Energy cycles in reactions — IB Chemistry HL Revision Notes & Topical Questions

Section 1 of 29Bond breaking and bond making

Bond breaking

• Bond breaking requires energy, so it is endothermic;
  • the energy needed is the bond dissociation enthalpy (bond energy).

Bond forming

• Bond forming releases energy, so it is exothermic, with the same magnitude but opposite sign.

Exothermic overall

• Exothermic overall more energy is released forming bonds than is needed to break bonds;
  • the products are more stable.

Endothermic overall

• Endothermic overall more energy is needed to break bonds than is released forming bonds;
  • the products are less stable.

Section 2 of 29Average bond enthalpy

Average bond enthalpy

Definition

Definition the energy needed to break one mole of bonds in a gaseous molecule, averaged over similar compounds.

Why averaged

• Why averaged bond energies depend on the environment, and the successive C–H bonds in methane need different energies.

Use

• Use it estimates ΔH_r when the value cannot be measured experimentally.

Equation

• ΔH_r = Σ(bonds broken) + Σ(bonds formed), with bonds broken positive and bonds formed negative.

Draw structures

• Draw structures draw full displayed structures so no bond is missed.

Coefficients

• Coefficients multiply each bond enthalpy by the number of bonds, including equation coefficients.

Working

• Working show each step, because bond enthalpy questions award marks for working.

Section 3 of 29Hess's law

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.

2Basis

• Basis the conservation of energy.
  • (the first law of thermodynamics)

3Use

• Use to find enthalpy changes that cannot be measured by calorimetry, such as the formation of propane from carbon and hydrogen.

4Energy cycle

• Energy cycle the direct route from elements to products equals the indirect route via the reactants.

5Relationship

• ΔH₂ = ΔH₁ + ΔH_r, so ΔH_r = ΔH₂ − ΔH₁.

6Understanding

• Understanding the principle matters more than the wording.

Section 4 of 29Solving Hess's law problems

1Cycles

• Cycles add the value when following an arrow and subtract it when going against an arrow.

2Brackets

• Brackets put values in brackets with the operator in front to avoid sign errors.

3Equations

• Equations reversing an equation changes the sign of ΔH, and multiplying an equation multiplies ΔH.

4Combine

• Combine add the adjusted equations and cancel species that appear on both sides.

5Either method

• Either method know both cycles and equations.

Section 5 of 29Using enthalpies of formation (HL)

1Cycle

• Cycle elements are placed at the bottom and the arrows point upwards, from elements to compounds.

2Equation

• ΔH_r = ΣΔH_f°(products) − ΣΔH_f°(reactants).

3Elements

• ΔH_f° of an element in its standard state is zero.

4Coefficients

• Coefficients multiply each value by its coefficient.

5Data

• Data values are in Section 13 of the data booklet.

Section 6 of 29Using enthalpies of combustion (HL)

1Cycle

• Cycle combustion products are at the bottom and the arrows point downwards.

2Equation

• ΔH_r = ΣΔH_c°(reactants) − ΣΔH_c°(products).

3Balance

• Balance check that the atoms of each element balance in the cycle.

4Direction

• Direction reverse the sign when the route goes against the arrow.

Section 7 of 29Born–Haber cycle definitions (HL)

1Born–Haber cycle

• Born–Haber cycle a Hess's law cycle for ionic compounds that finds the lattice enthalpy, which cannot be measured directly.

2Lattice enthalpy

• Lattice enthalpy the enthalpy change when one mole of an ionic compound separates into gaseous ions;
  • endothermic, an upward arrow.

3Atomisation

• Atomisation formation of one mole of gaseous atoms from the element in its standard state; endothermic.

4First and second ionisation energy

• First and second ionisation energy both endothermic, with the second larger than the first.

5First electron affinity

• First electron affinity can be exothermic, endothermic or neutral.

6Second electron affinity

• Second electron affinity endothermic because the electron is repelled by the negative ion.

Section 8 of 29Drawing a Born–Haber cycle (HL)

1

Place the elements in their standard states with state symbols about one third up.

2

Make gaseous atoms with upward arrows for atomisation.

3

Make gaseous ions: ionisation upwards and electron affinity downwards if exothermic.

4

Add the enthalpy of formation downwards (or upwards if endothermic).

5

Join the solid to the gaseous ions with the lattice enthalpy.

1Direction matters

• Direction matters up for endothermic and down for exothermic, but arrow length need not be to scale.

2Details

• Details show state symbols and the electron in the ionisation step.

