Background Information

Lattice enthalpies and Born-Haber Cycle

Lattice enthalpy measures the strength of the forces between ions in an ionic solid. The greater the lattice enthalpy, the stronger the forces. The forces will break down into gaseous ions, scattering them apart. This can be shown by a simple diagram. This diagram is known as the Born-Haber Cycle.

For sodium chloride, the lattice enthalpy is 787 kJ/mol and it measures the strength of attractions between the ions in the solid. Note that energy is released when bonds are made, and it requires to break bonds.

Factors affecting Lattice enthalpy

Two main factors affecting lattice enthalpy are

the charge on ions
the ionic radii (distance between the ions)

Covalent and Ionic Character

There are multiple kinds of attractive forces, some including covalent and ionic bonds. Covalent bond creates a partial sharing of electrons between two nuclei. Ionic bonding involves the transfer of electrons of opposite charges. These bonds are determined by the difference of electronegativity between the electrons. Electronegativity measures how accurate an assumption is. It tells us neither the electron is gained or lost. Electronegativity greatly affects the character of a bond. Bonds formed between two atoms are not purely ionic bonds. There are some covalent characters because of the electrons density shared between the atoms. So the larger the electronegativity difference, the more ionic and compound becomes. The smaller the electronegativity difference, the more covalent the compound becomes (Mott). This can significantly affect the percent difference of experimental and theoretical lattice enthalpy values the more covalent the compound will be.

Ionic Lattice

Ionic lattice is formed by the attractions between negative ions and positive ions. It will form an oppositely charged pattern in a 3-dimensional structure as seen in the right. The ionic radius can be seen between the ions (distant of ions). This tells us the attraction between the ions. The energy that is required to remove ions is called lattice energy.

The two (2) factors that affect the value of lattice enthalpy is ionic charge and radius. The higher the charge and the smaller the radius, the larger the value. Lattice energy measures the strength of attraction between ions and is dependent on the charge and size of the ion.

Ionic lattice has different geometry depending on the size of the ions. It is important to know this when using the Born-Landé equation to find theoretical lattice enthalpy. Coordination number is used to express the number of ions surrounding the given lattice.

I will be investigating monovalent ionic salts using the formula MX, where M is the alkali metal and X is the halides. The ionic salts will have a rocksalt lattice with the coordination number of six (6). The exception to the rocksalt lattice is CsF, CsCl, and CsBr. The ionic structure of CsCl, for example, is different from NaCl. Therefore, the coordination number will be eight (8). The Madelung constant value will also change to 1.76267 instead of the 1.74756 which is the rocksalt Madelung constant.

Born-Landé Formula

Born-Landé equation is used to calculate the theoretical lattice enthalpy value. The Born-Landé equation is also defined below, where E = ΔH_lat° .

E = N_a M z⁺z^– e² / 4πε₀r₀(1−(1/n))

N_A = Avogadro’s constant (6.02 x 10²³ mol^-1)

M = Madelung Constant

z⁺ = charge number of cation

z^–= charge number of anion

e = elementary charge (1.6022 x 10^-19 C°)

ε₀= permittivity of free space (8.854 x 10^-12 C² J^-1 m^-1)

r₀= distance to closest ion

n = Born exponent, between the number 5 and 12

Using the Born-Landé equation will give a more accurate lattice enthalpy value than using, for example, the Kapustinskii equation or ionic model formula from the IB textbook. In the Born-Landé equation, Madelung Constant, M, is related to the geometry of the ionic lattice. It is only related to the crystal structure and not the size or charge of the ion.

In addition, the equations use the Born exponent, which determines the measurement of the compressibility of the solid, experimental or theoretically. You can find the value of n by taking the average value depending on the ions electron configuration using the table below.

Excerpt 2: Hudson, “E12 Understanding Crystal Structures”

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