2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

Contents

What you need to be able to do.........................................................2

References.....................................................................................4
Exercises .......................................................................................5
(1) Lattice Enthalpy and the Born-Haber Cycle ...............................5
(2) The Born-Haber Cycle ......................................................... 13
(3) Enthalpy change of solution ................................................. 23
(4) Factors affecting the size of ΔLEHo & ΔhydHo .............................. 28
(5) Theoretical Compounds ....................................................... 35
(6) Measuring enthalpy change of solution .................................. 39
(7) Entropy ............................................................................ 46
(8) Free Energy ...................................................................... 49
(9) More questions on entropy and free energy ............................ 54
Summary .................................................................................... 60
(1) Lattice Enthalpy .................................................................... 60
(2) Entropy ............................................................................... 61
Review questions .......................................................................... 62
Equilibria, Energetics & Elements Exam Questions ........................... 62
Glossary ...................................................................................... 76
Answers to numerical questions ...................................................... 78

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

What you need to be able to do

This study pack relates to the following sections of the specification
5.2 Energy
5.2.1 Lattice Enthalpy
Learning outcomes Additional guidance
Learners should be able to
demonstrate and apply their
knowledge and understanding of

(a) explanation of the term lattice Definition required

enthalpy (formation of 1 mol of
ionic lattice from gaseous ions,
∆LEH) and use as a measure of
the strength of ionic bonding in a
giant ionic lattice
(b) use of the lattice enthalpy of a Relevant energy terms: enthalpy
simple ionic solid (i.e. NaCl, change of formation, ionisation
MgCl2) and relevant energy terms energy, enthalpy change of
for: atomisation, electron affinity.
(i) the construction of Born–Haber
Definition required for first
cycles
ionisation energy and enthalpy
(ii) related calculations change of formation only
(c) explanation and use of the terms: Definitions required
(i) enthalpy change of solution
(dissolving of 1 mol of solute,
∆solH)
(ii) enthalpy change of hydration
(dissolving of 1 mol of gaseous
ions in water, ∆hydH)
(d) use of the enthalpy change of
solution of a simple ionic solid
(i.e. NaCl, MgCl2) and relevant
energy terms (enthalpy change
of hydration and lattice enthalpy)
for:
(i) the construction of enthalpy
cycles
(ii) related calculations

(e) qualitative explanation of the

effect of ionic charge and ionic
radius on the exothermic value of
a lattice enthalpy and enthalpy
change of hydration.

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

5.2.2 Enthalpy and entropy

Learning outcomes Additional guidance
Learners should be able to
demonstrate and apply their
knowledge and understanding of
Entropy
(a) explanation that entropy is a
measure of the dispersal of energy
in a system which is greater, the
more disordered a system

(b) explanation of the difference in

magnitude of the entropy of a
system:
(i) of solids, liquids and gases
(ii) for a reaction in which there is a
change in the number of
gaseous molecules

(c) calculation of the entropy change

of a system, ∆S, and related
quantities for a reaction given the
entropies of the reactants and
products

Free energy
(d) explanation that the feasibility of a
process depends upon the entropy
change and temperature in the
system, T∆S, and the enthalpy
change of the system, ∆H
(e) explanation, and related
calculations, of the free energy
change, ∆G, as: ∆G = ∆H – T∆S
(the Gibbs’ equation) and that a
process is feasible when ∆G has a
negative value

(f) the limitations of predictions made

by ∆G about feasibility, in terms of
kinetics.

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References
The topics covered in this study pack are also dealt with on:
P 96 – 100, 126 - 127 & 138 – 141 (Yr 12 Revision)
&
p 346 – 371
of the Chemistry textbook “A-Level Chemistry for OCR A”, by Rob Ritchie
and Dave Gent, published by Oxford University Press.
ISBN 9780198351979
You may also find the following resources in the 5D Lattice Enthalpy
document library on Sharepoint useful:
• Chem Factsheets
There are a number of Chem Factsheets (mostly under B:Information),
which contain additional notes and questions, with answers, to provide
additional learning resources on various aspects of this topic.
• Notes
o notes - BornHaber.doc

• Powerpoints
o Born Haber Cycle (RAM).ppt
o Lattice Enthalpy.ppt

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

Exercises
(1) Lattice Enthalpy and the Born-Haber Cycle
By the end of this exercise, you should be able to:
• Define the term lattice enthalpy and write equations to represent
the change associated with it.
• Explain and write equations for the other enthalpy changes
associated with the formation of ionic compounds.

Read p 346 - 351 of your textbook

 Review appropriate sections of Study Pack 3B “Enthalpy Changes”

Lattice Enthalpy is a measure of the strength of the ionic bonding in an

ionic compound.
1. Explain what causes ions to bond together in an ionic lattice.

2. Write down the definition of lattice enthalpy, and give its symbol.

3. Look at the definition and explain whether this value is likely to be

positive or negative.

4. Give the equations for the changes represented by the lattice energy
of each of the following ionic compounds:-
Remember to include the state symbols
(a) NaCl

(b) Calcium iodide

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(c) Iron(II) oxide

(d) Magnesium nitride

(e) Potassium carbonate

Although lattice enthalpies can be calculated by considering the

attractions and repulsions between ions within the ionic lattice, this can be
rather a difficult task and requires a detailed understanding of the actual
structure of the lattice and also an accurate knowledge of the distances
between each ion. Even then, it is likely to be inaccurate because such
calculations invariably assume that each ion is a perfect sphere, which is
often not the case.
Instead, lattice enthalpies are often calculated indirectly using a special
type of Hess’s Law cycle, known as a Born-Haber cycle.
The Born-Haber cycle is simply an enthalpy level diagram showing a series
of enthalpy changes involved in the formation of an ionic compound.
5. Consider the symbol fHo:-
(a) What does this symbol mean?

(b) Write down its definition.

(c) Write the chemical equation (including state symbols)

corresponding to this enthalpy change for NaCl.

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6. Add arrows, with labels, to show the remaining enthalpy changes in

the Hess Cycle below. Think carefully about the directions in which
the arrows should point.

ELEMENTS IONIC COMPOUND

 rH o

GASEOUS IONS

The arrow labelled rH is the sum of all the enthalpy changes involved in
forming the gaseous ions from the appropriate elements in their standard
states.
One of these enthalpy changes is the ionisiation energy of the cation
(positive ion).
7. Write down:-
(a) The definition of first ionisation energy.