3Stoichiometry

• Stoichiometry for MgCl₂, include both ionisation energies of Mg and double the atomisation and electron affinity of Cl.

4Exam

• Exam completing a partly drawn cycle is more likely than drawing a whole one.

Section 9 of 29Born–Haber calculations (HL)

1Equation

• ΔH_f = ΔH_at + ΔH_at + ΔH_ie + ΔH_ea − ΔH_latt.

2Simplified

• ΔH_f = ΔH₁ − ΔH_latt, where ΔH₁ is the sum of the steps from elements to gaseous ions.

3Lattice enthalpy

• ΔH_latt = −ΔH_f + ΔH₁.

4Any step

• Any step the cycle can find any missing step if the others are known.

5Stoichiometry

• Stoichiometry multiply values for the numbers of ions formed.

6Data

• Data take values from the data booklet carefully.

Section 10 of 29More from the specification

1

Enthalpy of combustion per mole

• Enthalpy of combustion per mole measuring heat liberated when burning stoichiometric moles of fuel provides a reliable means to determine bond energies.

2

Born-Haber cycle

• An energy cycle applying Hess's Law to calculate experimental lattice enthalpy of an ionic solid from standard enthalpy terms.
  • (such as sodium chloride)

3

Enthalpy of atomisation

• The endothermic process required to produce one mole of separate gaseous atoms from an element in its standard state.

4

Ionisation energy and electron affinity

• First ionisation energy is endothermic, while first electron affinity for non-metals like chlorine is predominantly exothermic.
  • (removing electrons)

5

Hess's Law calculations

• The total enthalpy change for a chemical reaction is independent of the pathway taken between initial and final states.

6

Born-Haber cycle

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

7

Endothermic process

• Change, such as dissolving or melting, that absorbs thermal energy.

Section 11 of 29Hess's law

1Statement

• Statement the enthalpy change of a reaction is independent of the route taken, provided the initial and final conditions are the same.

2Basis

• Basis conservation of energy.

3Use

• Use to find enthalpy changes that cannot be measured directly.

4Example

• Example the enthalpy of formation of propane cannot be found experimentally because carbon and hydrogen do not react under standard conditions,
• but it can be calculated from combustion enthalpies.

5Cycle idea

• Cycle idea the direct route from elements to products equals the indirect route via the reactants and then the products.

Section 12 of 29Method 1: energy cycles

1

Write the balanced equation for the required reaction.

2

Draw a cycle with the reactants at one corner, the products at another and the common substances at the bottom.

3

Draw an arrow for each known enthalpy change in the direction of the reaction it describes.

4

Follow the route: add the value when going with an arrow, subtract it when going against.

1Moles

• Moles multiply by the number of moles in the balanced equation.

2Signs

• Signs check the sign of each step.

Section 13 of 29Method 2: combining equations

Reverse an equation

• Reverse an equation the sign of ΔH changes.

Multiply an equation

• ΔH is multiplied by the same factor.

Add

• Add add the manipulated equations to give the target equation.

Cancel

• Cancel remove species that appear on both sides.

Add enthalpies

• Add enthalpies the sum of the ΔH values is the target ΔH.

Choice of method

• Choice of method either gives the same answer, so know both.

Section 14 of 29Equations to reach a target

1

Find the given equation containing the wanted product and adjust it so the product matches.

2

Find the given equation containing the reactant and adjust it.

3

Reverse or multiply as needed, and change ΔH accordingly.

4

Add the equations, cancel common species and add the ΔH values.

Section 15 of 29Using enthalpies of formation

Equation

• ΔH_r° = ΣΔH_f°(products) − ΣΔH_f°(reactants).

Coefficients

• Coefficients each value is multiplied by its coefficient.

Elements

• ΔH_f° of an element in its standard state is zero by definition.

Data

• Data values are in Section 13 of the IB data booklet.

1

Write the balanced equation.

2

List ΔH_f° under each species with the coefficients.

3

Calculate products minus reactants.

4

Include units and sign.

Section 16 of 29More from the specification

1

Infrared spectroscopic confirmation

• Infrared spectroscopic confirmation identifying diagnostic bond vibration absorption peaks provides a definitive experimental means to identify organic functional groups.

2

Born-Haber cycle construction

• A Born-Haber cycle is an application of Hess's Law used to determine the experimental lattice enthalpy of ionic compounds by linking formation enthalpy to successive atomisation, ionisation,
• and electron affinity stages.

3

Standard atomisation and bond enthalpy

• Converting solid elements into gaseous atoms involves endothermic bond-breaking processes,
• such as the enthalpy of atomisation and standard covalent bond dissociation enthalpies.

