Factors Affecting Lattice Enthalpy

Learning Objectives (OCR Spec 5.2.1)

By the end of this lesson you should be able to:

• Recall that lattice enthalpy depends on ionic charge and ionic radius
• Predict the relative magnitude of lattice enthalpies for related compounds
• Justify trends in lattice enthalpy using the electrostatic model
• Compare experimental and theoretical lattice enthalpies and explain any discrepancy
• Relate lattice enthalpy magnitudes to physical properties such as melting point

Electrostatics: The Theoretical Basis

The energy of interaction between a cation with charge +Q_+ and an anion with charge -Q_- separated by distance r is given, in simplified form, by Coulomb's law:

E ∝ (Q_+ x Q_-) / r

Applying this to an entire crystal lattice gives a more complex expression (the Madelung constant enters), but the two factors that determine how strongly the ions attract each other remain:

1. The charges on the ions: doubling either charge approximately doubles the energy.
2. The sum of the ionic radii (r): smaller ions sit closer together, so the attraction is stronger.

A more negative (more exothermic) lattice enthalpy therefore corresponds to:

• larger charges (2+/2- vs 1+/1-)
• smaller ions (shorter r)

Effect of Ionic Charge

Doubling the charge on a cation or anion has a huge effect on lattice enthalpy because the product Q_+ Q_- appears in the expression. Compare:

Compound	Cation	Anion	Lattice enthalpy / kJ mol^-1
NaF	Na+	F-	-918
MgO	Mg^2+	O^2-	-3791

Mg^2+ and O^2- are similar in size to Na+ and F-, but because both charges double, the product of the charges is 2 x 2 = 4 times larger, and the lattice enthalpy becomes roughly 4 times more exothermic. The measured ratio is 3791/918 ~ 4.1, very close to the theoretical factor of 4.

Effect of Ionic Radius

Increasing the size of either ion increases r (the distance between centres of positive and negative charge), so the lattice enthalpy becomes less exothermic.

Group 1 fluorides (increasing cation radius):

Compound	r(cation) / pm	Lattice enthalpy / kJ mol^-1
LiF	76	-1031
NaF	102	-918
KF	138	-817
RbF	152	-783
CsF	167	-747

As cation radius increases down the group the lattice enthalpy becomes progressively less exothermic. The trend is smooth because only the cation changes.

Sodium halides (increasing anion radius):

Compound	r(anion) / pm	Lattice enthalpy / kJ mol^-1
NaF	133	-918
NaCl	181	-787
NaBr	196	-751
NaI	220	-705

Same principle: the larger the anion, the longer the inter-ionic distance, the weaker the electrostatic attraction, the less exothermic the lattice enthalpy.

Combining Charge and Size

To compare compounds with different charges AND different sizes, think about the dominant factor. Charge usually dominates because it enters Coulomb's law as a product.

Worked example: Predict which has the more exothermic lattice enthalpy: CaO or NaCl.

• CaO has 2+ and 2- ions; charge product = 4.
• NaCl has 1+ and 1- ions; charge product = 1.
• Ca^2+ (114 pm) and O^2- (140 pm) are comparable to Na+ (102 pm) and Cl- (181 pm), within a factor of about 1.3.
• The charge factor (x4) beats the size factor (x1.3), so CaO must be much more exothermic.

Accepted values confirm: CaO = -3401 kJ mol^-1, NaCl = -787 kJ mol^-1.

Ranking Exercise

Arrange MgCl2, CaCl2, SrCl2 and BaCl2 in order of increasing magnitude of lattice enthalpy (most exothermic to least).

The cations all have the same charge (+2) and the anion is the same in each. What changes is the cation size: Mg^2+ < Ca^2+ < Sr^2+ < Ba^2+. Smaller cation -> closer approach -> more exothermic lattice enthalpy.

Order: MgCl2 most exothermic > CaCl2 > SrCl2 > BaCl2 least exothermic.

Values:

• MgCl2: -2526 kJ mol^-1
• CaCl2: -2258 kJ mol^-1
• SrCl2: -2156 kJ mol^-1
• BaCl2: -2056 kJ mol^-1

Smooth trend.