Lattice energy

Lattice energy is the enthalpy change when 1 mole of an ionic compound is formed from its gaseous ions under standard conditions

Na+(g) + Cl-(g) =>NaCl(s) ΔH°_latt.= -787Kj/mol

Mg2+(g) + 2Cl-(g) =>MgCl2(s) ΔH°_latt.= -2526Kj/mol

The value of ΔH°_latt is always negative/exothermic, because the definition specifies the bonding together of ions, not the separation of ions. The more exothermic the lattice energy, the stronger the ionic bonding in the lattice.

Enthalpy change of atomization

The standard enthalpy change when 1 mole of gaseous atoms is formed form its elements under standard conditions

Li(S) => LI(G) ΔH°_at.= 161Kj/mol

Cl2(g) => 2Cl(g) ΔH°_at.=122Kj/mol

The value of ΔH°_at. is always positive/endothermic because energy must be supplied to break the bonds holding the atoms in the element together

Electron affinity

The first electron affinity, ΔH°_ea1_., is the enthalpy change when 1 mole of electrons is added to 1 mole of gaseous atoms to form 1 mole of gaseous 1-ions under standard conditions

Cl(g) +e- => Cl-(g) ΔH°_ea1_._{=-348 Kj/mol}

S(g) + e- => S-(g) ΔH°_ea1_._{=-200 Kj/mol}

_{The enthalpy change for the first electron affinity,}ΔH°_ea1_{is generally negative/exothermic.}

_{The second electron affinity,}ΔH°_ea₂_._{is the enthalpy change when 1 mole of electrons is added to 1 mole of gaseous 1-ions to form 1 mole of gaseous 2-ions under standard conditions}

_{1st electron affinity:}

_{O(g) +e- => O-(g)}ΔH°_ea1_.=-141Kj/mol

_{2nd electron affinity:}

_{O-(g) +e- => O2-(g)}ΔH°_ea₂_.=798Kj/mol

_{The 2nd electron affinity is always endothermic and so are the 3rd 4th and so on, The overall enthalpy change in forming an oxide ion, O2- is found by adding together the 1st and 2nd electron affinities which is 657Kj/mol}

Enthalpy cycle

ΔH°_lat_t.= lattice energy

Hf= Standard enthalpy change of formation

H1= Enthalpy changes involved in changing the elements

Step 1: convert solid lithium into gaseous lithium

Li(s) =>Li(g) ΔH°_at.= 161Kj/mol

Step 2: Convert gaseous lithium atoms to gaseous lithium ions, 1st ionization

Li(g) => Li+(g) +e- ΔH°_i1.= 520Kj/mol

Step 3: Convert fluorine molecules to fluorine atoms, atomization

F2(g) => 2F(g) ΔH°_at.= 79Kj/mol

Step 4: Convert gaseous fluorine atoms to gaseous fluorine ions, 1st electron affinity

F(g) + E- => F- ΔH°_ea1.= -328Kj/mol

Step 5: Add all these values together for ΔH°_at.= 161Kj/mol. The enthalpy change of formation of lithium fluorine is -617Kj/mol

Calculating lattice energy

ΔH°_latt=ΔH°_F- ΔH°₁

Thus the lattice energy will be -617 - 432 = -1049Kj/mol

Born Haber cycle energy diagram

Start by putting down the elements in their standard state on the left hand side
Complete the cycle by adding the enthalpy change of formation, atomisation, ionisation energy, electron affinity and Lattice energy

Factors affecting the value of lattice energy

Ion size

As the ion size increases, the lattice energy becomes less exothermic

For any given anion, F- the lattice energy gets less exothermic as the size of the cation increases from Li+ to Cs+
For any given cation, Li+ the lattice energy gets less exothermic as the size of the anion increases form F- to I-

Charge on ions

The lattice energy becomes more exothermic as the ionic charges increases. We ca see this by comparing lithium fluoride, LiF and magnesium oxide, MgO. These compounds have the same arrangement of ions in their lattice structure. The cations Li+ and Mg2+ have similar sizes and the anions F- and O2- also have similar sizes. The major difference is the ionic charge.

