Born-Haber Cycle

Section 15.1 (AHL)

Lattice Enthalpy

Of an ionic crystal: the heat energy absorbed (at constant pressure) when 1 mol of solid ionic compound is decomposed to form gaseous ions separated to an infinite distance from each other

The reverse of lattice enthalpy is the heat energy released when 1 mol of an ionic solid is formed from gaseous ions

More

Lattice energies are a measure of the stability of a crystal

The greater the lattice energy, the more stable the lattice, the higher the melting point and boiling point

Electron Affinity

The first electron affinity (ΔHθEA(1)) is the

energy released when 1 mol of gaseous atoms accepts 1 mol of electrons to form singly charged negative ions

2nd electron affinity, (ΔHθEA(2)) is the energy

absorbed when 1 mol of gaseous ions with a single negative charge accept 1 mol of electrons

Example

Cl(g)

+ e- → Cl-(g)

ΔHθEA(1) = -364 kJ mol-1

O-(g) + e- → O2-

(g) ΔHθEA(2) = +844 kJ mol-1

The 2nd electron affinity is always endothermic because energy is required to overcome the mutual repulsion between negatively charged oxygen ion and the electron

Enthalpy Change of Atomization

Standard enthalpy change of atomization is the enthalpy change required to produce one mole of gaseous atoms of an element from the element in the standard state

Na(s)

→ Na(g)

ΔHθat = +103 kJ mol-1

Lattice Enthalpies of Ionic Compounds

Magnitude of the lattice enthalpy depends upon the nature of the ions involved

The greater the charge on the ions, the greater the electrostatic attraction, the greater the lattice enthalpy and vice versa

The larger the ions, the greater the separation of charges, and the lower the lattice enthalpy and vice versa

Example

Born-Haber Cycle An indirect way to measure lattice enthalpies

Example of Na(s)

+ ½Cl2(g)

→ NaCl Enthalpy of formation of NaCl = -411 kJ mol-1

Enthalpy of atomization of Na = + 103 kJ mol-1

Enthalpy of atomization of Cl = + 121 kJ mol-1

Electron affinity of Cl = -364 kJ mol-1

Ionization energy of Na = + 500 kJ mol-1

Enthalpies of atomization + electron affinity + ionization energy = enthalpy of formation + lattice enthalpy

Calculations

103 + (+121) + (-364) + (+500) = (-411) + L.E. 360 = -411 + L.E. 771 = L.E. Lattice enthalpy is +771 kJ mol-1

Example 2 Use a Born-Haber cycle to calculate the value

of the lattice enthalpy for MgCl2

Enthalpy of atomization of Mg = + 147 kJ mol-1

Enthalpy of atomization for Cl = 2 x +121 kJ mol-1

1st ionization energy for Mg = +736 kJ mol-1

2nd ionization energy for Mg = +1451 kJ mol-1

Electron affinity for Cl = 2 x -364 kJ mol-1

Continued

Enthalpy of formation of MgCl2 = -641 kJ mol-1

Enthalpies of atomization + electron affinity + ionization energies = enthalpy of formation + lattice energy

+ 147 + 2(121) + 736 + 1451 + 2 (-364) = -641 + L.E.

1848 = -641 + L.E. Lattice enthalpy is +2489 kJ mol-1

Experimental vs Theoretical Lattice Enthalpies

The Born-Haber cycle provides a way to indirectly measure through experimental techniques

An ionic model can be used to calculate theoretical lattice enthalpies

The electrostatic attractive and repulsive forces between the ions can be summed

Sometimes it works and sometimes it doesn't

Comparison

Explanation The more “purely” ionic, the closer the values are to

each other When the bond is partially covalent, this strengthens

the bond and the actual lattice enthalpy is higher The closer the EN values, the lower the difference

between the two values, which indicates covalent character will occur in the bonding.

NaCl has an electronegativity difference of 2.1 while AgI is 0.6, hence NaCl values of calculated and actual lattice enthalpies are close, while the values for AgI are not as similar.