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

Section 1 of 27Enthalpy level diagrams

Enthalpy

• Enthalpy the total chemical energy (heat content) inside a substance; ΔH is the enthalpy change.

Exothermic reaction

• Exothermic reaction products have less energy than reactants, heat is given out and ΔH is negative.
• The temperature of the surroundings rises.
• Exothermic reactions are thermodynamically possible, but a very slow rate means they may not occur (kinetic control).

Endothermic reaction

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

State symbols must be given because a change of state changes the enthalpy: NaCl(s) → Na⁺(aq) + Cl⁻(aq) is +4 kJ mol⁻¹,

• but NaCl(g) → Na⁺(g) + Cl⁻(g) is +500 kJ mol⁻¹.

The system is the reacting substances; the surroundings are everything else, e.g. the flask.

Section 2 of 27Reaction profile diagrams

A reaction profile is like an enthalpy level diagram but also shows the activation energy.

Activation energy, Ea

• Activation energy, Ea the minimum energy reactant molecules need for a successful collision and to start the reaction.
• It is the difference between the reactant level and the peak of the curve.

Transition state

• Transition state the peak of the curve, where bonds are partly broken and partly formed.
• It is very unstable, cannot be isolated and is higher in energy than reactants and products.

In exothermic reactions the reactants are closer in energy to the transition state, so E_a is lower than for endothermic reactions.

Activation energy is not shown on enthalpy level diagrams.

Section 3 of 27Standard conditions and enthalpy definitions

Standard conditions and enthalpy definitions

Standard conditions

• A pressure of 100 kPa (101 kPa in older papers).
• A temperature of 298 K (25 °C).
• Each substance in its standard physical state.
• The symbol ⦵ shows standard conditions.

Standard enthalpy of formation, ΔfH

• Standard enthalpy of formation, ΔfH the enthalpy change when one mole of a compound forms from its elements in their standard states.

Standard enthalpy of combustion, ΔcH

• Standard enthalpy of combustion, ΔcH the enthalpy change when one mole of a substance burns completely in oxygen.

Standard enthalpy of neutralisation, ΔneutH

• Standard enthalpy of neutralisation, ΔneutH the enthalpy change when an acid and an alkali react to form one mole of water.

Standard enthalpy of reaction, ΔrH

• Standard enthalpy of reaction, ΔrH the enthalpy change for the molar quantities shown in the equation.

Standard enthalpy of atomisation, ΔatH

• Standard enthalpy of atomisation, ΔatH the enthalpy change when one mole of gaseous atoms forms from an element in its standard state.

Δ_fH of an element in its standard state is zero, e.g. O₂(g).

An enthalpy symbol needs Δ (change), H (enthalpy), ⦵ (standard) and a subscript for the type (c, f, neut, r).

Enthalpy values scale with the equation: doubling the moles doubles ΔH.

Section 4 of 27Calorimetry for reactions in solution

React the solution with an excess of one reagent in a polystyrene cup (or vacuum flask or metal can) and measure the temperature change.

Energy transferred

• Energy transferred q = mcΔT.

  What the symbols mean: E, Q or q = energy transferred (J) · m = mass · c = specific heat capacity (J kg⁻¹ °C⁻¹; water 4.18 J g⁻¹ °C⁻¹) · ΔT or Δθ = temperature change (°C or K)
  • (kg; g in chemistry calorimetry)
• The specific heat capacity of water is 4.18 J g⁻¹ K⁻¹.
• Convert q from J to kJ.

Enthalpy change per mole

• ΔH = −q ÷ n, where n is the moles of the limiting reagent;
  • a temperature rise gives a negative ΔH and a fall gives a positive ΔH.

Sample method for zinc and copper(II) sulfate

• Measure 25 cm³ of 1.0 mol dm⁻³ copper(II) sulfate into the cup.
• Weigh about 6 g of zinc powder, which is in excess.
• Record the temperature every half minute for 2.5 minutes while stirring.
• At 3 minutes add the zinc without recording that reading.
• Keep stirring and record for a further 6 minutes.

Assumptions

• The solution has the specific heat capacity and density of water (4.18 J g⁻¹ K⁻¹, 1 g cm⁻³).
• The heat capacity of the container is ignored.
• The reaction is complete and heat losses are negligible.

Sources of error include incorrect masses or volumes and heat loss; the temperature uncertainty is doubled because ΔT uses two readings.