The double charged Mg2+ and O2- ions in magnesium oxide will attract each other more strongly than the singly charged ions. Thus, the greater ionic charge, the greater the charge density resulting in stronger ionic bonds being formed

Ion polarization

• Many ionic compounds have covalent character due to bond polarisation

• Ions are not spherical in shape

• Positive charges on the cation may attract the electrons in the anion

• Resulting in distortion of the electron cloud

• Ability to attract electrons and distort an anion is called the polarizing power of the cation

Factors affecting ion polarization

The charge density of the anion or anion

EX: the cation is small and have a charge of 2+ while anion is big and have a charge of 2-

Size/radius of anion or cation

Longer radius results in more distribution of charge in the atom

Thermal stability of group 2 carbonates and nitrates

The relative stabilities of carbonates increases down the group in the order of Mg to Ba

The carbonate ion has a relatively large ionic radius so it is easily polarized by a small highly charged cation.
The ionic radius of group two metals increases down the group
The smaller the ionic radius, the better it is at polarizing the carbonate ion
Thus the degree of polarization of carbonate ion is from Ba2+ to Mg2+ increasing
The greater the polarization, the easier it is to weaken the carbon-oxygen bond

So we can say that Mg ions are better polarizers of carbonate ions compared to calcium ions

Enthalpy of solution

The energy absorbed or released when 1 mole of an ionic solid dissolves in sufficient water to form a very dilute solution

MgCl2(S) + aq => Mg2+(AQ) + 2Cl-(AQ) or MgCl(aq)

enthalpy values can be exothermic and endothermic and a compound is likely to be soluble in water only if ΔH°_sol. is negative or have a small positive value. Thus it is insoluble if the enthalpy has a large positive value

Enthalpy change of hydration

The enthalpy change when 1 mole of specified gaseous ion dissolves in sufficient water forming a very dilute solution

Ca2+(g) + aq =>Ca2+ (aq), ΔH°_hyd=-1650Kj/mol

The enthalpy change is always exothermic because ion dipole bonds are formed and the enthalpy change is more exothermic for ions with the same charge but smaller ionic radii and the same ionic radii but with a larger charge

Why do the ions break up in the water? When an ionic compound dissolves, they are attracted to the dipoles in the polar water molecules. The ions will break up and form ion-dipole bonds with the dipoles in the water molecule. The charge density affects the energy change in here too. The bigger the charge density, the more energy is released (for enthalpy of hydration).

Sulfates

Change in hydration enthalpy down the group

Smaller ions with the same charge have greater enthalpy changes of hydration
So the enthalpy change of hydration decreases, (gets less exothermic) in the order form Mg2+ to Ba2+

Change in lattice energy down the group

Lattice energy is greater if the ions forming the lattice are small
so the lattice energy decreases, (gets less exothermic) in the order of Mg2+ to Ba2+
Inversely proportional to radius

Hydroxides is the opposite of sulfates so we can remember by using OH LE, SO4 HE

Entropy

Entropy is a measure of the ‘disorder’ of a system, and that a system becomes more stable when its energy is spread out in a more disordered state
Standard molar entropy is the entropy when one mole of substance in its standard state
The values of all molar entropies are positive
Gases generally have much higher entropy values than liquids – which have higher entropy values than solids; hence the more gas molecules present, the greater the number of ways of arranging them.
For an exothermic reaction, energy released to the surroundings, increasing its arrangements – hence there is likely to be an increase in entropy and increase in the chance for chemical change to occur spontaneously
For an endothermic reaction, energy absorbed from the surroundings, decreasing its arrangements, hence there is likely to be a decrease in entropy and decrease in the chance for a chemical reaction to occur spontaneously
When the total enthalpy change is positive, the reaction will occur spontaneously, reaction is feasible
When it is negative, the reaction is not likely to occur (not feasible)

Enthalpy change of surroundings

surroundings= -△ H/T

△ H is the standard enthalpy change of the reaction

temperature is at kelvin

Gibbs free energy

Gibb's free energy is the measure of how feasible a reaction is. If the value is negative, then it is spontaneous, meaning that it will occur naturally/without doing anything. Rusting is an example of a spontaneous reaction.

The Gibbs free energy can be determined by the formula: G = H - TS

where

G - Gibbs free energy
H - enthalpy change of reaction (J)
T - Temperature (K)
S - Entropy change

Whether or not the reaction is spontaneous can be quickly predicted by the signs of the enthalpy change and the entropy change. If the enthalpy change is negative and the entropy change is positive, the Gibbs free energy is negative and therefore spontaneous. If the enthalpy change is positive and the entropy change is negative, the Gibbs free energy is positive and not spontaneous.