(b) The symbol for first ionisation energy.

(c) The chemical equation for this energy change for the following
elements:-
(i) Sodium.

(ii) Calcium.

(iii) Iron.

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8. By what name are the following ionisation energies known?

(a) Mg+(g) → Mg2+(g) + e-

(b) Ti3+(g) → Ti4+(g) + e-

9. Explain the sign of ionisation energy and what happens to the

numerical value as more electrons are removed.

The definition of ionisation energy states the need for individual atoms in
the gaseous state.
This leads to consideration of another of the enthalpy changes involved,
namely the standard enthalpy change of atomisation, atHo.
10. What is meant by the term standard enthalpy change of atomisation?

11. Write down the chemical equations for atHo for the following
elements:-
(a) Sodium

(b) Zinc

(c) Chlorine

12. State and explain what sign you would expect for these enthalpy
changes.

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Ionisation energies refer specifically to the removal of electrons from

atoms in order to form positively charged ions (cations).
The enthalpy change for the process of addition of electrons to atoms to
form negative ions (anions) is known as electron affinity. Electron
affinities are defined in a similar way to ionisation energies in that they
are stepwise processes (1 electron at a time) and are numbered 1st, 2nd,
3rd etc.

13. Write down the definition of 1st electron affinity and give its symbol.

14. Write chemical equations, including state symbols, for the following
enthalpy changes:-
(a)  EA1Ho(Cl)

(b)  EA3Ho(P)

(c)  EA2Ho(O)

15. State and explain the exo- or endothermic nature of:-

(a) The 1st electron affinity.

(b) Subsequent electron affinities.

Like ionisation energy, electron affinities require individual gaseous atoms,

which means that these need to be formed from the element in its
standard state first. Enthalpy of atomisation is exactly the same for non-
metals (which form negative ions) as it is for metals.

REMEMBER – All these enthalpy changes are defined in terms of

1 mole of something.
You need to know 1 mole of what (atoms, ions or compound)!

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Summary
16. Give the symbols for the following enthalpy changes under standard
conditions and classify them as exothermic or endothermic:-
(a) K(s) → K(g)

(b) Na(g) → Na+(g)

(c) S(s) → S(g)

(d) Mg(s) → Mg(g)

(e) O2(g) → 2O(g)

(f) Al+(g) → Al2+(g)

(g) Cl(g) → Cl-(g)

(h) O-(g) → O2-(g)

(i) Li+(g) + Br-(g) → LiBr(s)

(j) 2Fe3+(g) + 3O2-(g) → Fe2O3(s)

17. Give the symbols for the sequence of enthalpy changes needed to
work out the following enthalpy changes:-
eg. Mg(s) → Mg2+(g) atHo (Mg), IE1Ho (Mg), IE2Ho (Mg)
(a) ½ Br2(g) → Br-(g)

(b) S(s) → S2-(g)

(c) 2 Na(s) → 2 Na+(g)

(d) O2(g) → 2 O2-(g)

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18. Which of the following equations represents the standard enthalpy

change of atomisation of iodine?
A. I2(s) → 2I(g)
B. ½ I2(s) → I(g)
C. ½ I2(g) → I(g)
D. I2(g) → 2I(g)
19. Which of the following pairs of statements concerning the 3rd electron
affinity of nitrogen is true?

Equation Value
A N(g) + 3e- → N3-(g) Exothermic

B N(g) + 3e- → N3-(g) Endothermic

C N2-(g) + e- → N3-(g) Exothermic

D N2-(g) + e- → N3-(g) Endothermic

20. Calculate the total enthalpy change, ΔrHo, of forming the gaseous
ions of sodium and chloride given that:

-411 kJ mol-1
Na(s) + ½ Cl2(g) NaCl(s)

ΔrHo -780 kJ mol-1

Na+(g) + Cl-(g)

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21. Calculate the total enthalpy change, ΔrHo, of forming the gaseous
ions of magnesium and oxide given that:

-602 kJ mol-1
Mg(s) + ½ O2(g) MgO(s)

Δ r Ho -3791 kJ mol-1

Mg2+(g) + O2-(g)

22. Calculate the enthalpy change of formation of Silver Oxide (Ag2O)

given that:
LEHo (Ag2O) = -2970 kJ mol-1
rHo = +2938 kJ mol-1

23. Calculate the lattice enthalpy of Lead Bromide (PbBr2) given that:
fHo (PbBr2) = -279 kJ mol-1
rHo = +1935 kJ mol-1

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(2) The Born-Haber Cycle

By the end of this exercise, you should be able to:
• Draw and label Born-Haber cycles showing the formation of ionic
compounds of various stoichiometries.
• Identify enthalpy changes and species in partially labelled Born-
Haber cycles.
• Calculate values for specific enthalpy changes from Born-Haber
cycles.

Read p 346 - 351 of your textbook


The steps we outlined in exercise 1 are too many to all be shown easily in
a simple Hess cycle (generally drawn as a triangle). A new way of
showing all of these stages in a more logical way was devised by two
German scientists, Max Born and Fritz Haber.

fHo
ELEMENTS Route 1 IONIC COMPOUND

Route 2
rHo
GASEOUS IONS LEHo

We will always construct a Born-Haber cycle in the same way. A template

is shown below which, when suitably modified, can be applied to any ionic
compound.

atHo EAHo
Gaseous Ions
Enthalpy

Route 2
IEHo
LEHo

atHo
Elements

Route 1  fH o Ionic Compound

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The diagram can be completed by adding the following enthalpy changes

for each route.

Route 1: Enthalpy of formation.

Route 2: Step 1: Atomisation of the metal.

Step 2: Ionisation of the metal (may be several steps).
Step 3: Atomisation of the non-metal.
Step 4: Electron affinity of the non-metal (may be several
steps).
Step 5: Lattice enthalpy

1. Use the template to complete the labelling of the Born-Haber cycle

below for the formation of Rubidium Iodide (RbI). Label each level
with the appropriate species and complete each enthalpy change
symbol appropriately.

atHo ( ) EA1Ho ( )
Enthalpy

Gaseous Ions

IE1Ho( )
LEHo ( )
atHo ( )
Rb(s) + ½ I2(s)
Elements

 fH o ( )

Ionic Compound

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2. Modify the template above in order to construct a Born-Haber cycle

for the formation of Magnesium Oxide (MgO). Label each step with
the appropriate species and the symbol for the associated enthalpy
change.
Remember – Two electrons will needed to be removed from the Mg
(two steps) and added to the oxygen (think about whether each
electron affinity is exo- or endothermic).