Section 5 of 27Temperature correction graphs

• A slow reaction loses heat before the maximum temperature is reached, so the true maximum is never measured.

1

Record the temperature of the first reagent for a few minutes to get a steady value.

2

Add the second reagent and keep recording temperature and time.

3

Plot the graph and extrapolate the cooling section back to the time the second reagent was added.

4

Use the extrapolated lines to read the temperature change ΔT.

Temperature correction graphs

Use q = mcΔT with the mass of the total solution, then divide by the moles of the limiting reagent.

If the reagents start at different temperatures, work out the energy for each separately and add.

Section 6 of 27Calorimetry for enthalpy of combustion

1

The heat from burning a fuel raises the temperature of a known mass of water in a simple calorimeter.

2

Record

• The starting and final temperature of the water.
• The mass of the spirit burner before and after, to find the mass of fuel burned and its moles.

3

Not all the heat reaches the water.

• Some is lost to the surroundings and some is absorbed by the calorimeter.
• Minimise loss by keeping the calorimeter close to the flame, using a lid and draught shields.

4

The main sources of error are heat loss and incomplete combustion.

5

Combustion is exothermic, so Δ_cH is negative.

Section 7 of 27Hess's law and Hess cycles

1Hess's law

• Hess's law the total enthalpy change is independent of the route taken, as long as the initial and final conditions are the same.

2

It follows from conservation of energy and is used for enthalpy changes that cannot be measured directly, e.g. Δ_fH of propane.

3From enthalpies of formation

• Δ_rH = ΣΔ_fH(products) − ΣΔ_fH(reactants).
• Write the equation, put the elements with state symbols underneath, draw arrows up to each compound and multiply by the moles.
• Go from reactants to products, reversing the sign when the route goes against an arrow.

4From enthalpies of combustion

• Δ_rH = ΣΔ_cH(reactants) − ΣΔ_cH(products).
• Write the formation equation, put the combustion products underneath and draw arrows down to them.
• Balance the atoms of each element in the cycle.

5

Keep each value in brackets so that no minus sign is lost.

Section 8 of 27Bond enthalpies

Bond enthalpies

Bond enthalpy (bond dissociation enthalpy)

• Bond enthalpy (bond dissociation enthalpy) the energy needed to break a particular bond.

Breaking bonds is endothermic and making bonds is exothermic.

• The energy released on forming a bond equals the energy needed to break it, with the opposite sign.

Overall enthalpy change

• More energy released in bond making than needed for bond breaking gives an exothermic reaction with more stable products.
• More energy needed for bond breaking gives an endothermic reaction.

Average bond enthalpy

• Average bond enthalpy the energy needed to break one mole of bonds in gaseous molecules, averaged over similar compounds.
• Bond energies vary with the other atoms in the molecule, so an average is used.

Bonds with low enthalpies break first and react at lower temperatures; bonds with high enthalpies need heat or a catalyst.

Δ_rH = Σ(bonds broken) − Σ(bonds formed), using positive values for both sums.

Draw full displayed formulae so no bond is missed, and multiply by the coefficients in the balanced equation.

Section 9 of 27More on this topic

More on this topic

Bond breaking absorbs energy and bond making releases energy.

Using the formation-data rule for combustion data — the subtraction is reversed.

Section 10 of 27More from the specification

1Calculating Enthalpy Changes via Calorimetry

• In experimental calorimetry where a combustion or neutralisation takes place, heat energy transferred is determined using q = mc Delta T,
• allowing calculating enthalpy change per mole of limiting reactant from Delta H = -q / n.

2Enthalpy of Combustion of an Organic Liquid

• Measuring the enthalpy change of combustion of an organic liquid involves burning a known mass in a spirit burner beneath a copper calorimeter containing water and accounting for heat capacity and heat losses.
  • (such as an alcohol)

3Hess's Law Calculations

• Hess's law states that the total enthalpy change for a chemical reaction is independent of the route taken, enabling enthalpy calculations using standard enthalpy of formation (Delta H_f) or combustion (Delta H_c) cycles.

4Mean Bond Enthalpies and Reaction Energetics

• Bond-breaking is an endothermic process absorbing energy while bond-making is exothermic,
• so overall enthalpy change is calculated via Delta H = sum(bonds broken) - sum(bonds formed).

