Edexcel International A Level Chemistry

Topic 12: Entropy and Energetics

Two questions about energy that enthalpy alone cannot answer. Why do endothermic changes happen, and how strong is the bonding inside an ionic solid? The first is answered by entropy, the second by lattice energy.

The one idea

Enthalpy tells you how much heat a reaction gives out or takes in. It does not tell you whether the reaction will happen. Some endothermic changes occur spontaneously (a cold pack, or ammonium nitrate dissolving), and some exothermic ones never start.

The missing quantity is entropy, a measure of how widely particles and energy are dispersed. A change is feasible when the total entropy of the system and its surroundings increases. Heat given out raises the entropy of the surroundings, which is how enthalpy re-enters the rule.

The second half of the topic turns the same energy thinking to ionic solids. A Born-Haber cycle is Hess's law applied to forming an ionic lattice, and it gives a lattice energy you cannot measure directly. Comparing that with theory shows covalent character. Combining the lattice energy with hydration gives an enthalpy of solution, and with entropy the rule for solubility.

A route map in two rows. Block 12A, entropy: will a reaction happen? Enthalpy alone is not enough, then entropy is dispersal, then total entropy: system plus surroundings, then feasibility: temperature and speed. Block 12B, lattice energy: what is locked inside an ionic solid? Born-Haber cycles, then lattice energy and covalent character, then solution equals lattice plus hydration, then solubility needs entropy too. A dashed arrow joins the total entropy box to the solubility box, labelled the same total-entropy rule.
Route through the topic. The total-entropy rule from block 12A is used again for solubility at the end of block 12B.

The five jobs

Job Pages
Explain what entropy is, and say how it changes (solid, liquid, gas; moles of gas; dissolving) Enthalpy is not enough to Why entropy changes
Calculate ΔSsystem\Delta S_\text{system}, ΔSsurroundings\Delta S_\text{surroundings} and ΔStotal\Delta S_\text{total} Entropy change of the system and Surroundings and total entropy
Decide whether a reaction is feasible, find the temperature at which it becomes feasible, and separate this from speed Balance and temperature to Thermodynamic and kinetic stability
Define the enthalpy changes for ionic solids, then build and use a Born-Haber cycle Three definitions to Born-Haber calculations
Interpret lattice energies, calculate solution enthalpies, and predict solubility Covalent character to Group 2 solubility

What you need first

Values used in these notes

Quantity Value
gas constant, R 8.31 J mol⁻¹ K⁻¹ (only needed if you meet ΔG\Delta G)
temperature K = °C + 273
entropy J K⁻¹ mol⁻¹
enthalpy kJ mol⁻¹ (convert to J before dividing by T)

The standard entropy values used in the worked examples are given in the question, as they would be in an exam.

How to use these notes

Pages

  1. Enthalpy is not enough

    Some reactions take in heat and still happen by themselves. So the sign of ΔH cannot decide whether a reaction occurs, and we need a second quantity.

    8 min 12.1

  2. Entropy and dispersal

    Gases spread and energy spreads because spread-out arrangements vastly outnumber bunched-up ones. Entropy counts those arrangements, and natural change goes towards more of them.

    12 min 12.212.4

  3. Entropy of substances

    Entropy is zero for a perfect crystal at 0 K, rises with temperature, and jumps at melting and again, by more, at boiling. Solids have the lowest entropy and gases the highest.

    10 min 12.3

  4. Why entropy changes

    Entropy rises with changes of state to a gas, when an ionic solid dissolves, and when a reaction makes more moles of gas. Count the moles of gas first to predict the sign of the entropy change of the system.

    12 min 12.5(i)12.5(ii)12.5(iii)

  5. Entropy change of the system

    Add up the standard entropies of the products, subtract those of the reactants, and multiply each by its coefficient. The answer is in J K⁻¹ mol⁻¹, and its sign should match your prediction.

    10 min 12.7

  6. Surroundings and total entropy

    Heat passed to the surroundings changes their entropy by −ΔH / T. Add that to the entropy change of the system to get the total, and a change is feasible when the total is positive.

    14 min 12.412.612.8

  7. Balance and temperature

    Feasibility is a balance between the entropy change of the system and that of the surroundings. Temperature shifts the balance, because the surroundings term is −ΔH / T and shrinks as T rises.

    14 min 12.9(i)12.9(ii)12.10

  8. The feasibility temperature

    At the border of feasibility the total entropy change is zero, which gives T = ΔH ÷ ΔS for the system. Use it to say above or below which temperature a reaction goes.

    13 min 12.9(ii)

  9. Thermodynamic and kinetic stability

    Thermodynamic stability asks whether a change is feasible. Kinetic stability asks whether it is fast enough to see. A change can be feasible and still not happen, because of a high activation energy.

    9 min 12.11

  10. Three definitions for ionic solids

    Atomisation, electron affinity and lattice energy are the three new enthalpy changes behind a Born-Haber cycle. Each has a precise definition, and each is easiest to learn as an equation with state symbols.

    12 min 12.12(i)12.12(ii)12.12(iii)

  11. Building a Born-Haber cycle

    A Born-Haber cycle is Hess's law for an ionic solid. One route goes straight from the elements to the solid. The other goes through gaseous atoms and gaseous ions, and ends with the lattice energy.

    12 min 12.13

  12. Born-Haber calculations

    Rearrange Hess's law to get lattice energy = formation enthalpy minus the sum of the other steps. Watch the multiples for MgCl₂, the second ionisation energy, and the endothermic second electron affinity of oxygen.