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3. Modify the template again in order to construct a Born-Haber cycle

for the formation of Calcium Bromide (CaBr2). Label each step with
the appropriate species and the symbol for the associated enthalpy
change.
Remember – Two electrons will needed to be removed from the Ca
and that there are two bromine atoms / ions involved (what
difference does this make to the labelling?).

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4. Modify the template again in order to construct a Born-Haber cycle

for the formation of Sodium Sulfide (Na2S). Label each step with
the appropriate species and the symbol for the associated enthalpy
change.

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5. Draw a fully labelled Born-Haber cycle diagram for the formation of

aluminium sulfide. Label each step with the appropriate species and
the symbol for the associated enthalpy change.

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6. Consider the following partially labelled Born-Haber cycle for the

formation of barium chloride.
Ba2+(g) + 2e- + 2Cl(g)

2 x atHo(Cl) H3
Level B
Level C
Enthalpy

Ba+(g) + e- + Cl2(g)

H1 H2
Level A

Ba(s) + Cl2(g)

fHo (BaCl2)
BaCl2(s)

State what labels should be in the diagram in place of the following:-

Level A H1

Level B H2

Level C H3

Given that the Born-Haber cycle is an energy cycle, it follows that it must
obey Hess’s Law.
7. What does Hess’s Law state?

Given this, the Born-Haber cycle can be used to calculate any of the
enthalpy changes, as long as all the others are known. It is generally used
to calculate the lattice enthalpy, but this is not always the case.
For example, if we consider the Born-Haber cycle we constructed earlier
for Rubidium Iodide, then we can write:

fHo (RbI) = atHo (Rb) +  IE1Ho (Rb) + atHo (I) +

 EA1Ho (I) + LEHo (RbI)

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8. Use the following data to determine the lattice enthalpy of Caesium

Chloride.

Standard enthalpy change H / kJmol-1

Atomisation of Caesium +79.0

Atomisation of Chlorine +121

1st ionisation energy of Caesium +376

1st electron affinity of Chlorine -346

Formation of Caesium Chloride -433

Lattice enthalpy of Caesium chloride ?

9. Calculate the lattice enthalpy of Calcium Fluoride, given the

following data.

Standard enthalpy change H / kJmol-1

Atomisation of Calcium +178

Atomisation of Fluorine +79.0

1st ionisation energy of Calcium +590

2nd ionisation energy of Calcium +1145

1st electron affinity of Fluorine -328

Formation of Calcium Fluoride -554

Lattice enthalpy of Calcium Fluoride ?

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10. Use the following data to determine the 1st electron affinity of
Bromine.

Standard enthalpy change H / kJmol-1

Atomisation of Calcium +178

Atomisation of Bromine +122

1st ionisation energy of Calcium +590

2nd ionisation energy of Calcium +1145

1st electron affinity of Bromine ?

Formation of Calcium Bromide -683

Lattice enthalpy of Calcium Bromide -2176

11. The following data was recorded in relation to rubidium sufide.

Standard enthalpy change H / kJmol-1

Atomisation of Rubidium +80.9

Atomisation of Sulfur ?

1st ionisation energy of Rubidium +403

1st electron affinity of Sulfur -200

2nd electron affinity of Sulfur +640

Formation of Rubidium Sulfide -361

Lattice enthalpy of Rubidium Sulfide -1944

The value for atHo (S) is:-

A +175.2 kJ mol-1
B +256.1 kJ mol-1
C +578.2 kJ mol-1
D +659.1 kJ mol-1

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12. The following data were recorded for potassium oxide.

Standard enthalpy change H / kJmol-1

Atomisation of Potassium ?

Atomisation of Oxygen +249

1st ionisation energy of Potassium +419

1st electron affinity of Oxygen -141

2nd electron affinity of Oxygen +798

Formation of Potassium Oxide -361

Lattice enthalpy of Potassium Oxide -2232

The standard enthalpy change of atomisation of potassium can be

deduced to be:
A +424.5 kJ mol-1
B +273 kJ mol-1
C +127 kJ mol-1
D +63.5 kJ mol-1

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(3) Enthalpy change of solution

By the end of this exercise, you should be able to:
• Define the terms enthalpy change of solution and enthalpy change
of hydration.
• Use Hess cycles to calculate enthalpy changes associated with
dissolving ionic compounds.

Read p 352 - 357 of your textbook


Once again, a Hess cycle can help to explain the enthalpy changes
involved when an ionic solid dissolves in water.

SOLID IONIC Route 1 IONIC SOLUTION

COMPOUND

Route 2

GASEOUS IONS

Route 1 is a single step process, the enthalpy change for which is known
as the enthalpy change of solution. Write down the definition in the box
below.

Standard enthalpy change of solution, solHo

Route 2 is a two step process requiring that first the ionic lattice is
broken into its constituent gaseous ions. The enthalpy change associated
with this process is the inverse of the ………………………. …….…………………….
During the second step, the ions become surrounded by, and form
electrostatic interactions with, solvent molecules. When the solvent is
water, this process is referred to as “hydration” and the enthalpy change
is known as the enthalpy change of hydration, hydH. Write down the
definition in the box.

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Standard Enthalpy change of Hydration, hydHo

Using data, we can construct a Hess cycle from which we can work out the
enthalpy change of solution of Sodium Chloride.

Enthalpy change H / kJmol-1

Hydration of Na+(g) -390
Hydration of Cl-(g) -363
Lattice enthalpy of Sodium chloride -780

ΔsolHo
NaCl(s) Na+(aq) + Cl-(aq)

-LEHo so
 (hydHo) so
-(-780 kJ mol-1)
-390 + (-363) kJ mol-1

Na+(g) + Cl-(g)

1. Use the above Hess cycle to calculate the standard enthalpy change
of solution of sodium chloride.

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2. Use the following data to construct a Hess cycle from which you can
work out the enthalpy change of solution of Aluminium Bromide.