4

First ionisation energy and electron affinity

• The first ionisation energy is the endothermic process of removing an electron from neutral gaseous atoms,
• whereas first electron affinity is usually an exothermic process where gaseous atoms gain an electron to form 1- anions.

5

Lattice enthalpy of ionic crystals

• Lattice enthalpy is defined as the energy required to completely separate one mole of a solid ionic compound into its constituent gaseous ions under standard conditions.

6

Born-Haber cycle

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

7

Electron affinity

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

8

Bonds formed

• Product bonds, energy released

9

Bonds broken

• Reactant bonds, energy absorbed

10

Endothermic process

• Change, such as dissolving or melting, that absorbs thermal energy.

11

Electron

• Negative particle moving around the nucleus.

12

Endothermic

• A reaction that takes in thermal energy from the surroundings.

13

Lattice

• A regular, repeating three-dimensional arrangement of particles.

14

Ionisation

• The removal of an electron from an atom or molecule.

15

Exothermic

• A reaction that transfers thermal energy to the surroundings.

16

Atomisation

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

Section 17 of 29Born–Haber cycle

1Born–Haber cycle

• Born–Haber cycle a Hess's law cycle used to analyse the formation of ionic compounds.

2Purpose

• Purpose it finds the lattice enthalpy, which cannot be measured directly.

3Vertical energy

• Vertical energy endothermic processes go upward and exothermic processes go downward.

Section 18 of 29Steps and signs

Step	Process	Sign
Atomisation	Element(s) → gaseous atoms, e.g. Mg(s) → Mg(g)	Positive
First ionisation energy	M(g) → M+(g) + e−	Positive
Second ionisation energy	M+(g) → M2+(g) + e−	Positive, larger than the first
First electron affinity	X(g) + e− → X−(g)	Usually negative
Second electron affinity	O−(g) + e− → O2−(g)	Positive
Enthalpy of formation	Elements in standard states → compound	Usually negative
Lattice enthalpy	Ionic solid → gaseous ions	Positive (endothermic)

Section 19 of 29Standard values to recall

Standard values to recall

Lattice enthalpy

• CaF₂(s) → Ca²⁺(g) + 2F⁻(g), +2620 kJ mol⁻¹.

Atomisation

• Mg(s) → Mg(g), +148 kJ mol⁻¹.

Ionisation of magnesium

• +738 and +1451 kJ mol⁻¹.

Electron affinities of oxygen

• −141 and +798 kJ mol⁻¹.

Second ionisation

• Second ionisation endothermic and larger than the first.

Section 20 of 29Theoretical lattice enthalpy (HL)

Theoretical value

• Theoretical value assumes purely ionic bonding with spherical ions.

Close agreement

• Close agreement the experimental Born–Haber value is close, as for NaCl, showing nearly ideal ionic bonding.

Large difference

• Large difference as in AgCl or Al₂O₃, where the experimental value is larger than the theoretical value.

Cause

• Cause covalent character from polarisation of the anion's electron cloud by the cation.

Section 21 of 29Exam presentation

Electrons

• Electrons show the electron in the ionisation step or marks may be lost.

Axis

• Axis an energy axis is not needed.

State symbols

• State symbols each species needs its state symbol.

Direction

• Direction the direction of each arrow matters, but its length need not be to scale.

Section 22 of 29More from the specification

1

Molar enthalpy cycles

• Molar enthalpy cycles constructing thermodynamic Hess cycles across reaction moles provides a thermochemical means to calculate indirect formation enthalpies.

2

Hess's Law and Enthalpy Cycles

• Hess's law states that the total enthalpy change for a chemical reaction is independent of the route taken, provided initial and final conditions are identical.
  • (ΔH_direct = Σ ΔH_steps)

3

Born-Haber Cycles for Ionic Compounds

• A Born-Haber cycle is an enthalpy cycle that applies Hess's law to calculate experimental lattice enthalpies of ionic compounds from standard enthalpy of formation, atomisation, ionisation,
• and electron affinity.

4

Standard Enthalpy of Formation Calculations

• The standard enthalpy change of reaction is calculated from standard enthalpies of formation of reactants and products using ΔH_rxn = Σ ΔH_f(products) - Σ ΔH_f(reactants).

5

Bond Enthalpies in Gas-Phase Reactions

• Enthalpy changes in covalent gas-phase reactions are estimated from mean bond enthalpies: ΔH = Σ - Σ(bonds formed in products).
  • (bonds broken in reactants)

6

Born-Haber cycle calculations

• Born-Haber cycle calculations applies Hess's law to determine lattice enthalpy from atomisation, ionisation, electron affinity,
  • and formation enthalpy changes.