    14 min 12.13

  13. Covalent character in ionic bonds

    A lattice energy from a Born-Haber cycle is the real value. One from electrostatic theory assumes pure ionic bonding. The gap between them measures covalent character, which arises when a cation polarises an anion.

    12 min 12.1412.15

  14. Enthalpy of solution and hydration

    Dissolving an ionic solid is lattice energy reversed, followed by hydration of the gaseous ions. The enthalpy of solution is the small difference between two large numbers.

    14 min 12.1612.17

  15. Charge and radius

    Lattice energy and hydration enthalpy both become more exothermic as ionic charge rises and ionic radius falls, because the charges are bigger and closer. Learn to explain every trend with these two factors only.

    10 min 12.18

  16. Will it dissolve?

    Dissolving is one more change that happens when the total entropy change is positive. The enthalpy of solution fixes the surroundings term, and the system term is ions dispersing against water becoming ordered.

    12 min 12.19

  17. Group 2 solubility trends

    Group 2 sulfates become less soluble down the group, and hydroxides more soluble. Both trends come from two terms, lattice energy and hydration enthalpy, which both fall as the cation gets bigger. The size of the anion decides which falls faster.

    12 min 12.19

Also in this topic: Topic 12 on a page

Spec checklist

Every point you can be examined on in this topic, and where it is explained. Tick them off as you go.

SpecYou should be able toWhere
12.1understand that, since endothermic reactions can occur spontaneously at room temperature, enthalpy changes alone do not control whether reactions occurEndothermic, yet it happens
12.2understand entropy as a measure of disorder of a system in terms of the random dispersal of molecules and of energy quanta between moleculesEnergy spreads out too
Entropy
The natural direction of change
12.3understand that the entropy of a substance increases with temperature, that entropy increases as solid → liquid → gas and that perfect crystals at zero kelvin have zero entropyThe zero point
Entropy rises with temperature
Solid, liquid, gas
12.4be able to interpret the natural direction of change as being in the direction of increasing total entropy (positive entropy change), including gases spread spontaneously through a roomA gas spreads out
The natural direction of change
Total entropy decides the direction
12.5(i)understand why entropy changes occur during: changes of stateChanges of state
12.5(ii)understand why entropy changes occur during: dissolving of a solid ionic latticeDissolving an ionic solid
12.5(iii)understand why entropy changes occur during: reactions in which there is a change in the number of moles from reactants to productsReactions with a change in moles
12.6understand that the total entropy change of any reaction is the sum of the entropy change of the system and the entropy change of the surroundings, summarised by the expression: ΔStotal = ΔSsystem + ΔSsurroundingsSystem and surroundings
Total entropy decides the direction
12.7be able to calculate the entropy change of the system for a reaction, ΔSsystem, given the entropies of the reactants and productsThe calculation
12.8be able to calculate the entropy change in the surroundings, and hence ΔStotal, using the expression ΔSsurroundings = −ΔH / THeat and the surroundings
12.9(i)understand that the feasibility of a reaction depends on: the balance between ΔSsystem and ΔSsurroundings, so that even endothermic reactions can occur spontaneously at room temperatureThe balance
12.9(ii)understand that the feasibility of a reaction depends on: temperature, as higher temperatures decrease the magnitude of ΔSsurroundings so its contribution to ΔStotal is less. Students should be able to calculate the temperature at which a reaction is feasible. Students may also use ΔG = ΔH − TΔSsystem in answers, although this approach is not a requirement of the specification.Temperature changes the balance
Where the total is zero
Using ΔG
12.10understand that reactions can occur as long as ΔStotal is positive even if one of the other entropy changes is negativeOne negative term is fine
12.11understand and distinguish between the concepts of thermodynamic stability and kinetic stabilityTwo kinds of stable
12.12(i)be able to define the terms: standard enthalpy change of atomisation, ΔatHEnthalpy change of atomisation
12.12(ii)be able to define the terms: electron affinityElectron affinity
12.12(iii)be able to define the terms: lattice energy (as the exothermic process for the formation of one mole of an ionic solid from its gaseous ions)Lattice energy
12.13be able to construct Born-Haber cycles and carry out related calculationsTwo routes, one total
The steps, in order
Lattice energy from the cycle
Magnesium chloride: multiples and a second step
Magnesium oxide: an endothermic second electron affinity
Working backwards
12.14understand that a comparison of the experimental lattice energy value (from a Born-Haber cycle) with the theoretical value (obtained from electrostatic theory) in a particular compound indicates the degree of covalent bondingExperimental and theoretical values
12.15understand that polarisation of anions by cations leads to some covalency in an ionic bond, based on evidence from the Born-Haber cyclePolarisation of the anion
12.16be able to define the terms 'enthalpy change of solution, ΔsolH' and 'enthalpy change of hydration, ΔhydH of an ion'Two definitions
12.17be able to use energy cycles and energy level diagrams to calculate the enthalpy change of solution of an ionic compound, using enthalpy change of hydration and lattice energyThe solution cycle
12.18understand the effect of ionic charge and ionic radius on the values of enthalpy change of hydration and the lattice energy of an ionic compoundThe data
The explanation
12.19be able to use entropy and enthalpy changes of solution values to predict the solubility of ionic compounds and discuss trends in the solubility of ionic compounds covered in Unit 2The same test as before
Temperature and the four cases
The trends from Unit 2
Which term falls faster?