Enthalpy change H / kJmol-1

Hydration of Al3+(g) -4690
Hydration of Br-(g) -335
Lattice enthalpy of Aluminium Bromide -5247

AlBr3(s) Al3+(aq) + 3Br-(aq)

Al3+(g) + 3Br-(g)

As we saw in exercise 2 above, we can represent the Hess’ Cycle with a

Born-Haber type diagram.

 hydHo

LEHo

solHo

Enthalpy

Where  Hohyd represents the sum of the individual enthalpy changes of

hydration of the constituent gaseous ions.

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3. What will be the signs of:-

(a) LEHo

(b) hydHo

(c) solHo?

4. Use the following data to draw a Hess or Born-Haber cycle and work
out the enthalpy change of hydration of Mg2+.

Enthalpy change H / kJmol-1

Solution of Magnesium Fluoride -17.7
Hydration of F-(g) -506
Lattice enthalpy of Magnesium Fluoride -2957

5. Use the following data to work out the enthalpy change of hydration
of OH-(g).

Enthalpy change H / kJmol-1

Hydration of Na+(g) -406
Solution of Sodium Hydroxide -42.7
Lattice enthalpy of Sodium Hydroxide -887

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6. Use the following data to calculate the lattice enthalpy of

Copper(II) Iodide.

Enthalpy change H / kJmol-1

Hydration of Cu2+(g) -2100
Hydration of I-(g) -293
Solution of Copper(II) Iodide -26.4

You may be aware that the mobile cold packs used to treat sports injuries
often consist of a solid compound with a positive value for solH. When the
seal is broken, the solid dissolves into solution, and the mixture cools
down.
7. One such product contains 12.20g of ammonium chloride, NH4Cl.
When the pack is used, this NH4Cl dissolves in water to produce a
mixture which has a total mass of 103.4g.
Given that the enthalpy change of solution of ammonium chloride is
+14.8 kJ mol-1, calculate the temperature change of the pack.

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(4) Factors affecting the size of ΔLEHo & ΔhydHo

By the end of this exercise, you should be able to:
• State the factors which affect the magnitude of the lattice enthalpy
of an ionic compound and the enthalpy of hydration of an ion.
• State and explain the effect of these factors on the magnitude of
the enthalpy changes.

Read p 358 - 361 of your textbook


Lattice enthalpy is the energy released when one mole of an ionic solid is
formed from its constituent gaseous ions. It is a measure of the strength
of the electrostatic forces of attraction between the oppositely charged
ions. The more energy released, ie the more exothermic the lattice
enthalpy, the stronger the electrostatic attraction.
In order to understand the factors affecting the size (magnitude) of the
lattice enthalpy we need to understand the the factors which affect
electrostatic attraction.
The two main properties of an ion which will affect its attraction to other
ions and to solvent molecules (eg. water) are its
charge (ionic charge)
and its
size (ionic radius)

Ionic Radius
1. What four things do we need to consider when we think about the
radius of an ion? (three of them are the same as for an atom).

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2. Using your ideas from Q1, draw circles estimating the relative size of
the ions in the following table. To help you, Na+ and S2- are shown
with their correct relative sizes.

H+

Li+ F-

Na+ Mg2+ Al3+ Si4+ P3- S2- Cl-

K+ Ca2+ Br-

3. State and explain how the lattice enthalpy will change as the radius
of the cation decreases?

As values of lattice enthalpy are negative

(exothermic), it is important in such explanations to
refer to changes as being “more negative” or “less
negative” (or more or less exothermic).
Simply stating “bigger” or “smaller” will not be good
enough as it leads to confusion.

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4. State and explain how you think the lattice enthalpy will change as
the radius of the anion increases?

5. Explain what difference you would expect between the lattice

enthalpies of NaCl and CsI.

Ionic Charge
6. This question relates to sodium oxide, Na2O, and calcium oxide, CaO.
The ionic radius of the Na+ ion and the Ca2+ ion are similar.
(a) What is likely to be the effect on the lattice enthalpy of the
oxide if Na+ is replaced by Ca2+?

(b) Explain this prediction.

7. Using similar arguments, state and explain the difference in lattice

enthalpy between NaCl and Na2S (although Cl- is slightly smaller than
S2- the difference is very small).

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Lattice enthalpy is a measure of the attraction between oppositely charged

ions in an ionic compound.
8. Why do ionic compounds generally have high melting points?

9. What might be expected to be the relationship between melting point

and lattice enthalpy of an ionic compound.

10. Compounds such as magnesium oxide and aluminium oxide are often
described as “refractory”. In this context it means that they have
very high melting points. Such materials are often used in the linings
of kilns and furnaces.
Using the ideas in this exercise, explain why MgO and Al2O3 might be
suitable for this purpose.

Enthalpy change of hydration

As we have seen from the discussion above, ionic radius and ionic charge
are intimately linked with the relative magnitude of the lattice enthalpy.
This is because both of these factors have a significant effect on the
attraction between oppositely charged ions.
Since hydration involves forming bonds (which are essentially electrostatic
attractions) between ions and the appropriate (+ or -) ends of water
molecules, then the same issues will be relevant in discussing the relative
strength of these bonds and hence the value of the enthalpy of hydration.

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11. Using the ideas outlined above, explain the following trends in the
enthalpy change of hydration of the following sets of ions.
(a)

Ion hydHo / kJmol-1

K+ -322
Rb+ -301
Cs+ -276

(b)

Ion hydHo / kJmol-1

Na+ -406
Mg2+ -1920
Al3+ -4690

12. State and explain the trend you would expect between the enthalpies
of hydration of F-, Cl-, Br- and I-.

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Charge Density
The quantity known as charge density is not specifically mentioned in the
specification, but it is strongly related to this topic and may be a useful
concept to use in the exam.
Ionic charge and ionic radius actually both affect the magnitude of lattice
enthalpy and enthalpy of hydration because they both affect a quantity
called charge density.

13. What is the relationship between the charge on the ion, the size of
the ion and a property called the charge density?

14. For the following, label the arrows as either increasing charge density
or decreasing charge density.

Li+ F-

Na+ Cl-

K+ Br-

Rb+ I-

15. How does the lattice enthalpy change as the charge density on an ion
decreases?

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16. What would be the predicted effect on the lattice enthalpy of the
change between P3- (as in Na3P) and Cl- (as in NaCl)?
(a) considering only the effect of the change in ionic charge

(b) considering only the effect of the change in ionic radius?