Section 11 of 27Key terms for Born-Haber cycles

1

Lattice energy, ΔlattH

• Lattice energy, ΔlattH the enthalpy change when one mole of an ionic compound forms from its gaseous ions.
• It is strongly exothermic because the ions in the lattice attract strongly, so the solid is more stable than the gaseous ions.
• The more exothermic the value, the stronger the ionic bonding.
• Na⁺(g) + Cl⁻(g) → NaCl(s).
• It cannot be measured directly; an energy cycle is used.

2

Enthalpy of atomisation, ΔatH

• Enthalpy of atomisation, ΔatH the enthalpy change when one mole of gaseous atoms forms from an element in its standard state.
• It is always endothermic because bonds in the element must be broken.
• Na(s) → Na(g) is +108 kJ mol⁻¹; Hg(l) → Hg(g) is also an atomisation.

3

First electron affinity

• First electron affinity the enthalpy change when one mole of gaseous atoms gains one mole of electrons to form 1− ions.
• It is exothermic, e.g. Cl(g) + e⁻ → Cl⁻(g).

4

Second electron affinity can be endothermic.

• O⁻(g) + e⁻ → O²⁻(g) is positive because the electron must overcome repulsion by the negative ion.

Section 12 of 27Constructing a Born-Haber cycle

• A Born-Haber cycle is Hess's law applied to an ionic solid; energy increases up the diagram.

1

Draw the elements in their standard states with state symbols about a third of the way up.

2

Atomise each element with upward arrows (endothermic).

3

Ionise the metal atom, an upward arrow for the ionisation energy (Na → Na⁺).

4

Add electrons to the non-metal atom, a downward arrow for the exothermic first electron affinity (Cl → Cl⁻).

5

Add Δ_fH as the direct route from the elements to the solid.

6

Add the lattice energy as the formation of the solid from gaseous ions.

Constructing a Born-Haber cycle

For MgO, include both ionisation energies of magnesium and both electron affinities of oxygen.

Δ_fH can be drawn above the elements for an endothermic formation.

Section 13 of 27Calculating lattice energy

Calculating lattice energy

Hess's law gives Δ_fH = Δ_atH(metal) + Δ_atH(non-metal) + IE + EA + Δ_lattH.

So Δ_lattH = Δ_fH − (sum of all the other steps), where the quantity being found is the direct route.

Double or halve values to match the formula: MgCl₂ needs two chlorine atoms and two first electron affinities.

Compound	Data (kJ mol−1)	Result
KCl	ΔfH -437; ΔatH(K) +90; ΔatH(Cl) +122; IE1(K) +418; EA1(Cl) -349	ΔlattH = -437 - (90 + 122 + 418 - 349) = -718
MgO	ΔfH -602; ΔatH(Mg) +148; ΔatH(O) +248; IE1 +736; IE2 +1450; EA1(O) -142; EA2(O) +770	ΔlattH = -602 - (148 + 248 + 736 + 1450 - 142 + 770) = -3812

• Any step of the cycle can be found the same way, e.g. Δ_fH from a given lattice energy.

Section 14 of 27Polarisation and covalent character

1

The theoretical lattice energy assumes a perfect ionic model: 100% spherical ions, complete electron transfer and purely electrostatic attraction.

2

Experimental lattice energy (from a Born-Haber cycle) is more exothermic than the theoretical value when there is covalent character.

• The cation attracts electron density from the anion and distorts it.

3

Polarising power of a cation increases with charge density.

• Li⁺ polarises more than K⁺ because it is smaller.
• Mg²⁺ polarises more than Na⁺ because its charge is larger.

4

Polarisability of an anion increases with ionic radius.

• Br⁻ is more polarisable than Cl⁻.

5

MgCl₂ has more covalent character than NaCl because Mg²⁺ has the higher charge density, so its experimental and theoretical values differ more.

6

Close agreement of the two values, as in NaCl, shows an almost purely ionic compound.

Section 15 of 27Enthalpy of solution and hydration

Enthalpy of solution and hydration

Standard enthalpy of solution, ΔsolH

• Standard enthalpy of solution, ΔsolH the enthalpy change when one mole of an ionic solid dissolves in enough water to form an infinitely dilute solution.
• (aq) shows the solid is dissolved in sufficient water, e.g. KCl(s) + aq → K⁺(aq) + Cl⁻(aq).
• It can be exothermic or endothermic.