7

Enthalpy change from bond enthalpies

• Enthalpy change from bond enthalpies reaction enthalpy equals sum of bonds broken in reactants minus sum of bonds formed in products.

8

Standard enthalpy of formation

• Standard enthalpy of formation enthalpy change when one mole of a compound is formed from its constituent elements in standard states.

9

Enthalpy change

• The thermal energy transferred during a reaction, ΔH.

10

Born-Haber cycle

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

11

Bonds formed

• Product bonds, energy released

12

Bonds broken

• Reactant bonds, energy absorbed

13

Standard conditions

• 298 K and 101 kPa.

14

Product

• A substance formed in a reaction.

15

Reactants

• The substances that react together at the start of a reaction.

16

Combustion

• Burning in oxygen

Section 23 of 29Enthalpy changes in the cycle

1Lattice enthalpy, ΔHlatt

• Lattice enthalpy, ΔHlatt one mole of ionic solid separated into gaseous ions, for example CaF₂(s) → Ca²⁺(g) + 2F⁻(g), +2620 kJ mol⁻¹;
  • always endothermic.

2Atomisation, ΔHat

• Atomisation, ΔHat one mole of gaseous atoms from the element, for example Mg(s) → Mg(g), +148 kJ mol⁻¹;
  • endothermic.

3First ionisation energy

• Mg(g) → Mg⁺(g) + e⁻, +738 kJ mol⁻¹; endothermic.

4Second ionisation energy

• Mg⁺(g) → Mg²⁺(g) + e⁻, +1451 kJ mol⁻¹; endothermic and larger than the first.

5First electron affinity

• O(g) + e⁻ → O⁻(g), −141 kJ mol⁻¹; may be exothermic, endothermic or close to zero.

6Second electron affinity

• O⁻(g) + e⁻ → O²⁻(g), +798 kJ mol⁻¹; endothermic because the electron is repelled.

Section 24 of 29Drawing the cycle for sodium chloride

1

Place Na(s) + ½Cl₂(g) with state symbols about one third of the way up.

2

Make gaseous atoms with upward arrows: Na(s) → Na(g), +108 kJ mol⁻¹, and ½Cl₂(g) → Cl(g), +121 kJ mol⁻¹.

3

Make gaseous ions: Na(g) → Na⁺(g) + e⁻, +500 kJ mol⁻¹ (up), and Cl(g) + e⁻ → Cl⁻(g), −364 kJ mol⁻¹ (down).

4

Add the formation Na(s) + ½Cl₂(g) → NaCl(s), −411 kJ mol⁻¹, downwards at the bottom left.

5

Join the solid to the gaseous ions with the lattice enthalpy NaCl(s) → Na⁺(g) + Cl⁻(g).

1Direction

• Direction endothermic arrows point up and exothermic arrows point down.

2Scale

• Scale arrow lengths need not match the energy sizes.

3Endothermic formation

• Endothermic formation drawn above the elements.

Section 25 of 29Multiples in the cycle for MgCl₂

1Label

• Label each enthalpy change needs its own arrow, label, equation with state symbols and electrons, and value.

2Two ionisations

• Two ionisations both ionisation energies of magnesium are included because Mg²⁺ forms.

3Two chlorines

• Two chlorines the atomisation and electron affinity of chlorine are doubled.

4Data for MgCl₂

• Data for MgCl₂ atomisation of Mg +148, atomisation of Cl +122, IE₁ +738, IE₂ +1451, electron affinity of Cl −349, formation −641 and lattice enthalpy +2524 kJ mol⁻¹.

5Exam

• Exam you are more likely to complete a partly drawn cycle than draw a whole one.

Section 26 of 29Calculating lattice enthalpy

Two routes

• ΔH_f = ΔH_at + ΔH_at + ΔH_ie + ΔH_ea − ΔH_latt.

Simplified

• Simplified with ΔH₁ the sum of the four steps from elements to gaseous ions, ΔH_f = ΔH₁ − ΔH_latt.

Rearranged

• ΔH_latt = −ΔH_f + ΔH₁.

Flexibility

• Flexibility the cycle can find any step if the others and the lattice enthalpy are known.

1

Identify the direct route (formation) and the indirect route (via gaseous atoms and ions).

2

Write the equation linking all enthalpy changes and rearrange for the unknown.

3

Check the stoichiometry: MgCl₂ makes two Cl⁻, so the electron affinity of Cl is doubled.