Predicting which effect will be greater is a conundrum which can be

solved by considering the charge density, since it is actually this
which governs the magnitude of these enthalpy changes.

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(5) Theoretical Compounds

This exercise is beyond the specification, but may help you to understand
why a knowledge of lattice enthalpy is important.
The Born-Haber cycle and the concept of lattice enthalpy can be used to
explain why some compounds exist while others do not.
Consider, for example, the compound between strontium and chlorine.
You are all well aware (or you should be) that strontium chloride has the
formula SrCl2. The question arises, therefore, why it is not SrCl or SrCl3. I
am sure you will all think about an explanation about strontium being in
group 2 and therefore having 2 electrons in its outer shell. While this
explanation may be appropriate for strontium, it is not an explanation
which will work for other elements, especially transition elements.
The real core of the explanation (and this relates to main group elements
such as Sr, just as much as to transition elements) is a consideration of
the energy changes involved.
1. Consider the theoretical compound SrCl (strontium(I) chloride).
The enthalpy changes involved are as follows:-

Standard enthalpy change H / kJmol-1

Atomisation of Strontium +164

Atomisation of Chlorine +122

1st ionisation energy of Strontium +550

1st electron affinity of Chlorine -349

Formation of Strontium(I) Chloride

-632
Lattice enthalpy of Strontium(I) Chloride
(calculated)

The lattice enthalpy of SrCl is calculated theoretically by considering

the ionic charges and distances between them in the suggested
structure.
(a) Use this data to calculate the standard enthalpy change of
formation, fHo of the theoretical compound SrCl.

(b) What does this value suggest about the likely existence of SrCl.

This may surprise you – and may lead to some questions…..!

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2. Now consider the real compound SrCl2. The additional enthalpy

changes you will need are:-

Standard enthalpy change H / kJmol-1

2nd ionisation energy of Strontium +1064

Formation of Strontium(II) Chloride

Lattice enthalpy of Strontium(II) Chloride -2154

(a) Explain why the lattice enthalpy of this compound is more

exothermic than that calculated for SrCl.

(b) Calculate the standard enthalpy change of formation, fHo of

SrCl2.

3. In order to explain the non-existence of SrCl, we need to consider

the following potential reaction:-
2SrCl(s) → Sr(s) + SrCl2(s)
(a) Explain what special type of redox reaction this represents.

(b) Use your values of fHo for SrCl and SrCl2 from questions 1 and
2 to calculate the enthalpy changes for the above reaction.

(c) Use your answer to (b) to suggest why SrCl does not exist.

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4. We can now consider the theoretical compound SrCl3. In this case,

you will also need the following enthalpy changes:-

Standard enthalpy change H / kJmol-1

3rd ionisation energy of Strontium +4138

Formation of Strontium(III) Chloride

-4560
Lattice enthalpy of Strontium(III) Chloride
(calculated)

(a) Explain why the 3rd ionisation energy of strontium is

significantly higher than the 2nd.

(b) Use this information to calculate the standard enthalpy change

of formation, fHo of SrCl3.

(c) Explain what this suggests about the likelihood of SrCl3

existing?

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5. Another way of looking at the possible existence of SrCl3 is to

consider the following potential redox reaction:-
2SrCl3 → 2SrCl2 + Cl2
(a) Use your values of fHo for SrCl2 and SrCl3 from questions 2 and
4 to calculate the enthalpy changes for the above reaction.

(b) Use this to explain why SrCl3 is unlikely to exist.

Your answers to the above questions should show you that the existence
of only SrCl2 rather than SrCl or SrCl3 can actually be explained in terms
of the energy changes involved. The explanation based on number of
electrons in the outer shell (which only works for some elements anyway)
is only relevant because of its importance in determining some of the
enthalpy changes involved, most particularly ionisation energies. It is
useful in that it points in the direction of the point where the maximum
beneficial (ie. exothermic) overall enthalpy change of formation will occur.

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(6) Measuring enthalpy change of solution

By the end of this exercise and the associated practical you should be able
to:
• Describe an experiment to measure the enthalpy change of
solution.
• Carry out calculations associated with such experiments.
• State and explain any issues and assumptions made in such
experiments
• Use experimental and other data to construct labelled energy cycles
linked to enthalpy of solution and carry out associated calculations.
You should complete this exercise after you have done Practical 5D (1) to
summarise the key points from your experiment.

This exercise is linked to Practical 5D (1)

 Remind yourself about p 352 - 354 of your textbook

p 116 of your text book “Halide tests”
1. A student carried out an experiment to determine the enthalpy
change of solution of anhydrous sodium thiosulfate, Na2S2O3. He
measured approximately 25cm3 of water into a plastic cup inside a
polystyrene cup all in a 250cm3 beaker.
He then added a known mass of anhydrous sodium thiosulfate,
stirred the mixture and recorded the temperature once it had
stopped changing. He recorded the following results:-
Mass readings

Mass of small beaker + Na2S2O3(s) / g 43.01

Mass of empty small beaker / g 37.00

Mass of Na2S2O3(s) used / g

Mass of 250cm3 beaker + cup / g 112.36

Mass of 250cm3 beaker + cup + solution formed / g 142.68

Mass of solution formed / g

Temperature readings

Final temperature / °C 27.0

Initial temperature / °C 22.0

Temperature change / °C

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Analysis
(a) Complete the tables to show the mass of solid and solution, and the
temperature change.
(b) Calculate the amount, in mol, of Na2S2O3(s) that dissolved.

amount of Na2S2O3(s) = ……………………………………………… mol

(c) Calculate the enthalpy change of solution, ΔsolH, of Na2S2O3(s), in

kJ mol-1.
Na2S2O3(s) + (aq) → Na2S2O3(aq)
Specific heat capacity of an aqueous solution = 4.18 J g-1 K-1.
Include the sign of your enthalpy change.
Show all your working.

ΔsolH of Na2S2O3(s) = ………………………………………… kJ mol-1

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Practical considerations
(d) Why was the polystyrene cup used to surround the experiment?

(e) In this calculation, the mass of the entire solution was used, rather
than simply the mass of water.
(i) Why was this approach taken?

(ii) What would have been the effect on the result obtained of using
only the mass of water in the calculation?

