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Revision notes on energetics - enthalpy changes associated with dissolving & lattice enthalpy - for Advanced A/AS Level Theoretical-Physical Chemistry:

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Part 2 ΔH Enthalpy Changes contd. – Lattice Enthalpy, Enthalpies of Solution, Enthalpies of Ion Hydration

2.1a–c Important enthalpy definitions and what happens when an ionic compound dissolves in water and the energetics of why?

What energy changes are associated with an ionic solid dissolving in water? A particle model is used to illustrate the dissolving of an ionic solid in water and the subsequent hydration of the free ions. The enthalpy of solution, lattice enthalpy and the hydration enthalpies of gaseous ions are then introduced and are all connected using a thermochemical cycle to theoretically explore 'some' of the factors that affect how soluble a salt/oxide etc. is soluble, i.e. does it dissolve appreciably or is it insoluble.

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2.1 What happens when an ionic compound dissolves in water and the energetics of why?

Section 2.1 discusses a dissolving enthalpy cycle – another application of Hess's Law – in which the process of dissolving an ionic compound such as a halide salt or a metal oxide, is broken down into theoretical stages to help understand the factors involved in deciding whether of not a substance will dissolve readily or not at all. For the moment, only enthalpy changes will be considered but eventually entropy changes must be discussed too!

This ΔH is called the ENTHALPY of SOLUTION
(i) ionic compound(s) + aq (c) doc b cations(aq)  +  anions(aq)
(ii) solid ionic compound vapourised to give gaseous ions – this ΔH is called the LATTICE ENTHALPY (c) doc b

(endothermic)

 

 

gaseous cations and anions

(exothermic)

 (iii) hydration of the cations and anions – these ΔHs are called the ENTHALPIES of HYDRATION of the ION
In terms of enthalpy changes: (i) = (ii) + (iii)

Enthalpy of solution ΔHsolution(compound) is defined as the heat absorbed or released when 1 mole of compound dissolves in water

Lattice enthalpy ΔHLE(compound) is defined as the energy released when 1 mole of a solid ionic is formed from its separated constituent gaseous ions (an exothermic definition).

Lattice enthalpy can also be defined as the energy required to completely dissociate 1 mole of an ionic compound into its gaseous constituent ions (endothermic definition).

Enthalpy of hydration is defined as the energy released when 1 mole of gaseous ions interacts with water to give a solution of the hydrated ions

Standard values of these enthalpy changes are usually at 298K and 1 atm./101kP pressure.

All three enthalpy terms are re–defined in more detail and explained further as  the discussion proceeds.

2.1a The changes that occur in the dissolving process

Despite the strong ionic bonding forces in most salts or simple binary compounds like oxide or chloride crystals i.e. the strong electrostatic attraction between positive ions (cations) and negative ions (anions) many ionic compounds readily dissolve in water. Therefore, not surprisingly, a great deal of energy is required to separate the ions, but dissolving can still take place. So how can we explain this?

Water consists of highly polar molecules due to the great electronegativity difference between hydrogen and oxygen (O > H hence the polarity of the bond δ–O–Hδ+). When salts dissolve in water a process of solvation occurs in which the ions become solvated by association with the solvent molecules. If water is the solvent, the process is called hydration and is exothermic because it involves particles coming together via intermolecular forces or covalent bonds in the case of aqua–cation complex ions – so this is a compensating source of energy.

In some cases cations become hydrated via dative covalent bonds to form a complex ions e.g.

Li(H2O)4]+, Cu(H2O)4]2+, Mg(H2O)6]2+,  Al(H2O)6]3+ etc. because in the case of water, the most electronegative part of the highly polar water molecule (>Oδ–) will be attracted to the positive ion and, since the oxygen atom has two lone pairs of electrons, it is also the source of the dative covalent bond by donation of one of these pairs of electrons into a vacant metal ion orbital.

In the case of anions, the positive ends of the water molecules (–Hδ+) will orientate themselves towards the negative anion and the water molecules become weakly associated with anion, but no covalent bonds are formed.

This solvation of the ions means the ions are effectively bigger particles which makes the distance between the positive and negative ion centres greater, and by the laws of electrostatics, the attractive forces is weakened and the hydration process is always exothermic.

PLEASE note that dissolving a solute in this situation cannot be simply regarded as a physical change. The ionic lattice is broken down, but NOT by melting, and chemical bonds are formed between the cation and water molecules to form hydrated ions or aqua–ions such as those listed above.

