dissociation

5

Forgetting to convert kJ to J before dividing by T in ΔS_surroundings