2. The student then carried out a similar experiment to determine the

enthalpy change of solution of hydrated sodium thiosulfate,
Na2S2O3•5H2O.
He recorded the following results:-
Mass readings

Mass of small beaker + Na2S2O3•5H2O(s) / g 37.79

Mass of empty small beaker / g 31.79

Mass of Na2S2O3•5H2O(s) used / g

Mass of 250cm3 beaker + cup / g 111.73

Mass of 250cm3 beaker + cup + solution formed / g 142.26

Mass of solution formed / g

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Temperature readings

Final temperature / °C 13.5

Initial temperature / °C 22.0

Temperature change / °C

Analysis
(a) Complete the tables.
(b) Calculate the enthalpy change of solution, ΔsolH, of Na2S2O3•5H2O(s),
in kJ mol-1.
Na2S2O3•5H2O(s) + (aq) → Na2S2O3(aq)
Include the sign of your enthalpy change.
Show all your working.

ΔsolH of Na2S2O3•5H2O(s) = ………………………………………… kJ mol-1

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3. Use the answers from Questions 1 & 2 to determine the enthalpy

change of reaction, ΔrH, for the reaction shown in the equation
below:
Na2S2O3(s) + 5H2O(l) → Na2S2O3•5H2O(s)
Give your answer to the nearest whole number.
Include the sign of your enthalpy change.
Show all your working.

ΔrH = ………………………………………… kJ mol-1

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4. The lattice enthalpy, ΔLEH, of Na2S2O3(s) can be calculated using a

Born-Haber cycle, and the data provided in the following table.

Letter Enthalpy change Value / kJ mol-1

Enthalpy change of atomisation of Na, ΔatH
A 107
(Na)

B First ionisation energy of Na, Δ IE1H (Na) 496

Enthalpy change of formation of

C -267
Na2S2O3(s), ΔfH (Na2S2O3(s))
Enthalpy change of reaction, ΔrH, for the
D following: 608
2S(s) + 1½O2(g) + 2e- → S2O32-(g)
Lattice enthalpy of Na2S2O3(s),
E To be calculated
ΔLEH (Na2S2O3(s))

(a) Complete the Born-Haber cycle below by adding the correct species,
including state symbols.
Label the enthalpy changes with their respective letters from the table
above.

2Na+(g) + S2O32-(g)

(b) Calculate the lattice enthalpy, ΔLEH, of Na2S2O3(s).

Show your working.

ΔLEH (Na2S2O3(s)) = ………………………………………… kJ mol-1

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5. Using the experimental results, the calculated lattice enthalpy for

Na2S2O3(s) from question 4, and the enthalpy change of hydration of
Na+ given below, determine the enthalpy change of hydration of
thiosulfate ions, ΔhydH (S2O32-).
Enthalpy change of hydration of Na+, ΔhydH (Na+) = -424 kJ mol-1
(a) Draw an enthalpy cycle that links lattice enthalpy and enthalpy
change of hydration to help you carry out this calculation.
Include all the enthalpy changes, the appropriate species and state
symbols.

(b) Calculate the enthalpy change of hydration of thiosulfate ions,

ΔhydH (S2O32-).
Show your working.

ΔhydH (S2O32-) = ………………………………………… kJ mol-1

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(7) Entropy
By the end of this exercise, you should be able to:
• Explain what is meant by the concept of entropy and state its units.
• State that processes with positive entropy changes are generally
favoured.
• Explain that entropy changes are often associated with changes in
physical state.
• Calculate enthalpy changes for some reactions.

Read p 362 - 364 of your textbook


Making a solution
As you will be aware from exercise (3), the process of dissolving an ionic
compound to form a solution can be exothermic or endothermic.
In the following table, the enthalpies of solution of the Group I chlorides
are compared with their solubilities (in moles of solute saturating 100 g of
water at 298 K).

Solubility
Enthalpy of solution
(mol /100 g of
(kJmol-1)
water)
NaCl +3.9 0.615
KCl +17.2 0.481
RbCl +16.7 0.781
CsCl +17.9 1.13

Each compound’s enthalpy of solution is endothermic yet the compound is

soluble. It may surprise you to notice that the more endothermic the
change, the more soluble the compound!
Despite the process of dissolving NaCl in water being endothermic, we all
know that salt freely dissolves (and in fact this process is very difficult to
prevent!).
We need to ask the question “WHY, when endothermic processes are
generally not favoured, do some of them still occur?”
The answer is to be found by considering a quantity called ENTROPY.
Write down the definition of the term “Entropy”

Entropy is

It is given the symbol

It is measured in units of

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Just as is the case with enthalpy changes, H, chemists are often
interested in entropy changes, ΔS. Changes in entropy are often
associated with changes of physical state.
1. Place the following physical states in order of increasing entropy
Liquid, Gas, Plasma, Solid

Lowest Entropy -------------------------------------- Highest Entropy

A solution is similar to a liquid, except it has a slightly higher entropy

because there is more than one material present.
2. Consider the following processes and decide what happens to the
entropy S.
Process Entropy
increase decrease

solid butter melts

water turns into steam
a precipitate of AgCl is formed when
silver nitrate and potassium chloride
solutions are mixed
solid sodium chloride dissolves in
water
perfume diffuses through a room
two liquids mix
magnesium reacts with oxygen to
produce solid MgO
hydrogen and oxygen react to make
H2O
Unlike with enthalpy, it is actually possible to calculate a value for the
Entropy, S of a material, using statistics.
Except for at 0 K (which has never been reached), entropy values are
always positive. There is always a certain amount of randomness in a
system.
The fact that Entropy can often be calculated means that changes in
Entropy, S, can also often be calculated.

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3. Calculating entropy changes ΔS:

ΔS = ΣS products - ΣSreactants Σ means ‘sum of’

species So/ JK-1mol-1 species So/ JK-1mol-1

C(graphite) 6 H2O(g) 189

C(diamond) 3 H2O(l) 70

H2(g) 131 CH4(g) 186

CO(g) 198 CaO(s) 40

CO2(g) 214 CaCO3(s) 90

O2(g) 205

Calculate the entropy changes ΔS for the following reactions:

(a) H2O(l)  H2O(g)

(b) C (graphite)  C (diamond)

(c) C (graphite) + O2(g)  CO2(g)

(d) CH4(g) + 2 O2(g) CO2(g) + 2 H2O(g)

(e) 2 CO(g) + O2(g)  2 CO2(g)

(f) CaCO3(s)  CaO(s) + CO2(g)

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4. We know that exothermic processes (those with negative values for

H) tend to be more favoured than endothermic ones.
As far as entropy changes, S, are concerned, what type of
processes tend to be favoured, those with positive values for S, or
those with negative values?