2.1b Diagram illustrating the dissolving–solvation–hydration process for sodium chloride crystals forming salt solution

  • For diagram simplicity, each ion is surrounded by four water molecules, though in reality, much more than this – see later.

  • The strong crystal lattice (giant ionic structure) is broken down by the solvation process so the salt dissolves and the ions are free to move around in the water solvent.

  • Its worth noting that this involves an increase in entropy – the solution is more disordered (more possible arrangements of the particles) compared to the pure liquid solvent and the highly ordered crystal lattice of very limited possible arrangements.

    • This increase in entropy favours the dissolving process, (as well as a very exothermic value for the enthalpy of solution!).

  • However, when the ions become hydrated there is a decrease in entropy, which counts against a substance dissolving. This decrease in entropy is due to the orientation of the water molecules when they associate with the cations and anions i.e. a decrease in the possible ways the water molecules can be arranged.

    • In other words the hydrated ions produce a more ordered arrangement of some of the water molecules.

    • This decrease in entropy does not favour dissolving, (and neither does a very endothermic enthalpy of solution)

  • Therefore you need to consider entropy changes to fully explain why substances do/do not dissolve – especially when the enthalpy of solution is positive or only slightly negative.

In order to try to understand processes you can use a Hess's Law cycle to break the process down into theoretical steps, each of which can measured experimentally or theoretically calculated. The relative magnitude of each energy change can help understand why a substance will dissolve or be insoluble. However, this cycle only uses enthalpy values and excludes entropy changes – which I'll deal with later.

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2.1c The connection between lattice enthalpy, enthalpies of ion hydration and enthalpy of solution

(i) The energy change for a substance dissolving in a solvent is called the enthalpy of solution.

The enthalpy of solution ΔHsolution(compound) is defined as the heat absorbed or released when 1 mole of compound (the solute) dissolves in a solvent to form an 'infinitely' dilute solution where no further heat change takes place at 298K e.g.

NaCl(s) + aq ===> Na+(aq) + Cl–(aq)  ΔHsolution(sodium chloride) = +4 kJ mol–1

Al2(SO4)3(s) + aq ===> 2Al3+(aq) + 3SO42–(aq)  ΔHsolution(aluminium sulfate) = –318 kJ mol–1

Examples of enthalpy of solution (kJ mol–1) are tabulated below and refer to an infinitely dilute solution

cation\anion OH– F– Cl– Br– I– CO32– NO3– SO42–
Li+ –21.2 +4.5 –37.2 –49.1 –63.3 –17.6 –2.7 –30.2
Na+ –42.7 +0.3 +3.9 –0.6 –7.6 –24.6 +20.5 –2.3
K+ –55.2 –17.7 +17.2 +20.0 +20.5 –32.6 +34.9 +23.8
NH4+ – +5.0 +15.2 +16.2 +13.4 – +25.8 +6.2
Mg2+ +2.8 –17.7 –155 –186 –214 –25.3 –85.5 –91.2
Ca2+ –16.2 +13.4 –82.9 –110 –120 –12.3 –18.9 –17.8
Sr2+ –46.0 +10.9 –52.0 –71.6 –90.4 –3.4 +17.7 –8.7
Al3+ – –209 –332 –360 –378 – – –318

Comments on the enthalpy of solution values

  • Quite a few of the values are relatively endothermic and perhaps at first sight dissolving seems unfavourable e.g. potassium nitrate (+34.9) and ammonium nitrate (+25.8), but both these salts are very soluble in water – you need to consider entropy too! (in Part 3)

  • The value depends on the structure and strength of the ionic lattice and the hydration enthalpies of the constituent ions.

  • You can get simple trends, but they are not easy to explain at times e.g.

    • For Group 1 hydroxides and fluorides delta H solution gets more exothermic/less endothermic BUT the chlorides, bromides and iodides get less exothermic/more endothermic on dissolving.

    • Group 2 compounds show a mixture of trends i.e. down the group more endothermic or more exothermic.

    • Aluminium compounds show the most exothermicity on dissolving, perhaps because of the high charge on the ion giving a large ion hydration enthalpy (see section below).

You can derive an alternative route to form the solution employing Hess's Law ...

(ii) The ionic crystal lattice is vapourised into its gaseous positive ion (cation) and gaseous negative ion (anion) constituents.

This is always a very endothermic process because you are separating strongly attracted oppositely charged ions.

This process is defined as happening in the reverse exothermic direction and is called the lattice enthalpy (lattice energy).

The lattice enthalpy ΔHLE(compound) is defined as the energy released when 1 mole of a solid is formed from its separated gaseous ions at 298K and is very exothermic e.g.