Standard enthalpy of hydration, ΔhydH

• Standard enthalpy of hydration, ΔhydH the enthalpy change when one mole of a specified gaseous ion dissolves in enough water to form an infinitely dilute solution.
• Mg²⁺(g) + aq → Mg²⁺(aq).
• It is always exothermic because the ions attract water molecules.

Water is polar, with δ− oxygen and δ+ hydrogen.

• Oxygen is attracted to cations and hydrogen to anions by ion-dipole attractions, so the ions become hydrated.

Section 16 of 27Calculating enthalpies of solution and hydration

Draw an energy cycle with two routes from gaseous ions to aqueous ions.

Route 1 (indirect)

• Route 1 (indirect) gaseous ions → solid → aqueous ions, with enthalpy Δ_lattH + Δ_solH.

Route 2 (direct)

• Route 2 (direct) gaseous ions → aqueous ions, with enthalpy ΣΔ_hydH.

By Hess's law Σ Δ_hydH = Δ_lattH + Δ_solH, so Δ_solH = −Δ_lattH + ΣΔ_hydH(ions).

Typical questions give the lattice energy, enthalpy of solution and one hydration enthalpy and ask for the other.

Count each ion as it appears in the formula.

• For MgCl₂, double Δ_hydH(Cl⁻).
• Δ_hydH(Cl⁻) from KCl data: (−711) + (+26) − (−322) = −363 kJ mol⁻¹.
• Δ_hydH(Mg²⁺) = (−2592) + (−55) − 2(−363) = −1921 kJ mol⁻¹.

Either a Hess cycle or a Born-Haber style energy-level diagram can be used if the arrows match the definitions.

Section 17 of 27More from the specification

More from the specification

Lattice enthalpy of magnesium oxide

• Lattice enthalpy of magnesium oxide intense electrostatic forces between divalent magnesium and oxide ions create exceptionally high lattice dissociation energies.

Sodium chloride

• Compound of sodium and chlorine; common salt.

Electrostatic force

• Force of attraction between opposite charges.

Section 18 of 27Ionic radius and lattice energy

Ionic radius and lattice energy

Lattice energy becomes less exothermic as ionic radius increases.

The charge is spread over a larger ion and the ion centres are further apart.

• The electrostatic attraction between oppositely charged ions is therefore weaker.

CsF is less exothermic than KF because Cs⁺ is larger than K⁺.

Section 19 of 27Ionic charge and lattice energy

Lattice energy becomes more exothermic as ionic charge increases.

Greater charge gives a higher charge density and stronger electrostatic attraction.

• CaO is more exothermic than KCl because Ca²⁺ and O²⁻ carry greater charge.
• Ca²⁺ and O²⁻ are also smaller than K⁺ and Cl⁻, which adds to the effect.

Charge density

• Charge density the charge of an ion divided by its radius;
  • a higher charge and smaller size give a higher value.

Section 20 of 27Factors affecting hydration enthalpy

1

Hydration enthalpies are exothermic because energy is released when water molecules bond to the ions.

2

Cations attract the δ− oxygen of water; anions attract the δ+ hydrogens.

3

Higher charge density gives a more exothermic hydration enthalpy.

• F⁻ is more exothermic than Cl⁻.
• Mg²⁺ is more exothermic than Ba²⁺.

4

Both lattice energy and hydration enthalpy become more exothermic as charge density increases.

Section 21 of 27Entropy and solubility

1

Two changes occur when an ionic solid dissolves.

• The lattice breaks down, which is endothermic (the reverse of lattice energy) and increases entropy because more particles are free.
• The ions are hydrated, which is exothermic and orders the water molecules, decreasing their entropy.

2

Both enthalpy and entropy must be considered to explain solubility.

3

ΔS_total = ΔS_system + ΔS_surroundings, where ΔS_surroundings = −Δ_solH ÷ T.

• A positive ΔS_total means dissolving is thermodynamically spontaneous.
• Solubility therefore depends on ΔS_system, Δ_solH and the temperature in kelvin.

4

A salt can dissolve even if its enthalpy of solution is slightly positive, because dissolving increases disorder.

Section 22 of 27Solubility trends down Group 2

1

Down Group 2 (Mg²⁺ to Ba²⁺) the cation radius increases, so charge density falls.