We know this from experience.

If you drop a set of sticks, they do not tend to land all standing
on end in a neat group! In fact, if they did, we would all be
shocked. They also do not tend to land on the floor all facing the
same direction.
The fact is that there are simply many more possible
arrangements of the sticks which appear to be random, than
there are which are neat. It is therefore far more likely that
there will be a random arrangement than a neat one, and this is
why that is what tends to happen.
The more particles there are, the greater this tendency
becomes, so given that with molecules there are so many….!

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(8) Free Energy

By the end of this exercise, you should be able to:
• Give the symbol for a free energy change and state its units.
• Write the equation which links the free energy change for a process
to the enthalpy change and the entropy change for that process.
• Carry out calculations based on this equation.
• Explain the relationship between the free energy change of a
process and its feasibility.

Read p 365 - 369 of your textbook


You should now be aware that dissolving an ionic compound in water will
always result in an increase in entropy (disorder or randomness), in other
words, S is positive. This means in principle that it is a favourable
process.
You will also be able to extend this idea to many other processes which
will involve an increase in entropy (eg. milk mixing into coffee, CO2
dispersing into the air from a reaction between marble chips and
hydrochloric acid or even oil dispersing into and mixing with water).
However, whilst you know that in the cases of milk and coffee and of CO2
and air, they will mix as described (and in both cases it is difficult to
prevent), the oil will not easily mix with the water.
The question arises, therefore, why certain processes which have
favourable entropy changes tend to happen (even many with
unfavourable enthalpy changes) whilst others do not.
1. Suggest why it is that milk and coffee will mix easily whereas oil and
water will not (you will need to think in terms if intermolecular
forces).

2. Suggest why MgO does not dissolve in water, while NaCl is soluble?

It turns out that there is a relationship between the enthalpy change, ΔH,
the entropy change, ΔS, and whether a process is likely to occur. The
temperature of the system is also important, which explains why some
processes are temperature dependent (eg. solid ice will become liquid
water at temperatures of 0oC or above, but not at temperatures below
0oC).

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A process which can occur naturally is described as feasible.

In order to predict whether a process is likely to be spontaneous, we need
to consider BOTH the enthalpy change, H, AND the entropy change, S,
and also the temperature, T.
These three quantities can be combined into one quantity, known as the
Free Energy Change. It is given the symbol G. The G symbol
arisies because the quantity is officially known as Gibbs Free Energy, after
the nineteenth century mathematician and physicist Josiah Willard Gibbs.
3. Write down the definition (formula) for Free Energy Change.

G =

It is generally measured in units of

4. Generally, what are the units of

(a) H

(b) S?

5. What MUST be the units of T?

6. What must be done to the units of S to make the equation for G

consistent?

7. State the condition for G for any process to be feasible.

8. Why might a feasible process not actually appear to occur?

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9. Consider the following reaction:-

CaCO3(s)  CaO(s) + CO2(g) ΔH = + 178 kJ mol-1.
(a) Using the data table given in exercise 7 (Page 48), calculate G
at 298K

(b) Use your answer to explain whether the reaction is feasible

under standard conditions?

(c) State what will happen to the value of G if the temperature is

increased above 298K.

(d) At a certain temperature, the value of G will be zero. Calculate

the temperature at which this is the case.

(e) Explain the significance of this temperature in terms of the

feasibility of the reaction.

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10. Complete the following table to show the sign of G and hence the
feasibility of a reaction.

Enthalpy Entropy Temperature, Free energy Feasible?

change, change, T change, G
H S
Positive Positive High
Low
Positive Negative High
Low
Negative Positive High
Low
Negative Negative High
Low
If the process requires a high or a low temperature in order to be feasible,
then there will be a minimum or a maximum temperature at which the
process is feasible. The change occurs at the point that G = 0.
It is very common for you to be asked about this in exam questions (eg.
see question 9)!

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(9) More questions on entropy and free energy

Whether a chemical reaction is feasible depends on the free energy
change, which under standard conditions is denoted ΔGo. This is related to
the standard entropy and enthalpy changes by the equation
ΔGo = ΔHo - TΔSo
Use this information, where relevant, to answer the questions which
follow.
1. Water boils at atmospheric pressure only if the surrounding
temperature rises above 100°C.
(a) State the signs of the enthalpy and entropy changes during
boiling.
(i) Sign of ΔHo

(ii) Sign of ΔSo

(b) By considering the above, explain why water does not boil at
temperatures below 100°C.

[4]
2. When solid potassium hydrogen carbonate is added to dilute
hydrochloric acid, a reaction occurs and the temperature of the
reaction mixture drops.
(a) Write the equation, including state symbols, for the reaction.

(b) State the sign of the enthalpy change, H.

(c) Explain why, given the sign of H, the reaction still takes place.

[4]

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3. The combustion of propane (Calor gas) in excess oxygen produces

carbon dioxide and steam.
Give the signs of the enthalpy change, of the entropy change and of
the free energy change for the combustion of propane. In each case
give a reason for your answer.
(a) Write the equation, including state symbols, for this reaction.

(b) Sign of ΔHo

Reason

(c) Sign of ΔSo

Reason

(d) Sign of ΔGo

Reason

[7]

4. Consider a reaction which, at a given temperature, has a positive

value for ΔG and a negative value for ΔS.
(a) Explain whether the reaction is feasible.

(b) State and explain whether increasing the temperature would

make ΔG less positive?

[3]

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5. Potassium chlorate(V) decomposes on heating according to the

equation
4KClO3(s) → 3KClO4(s) + KCl(s) ΔHo = +16.8 kJ mol-1
The standard molar entropy, So, for each species involved in the
reaction is shown below.
Substance So/ J K-1 mol-1
KClO3(s) 112
KClO4(s) 134
KCl(s) 83
(a) Calculate the standard entropy change for the above reaction.

[2]
(b) Calculate the free energy change, at 25 C, for the above
o

reaction.

[3]
(c) In terms of free energy, state the necessary condition for a
change to be feasible.

[1]
(d) Assuming that ΔH and ΔS do not vary with temperature,
determine the lowest temperature at which the above reaction
will become feasible.