Na+(g) + Cl–(g)  ==> NaCl(s)   ΔHLE(sodium chloride) = –774 kJ mol–1

2Al3+(g) + 3O2–(g)  ==> Al2O3(s)   ΔHLE(aluminium oxide) = –15916 kJ mol–1

Factors affecting the lattice energy:

The greater the force of attraction the greater the energy needed to vapourise the lattice OR the greater the energy released on forming the ionic lattice.

The size of the ion radius and the ionic charges are the most important factors to consider.

(i) The smaller the ion radius or the greater the ion charge the greater the lattice enthalpy i.e. more exothermic. This effectively means the ions are closer together, so the centres of charge are closer together, hence a greater attractive force.

(ii) The greater the charge on the ion, the greater the attractive force between it and neighbouring ions.

The law of attraction of electric charges states that the force of attraction is proportional to the product of the charges divided by the distance between them

The attractive force is proportional to C+ x C– / d2

d = the distance between the ion centres

d is effectively the sum of the cation and anion radius for simple lattice structures

C+ and C– = the numerical charges on the cation and anion respectively

The greater the force of attraction, the greater the energy needed to separate the ions in the crystal.

This would be indicated by increase in melting point and enthalpy of fusion, boiling point and enthalpy of vaporisation, and of course, the lattice enthalpy.

The data table below illustrates the general rules outlined above.

Series and comments on examples of lattice enthalpies ΔHLE LE quoted as –ΔHLE(compound) in kJ mol–1
Comparing Group 1 halide salts - varying the halide

Decrease from F to I as the anion radius increases down group 7 (same trend for Na, K, Rb and Cs halides)

 LiF, 1022 LiCl, 846 LiBr, 800 LiI, 744
Comparing Group 1 halide salts - varying the cation

Decrease from Li to Cs as the cation radius increases down group 1 (same trend with group 1 chlorides, bromides or iodides)

 LiF, 1022 NaF, 902 KF, 801 RbF, 767
Comparing sodium chloride and magnesium oxide.

Neglecting radii differences, MgO has over 4x the lattice energy of sodium chloride because the ion charges are doubled i.e. 1+ x 1– compared to 2+ x 2–, a ratio of 1 : 4.

 NaCl

774

 MgO

3889

    
The first three Period 3 oxides

From left to right, increasing cation charge AND decreasing cation radius both lead to increase in lattice enthalpy.

Emphasised by considering the LE per mole of cation.

 Na2O

2488

1244 per mole of cation

 MgO

3889

3889 per mole of cation

 Al2O3

15916

7958 per mole of cation

  
         

(iii) The gaseous ions interact with water to give the hydrated ions in aqueous solution.

This is always a very exothermic process.

This energy change is called enthalpy of hydration.

The enthalpy of hydration is defined as the energy released when 1 mole of gaseous ions interacts with water to give a solution of the hydrated ions at 298K e.g.

Na+(g) + aq ==> Na+(aq)   ΔHhyd(Na+(g)) = –364 kJ mol–1

Cl–(g) + aq ==> Cl–(aq)   ΔHhyd(Cl–(g)) = –406 kJ mol–1

Factors affecting the ion hydration energy:

The size of the ion radius and the ion charge are the most important factors to consider here.

The smaller the ion radius or the greater the ion charge, the greater the ion hydration enthalpy i.e. more exothermic. The smaller the radius OR the higher the charge, the greater is the intensity–potential of the electric field so interaction with an oppositely charged particle (ion or polar molecule) is stronger and therefore more 'energetic' i.e. more exothermic.

Series and comments for the process Mn±(g) + aq ==> Mn±(aq) (always exothermic) – ion hydration enthalpies ΔHhyd(cation/anion) quoted as ΔHhyd(ion(g)) kJ mol–1
The first three Period 3 cations – decreasing radius and increasing charge – double trend effect, so more dramatic increase from left to right Na+(aq) –406 Mg2+(aq) –1920 Al3+(aq) –4690  
Group 1 cation trend, shows the effect of increasing radius down the group with decreasing enthalpy of ion hydration Li+(aq) –519 Na+(aq) –406 K+(aq) –322 Rb+(aq) –301
Group 7 halide anions, shows a similar effect of increasing radius F–(aq) –506 Cl–(aq) –364 Br–(aq) –335 I–(aq) –293
Comparing the iron(II) ion with the smaller and more highly charged iron(III) ion giving a considerable increase in hydration enthalpy Fe2+(aq), –1950 Fe3+(aq), –4430
         

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