2

Both the lattice energy and the cation hydration enthalpy become less exothermic; the balance of which falls faster decides the enthalpy of solution.

3

Hydroxides become more soluble.

• OH⁻ is small, so the lattice energy depends strongly on cation radius and falls steeply.
• It falls by more than the hydration enthalpy, so dissolving becomes more favourable.

4

Sulfates become less soluble.

• SO₄²⁻ is very large, so the lattice energy changes little as the cation grows.
• The hydration enthalpy falls markedly, so dissolving becomes less favourable.

Section 23 of 27Ionic charge and solubility in general

Ionic charge and solubility in general

Compounds of doubly charged ions usually have much more exothermic lattice energies than those of singly charged ions,

• and hydration cannot always compensate.

In general, the greater the ionic charge, the less soluble the compound, e.g. 356.9 g of NaCl but only 74.4 g of CaCl₂ dissolve in 1 dm³ of water.

This is a general rule with many exceptions.

Section 24 of 27Strategy for energy cycle questions

1

Identify the enthalpy changes given and the one required.

2

Write the definition equation of each with state symbols.

3

Draw the cycle with endothermic steps pointing up and exothermic steps pointing down.

4

Write the Hess's law equation: route 1 = route 2.

5

Match the moles of each species to the formula.

6

State the answer with sign and unit kJ mol⁻¹.

Section 25 of 27More from the specification

1

Theoretical lattice energies from Born-Haber cycles

• Theoretical lattice energies from Born-Haber cycles analyzing thermodynamic Born-Haber cycles measures the cohesive electrostatic forces governing ionic salts.

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

Electrostatic force

• Force of attraction between opposite charges.

6

Covalent character

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

7

Chloride

• Salt of hydrochloric acid.

8

Atomisation

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

Section 26 of 27Key terms

Term	Meaning
Enthalpy change (ΔH)	The heat energy change at constant pressure, in kJ mol−1.
Activation energy	The minimum energy needed for a successful collision.
Transition state	The unstable peak of a reaction profile where bonds are partly broken and formed.
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.
Average bond enthalpy	The energy to break one mole of a bond averaged over similar gaseous compounds.

Term	Meaning
Born-Haber cycle	An application of Hess's law to an ionic solid, used to find lattice energy.
Lattice energy	The enthalpy change when one mole of an ionic compound forms from its gaseous ions.
Electron affinity	The enthalpy change when one mole of gaseous atoms gains one mole of electrons.
Polarisation	The distortion of an anion's electron cloud by a nearby cation.
Covalent character	The degree to which electron density is shared in an ionic bond.
Enthalpy of solution	The enthalpy change when one mole of solute dissolves in enough water to give an infinitely dilute solution.
Enthalpy of hydration	The enthalpy change when one mole of gaseous ions dissolves in water to form aqueous ions.

Term	Meaning
Charge density	The charge of an ion relative to its size.
Lattice energy	The enthalpy change when one mole of an ionic compound forms from its gaseous ions.
Hydration enthalpy	The enthalpy change when one mole of gaseous ions forms aqueous ions.
Entropy	A measure of the disorder of a system.
Solubility	The mass of a substance that dissolves in a given amount of solvent.
Spontaneous change	A change with a positive total entropy change.

Section 27 of 27Exam technique

1

Confusing endothermic with bond breaking and exothermic with bond making — breaking bonds is endothermic.

2

Forgetting to convert q from J to kJ before dividing by moles.

3

Giving the wrong sign — a temperature rise means a negative ΔH.

4

Omitting state symbols — a change of state changes the enthalpy.

5

Forgetting the coefficients in bond enthalpy sums — multiply each bond by the number in the equation.

1

Forgetting the second ionisation energy for Group 2 ions — Mg needs both IE1 and IE2.

2

Using a negative second electron affinity for oxygen — it is positive.

3

Not doubling terms for the number of ions in the formula — MgCl₂ needs two chloride terms.

4

Saying hydration is endothermic — hydration enthalpies are always exothermic.

1

Saying lattice energy depends only on charge — it depends on both charge and radius.

2

Confusing lattice energy (gaseous ions to solid) with hydration (gaseous ions to aqueous).

3

Explaining a solubility trend with only one enthalpy term — compare both lattice energy and hydration enthalpy.

4

Ignoring entropy when explaining solubility — dissolving increases disorder of the ions.