[2]
(e) Explain why, even at temperatures higher than this, the above
reaction might still not take place.

[2]
[Total: 10]

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6. On heating, sodium hydrogen carbonate (NaHCO3) decomposes into

sodium carbonate, carbon dioxide and steam. At 298K, the standard
enthalpy change, ΔHo, for the decomposition of one mole of NaHCO3
is +65 kJ mol-1 and the corresponding standard entropy change, ΔSo,
is +168 J K-1 mol-1.
(a) Write an equation for the decomposition of NaHCO3

[1]
(b) Determine the standard Gibbs free energy change, ΔG , for this
o

decomposition at 298K.

[2]
(c) Explain why heating to a higher temperature is likely to make
the reaction feasible.

[3]
(d) Calculate the necessary temperature.

[2]
[Total: 8]

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7. Solid mercury(II) oxide, HgO(s), exists in two allotropic forms,

named “red” and “yellow”. Some thermodynamic data on the two
allotropes is shown in the table:-

Allotrope ΔfHo / kJ mol-1 So / J K-1 mol-1

HgO (red) -90.7 72.0
HgO (yellow) -90.2 73.0

(a) By drawing a suitable Hess cycle, calculate the standard

enthalpy change, ΔHo, for the process of converting the red
form to the yellow form:-
HgO(s) (red) → HgO(s) (yellow)

(b) What is the standard free energy change, ΔGo, for this process?

(c) By considering how this free energy change value will vary with
temperature, calculate the maximum temperature at which the
red form is likely to be thermodynamically stable with respect to
changing into the yellow form.

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8. But-2-ene exists as two stereoisomers, named E-but-2-ene and

Z-but-2-ene. The standard enthalpy change of formation, ΔfHo, of
E-but-2-ene is -10.1 kJ mol-1 , and its standard entropy, So, is
296 J K-1 mol-1.
The standard enthalpy change, ΔHo, for the interconversion of these
two isomers is shown.
E-but-2-ene → Z-but-2-ene ΔHo = +4.4 kJ mol-1
At 298K, E-but-2-ene is thermodynamically more stable and the
above conversion has a positive value for ΔGo. The conversion
becomes feasible at temperatures above 607oC.
(a) Draw the structures of E-but-2-ene and Z-but-2-ene and
explain why this type of isomerism arises in alkenes.

(b) Calculate the standard enthalpy change of formation, ΔfHo, of

Z-but-2-ene.

(c) Use the information above to deduce the standard entropy, So,
of Z-but-2-ene.

(d) Suggest why, even at high temperatures, the interconversion

may still not occur.

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Summary
(1) Lattice Enthalpy
Label each arrow with the symbol associated with the enthalpy change.

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(2) Entropy

Entropy is a quantitative measure of the degree of disorder in a system.

1. List four ways in which the entropy can be increased in a system:

2. How is entropy linked to Gibbs free energy ΔG?

3. In terms of free energy, what is a spontaneous reaction?

4. Why might a spontaneous reaction not actually happen at a certain

temperature?

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Review questions
Equilibria, Energetics & Elements Exam Questions

Please be aware that the symbols for the enthalpy changes have changed
slightly, such that, for example, the symbol for standard enthalpy change
of formation in these questions is Hfo, whereas you know it as fHo. Other
symbols have changed similarly. The meanings and definitions of these
terms, however, have not changed.

1. June 2011 Q1

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2. June 2012 Q1

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3. February 2012 Q2

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

Please be aware that the terminology around free energy changes has
changed with the new specification.
In situations where G < 0 (ie. negative), these questions use the word
“spontaneous” to describe such a reaction. This terminology has now
changed to “feasible”, which is the word you have learned to describe this
situation.
Please therefore substitute the word “feasible” for the word “spontaneous”
in these questions, and you should then be able to answer them.

4. January 2011 Q5

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

5. June 2011 Q5

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

6. February 2012 Q6

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

Glossary
Write down the meaning of the following terms and LEARN THEM!!!
(Use your textbook glossary to help you)

(first) Electron
Affinity

(second) Electron
Affinity

Endothermic

Enthalpy, H

(Standard)
Enthalpy Change of
Atomisation

(Standard)
Enthalpy Change of
Formation

(Standard)
Enthalpy Change of
Hydration

(Standard)
Enthalpy Change of
Solution

Enthalpy Cycle

Exothermic

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

Hess’ Law

Ion

(first) Ionisation
Energy

(second)
Ionisation Energy

Lattice Enthalpy

Standard
Conditions

Entropy

Free energy
change, ΔG

Feasible reaction

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

Answers to numerical questions

Exercise 1
20. +369 kJ mol-1 21. -3189 kJ mol-1
22. -32 kJ mol-1 23. -2214 kJ mol-1

Exercise 2
8. -663 kJ mol-1 9. -1969 kJ mol-1
10. -332 kJ mol-1 11. A = +175.2 kJ mol-1
12. D = +63.5 kJ mol-1

Exercise 3
1. +27 kJ mol-1 2. -448 kJ mol-1
4. -1962.7 kJ mol-1 5. -523 kJ mol-1
6. -2659.6 kJ mol-1 7. (-) 7.81oC

Exercise 5
1a -145 kJ mol-1
2b -830 kJ mol-1
3b -540 kJ mol-1
4b +675 kJ mol-1
5a -3010 kJ mol-1

Exercise 6
1b 0.0380 mol 1c -16.7 kJ mol-1
2b +44.9 kJ mol-1
3 -61.6 kJ mol-1
4b -2081 kJ mol-1
5b -1250 kJ mol-1

Exercise 7
4a +119 J K-1 mol-1 4b -3 J K-1 mol-1
4c +3 J K-1 mol-1 4d -4 J K-1 mol-1
4e -173 J K-1 mol-1 4f +164 J K-1 mol-1

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2nd Year P & I Chemistry 2019 - 2021 Study Pack 5D

Exercise 8
9a +129 kJ mol-1 9d 1085K

Exercise 9
5a +37 J K-1 mol-1 5b +5.77 kJ mol-1 5d 454 K
6b +14.9 kJ mol-1 6c 387K
7a +0.50 kJ mol -1
7b +0.20 kJ mol-1 7c 500K
8b -5.7 kJ mol-1 8c 301 J K-1 mol-1

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