4

Substitute using brackets and signs, then evaluate.

Section 27 of 29More from the specification

1

Lattice dissociation energy per mole

• Lattice dissociation energy per mole summing Born-Haber cycle terms for ionic moles provides a theoretical means to calculate electrostatic lattice energy.

2

Born-Haber thermochemical cycles

• A Born-Haber cycle applies Hess's law to calculate experimental lattice enthalpies from enthalpy of formation, atomisation, ionisation energy,
• and electron affinity.

3

Theoretical ionic model vs covalent character

• Discrepancies between experimental Born-Haber lattice enthalpies and theoretical electrostatic values indicate polarization and partial covalent character.

4

Enthalpies of atomisation and bond dissociation

• Atomisation enthalpy is the energy required to produce one mole of separate gaseous atoms from an element in its standard state.

5

Standard enthalpy of combustion

• Standard enthalpy of combustion heat energy evolved when one mole of a substance undergoes complete combustion in excess oxygen under standard conditions.

6

Hess's law thermochemical cycles

• Hess's law thermochemical cycles overall enthalpy change for a chemical process is independent of the reaction route taken from reactants to products.

7

Average covalent bond enthalpies

• Average covalent bond enthalpies breaking covalent bonds in gaseous reactant molecules is endothermic,
  • whereas forming bonds in products is exothermic.

8

Born-Haber cycle

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

9

Bonds formed

• Product bonds, energy released

10

Bonds broken

• Reactant bonds, energy absorbed

11

Endothermic process

• Change, such as dissolving or melting, that absorbs thermal energy.

12

Standard conditions

• 298 K and 101 kPa.

13

Product

• A substance formed in a reaction.

14

Reactants

• The substances that react together at the start of a reaction.

15

Combustion

• Burning in oxygen

Section 28 of 29Key terms

Term	Meaning
Bond enthalpy	Energy to break one mole of a bond in the gas phase.
Hess's law	Enthalpy change is independent of route.
Born–Haber cycle	A Hess cycle for forming an ionic compound from its elements.
Lattice enthalpy	Energy to separate one mole of an ionic solid into gaseous ions.
Enthalpy of atomisation	Energy to form one mole of gaseous atoms from an element.
Electron affinity	Enthalpy change when gaseous atoms gain electrons.

Term	Meaning
Hess's law	The enthalpy change of a reaction is independent of the route.
Energy cycle	A diagram linking reactants, products and a common set of substances.
Enthalpy of formation	Enthalpy change to form one mole of a compound from its elements.
Direct route	The one-step path between starting and final substances.
Indirect route	The multi-step path between the same substances.

Term	Meaning
Lattice enthalpy	Energy to separate one mole of an ionic solid into gaseous ions.
Atomisation	Formation of gaseous atoms from an element in its standard state.
Polarisation	Distortion of an anion's electron cloud by a cation.
Theoretical lattice enthalpy	Value calculated assuming purely ionic bonding.

Term	Meaning
Enthalpy of atomisation	Enthalpy change to form one mole of gaseous atoms from an element.
First ionisation energy	Enthalpy change to remove one electron from each of one mole of gaseous atoms.
Second electron affinity	Enthalpy change when gaseous 1− ions gain an electron.
Lattice enthalpy	Energy to separate one mole of an ionic solid into gaseous ions.
Born–Haber cycle	A Hess cycle that includes lattice enthalpy.

Section 29 of 29Exam technique

1

Giving bonds broken a negative sign and bonds formed a positive sign.

2

Forgetting to multiply bond enthalpies by the equation coefficients.

3

Forgetting to reverse the sign when going against an arrow in a cycle.

4

Forgetting to double the electron affinity and atomisation of chlorine for MgCl₂.

1

Using reactants minus products for the formation enthalpy equation.

2

Forgetting to multiply ΔH by the equation coefficient.

3

Forgetting that ΔH_f of an element is zero.

4

Forgetting to reverse the sign of ΔH when reversing an equation.

1

Defining lattice enthalpy as a formation process while using the dissociation values — be consistent with the sign and direction.

2

Forgetting that the second electron affinity of oxygen is endothermic.

3

Drawing arrows in the wrong direction for exothermic and endothermic steps.

4

Omitting the electron in the ionisation equation.

1

Using a single chlorine atomisation for MgCl₂ — it needs two.

2

Treating all electron affinities as exothermic.

3

Forgetting the second ionisation energy of magnesium.

4

Mixing up the sign of lattice enthalpy when it is defined as the separation of the solid into ions.