Lattice Energy Born Haber Cycle

Calculations Using Born-Haber Cycles

In one case a Born-Haber cycle has been constructed, information technology is possible to calculate the lattice energy (ΔH_latt ^ꝋ) past applying Hess'south law and rearranging:

ΔH_f ^ꝋ= ΔH_at ^ꝋ+ ΔH_at ^ꝋ+ IE + EA + ΔH_latt ^ꝋ

If we simplify this into three terms, this makes the equation easier to run into:
- ΔH_latt ^ꝋ
- ΔH_f ^ꝋ
- ΔH₁ ^ꝋ(the sum of all of the diverse enthalpy changes necessary to convert the elements in their standard states to gaseous ions)
The simplified equation becomes

ΔH_f ^ꝋ= ΔH_ane ^ꝋ + ΔH_latt ^ꝋ

So, if we rearrange to calculate the lattice free energy, the equation becomes

ΔH_latt ^ꝋ= ΔH_f ^ꝋ - ΔH₁ ^ꝋ

When calculating the ΔH_latt ^ꝋ, all other necessary values will be given in the question
A Born-Haber cycle could be used to calculate any stage in the cycle
- For example, you could exist given the lattice energy and asked to calculate the enthalpy change of formation of the ionic compound
- The principle would be exactly the same
- Work out the direct and indirect route of the cycle (the stage that you are being asked to summate will e'er be the direct road)
- Write out the equation in terms of enthalpy changes and rearrange if necessary to calculate the required value
Recall: sometimes a value may need to exist doubled or halved, depending on the ionic solid involved
- For example, with MgCl_two the value for the first electron affinity of chlorine would need to exist doubled in the adding, because there are two moles of chlorine atoms
- Therefore, y'all are calculation 2 moles of electrons to 2 moles of chlorine atoms, to grade ii moles of Cl^- ions

Worked example: Computing the lattice energy of KCl

Chemical Energetics - Worked example_Calculating the lattice energy of KCl, downloadable AS & A Level Chemistry revision notes

Answer

Stride i: The corresponding Built-in-Haber bicycle is:

Chemical Energetics - Constructing a Born-Haber cycle for KCl Cycle 1, downloadable AS & A Level Chemistry revision notes

Step ii: Applying Hess' law, the lattice energy of KCl is:

ΔH_latt ^ꝋ = ΔH_f ^ꝋ - ΔH₁ ^ꝋ

ΔH_latt ^ꝋ = ΔH_f ^ꝋ - [(ΔH_at ^ꝋ G) + (ΔH_at ^ꝋ Cl) + (IE₁ K) + (EA_ane Cl)]

Footstep 3: Substitute in the numbers:

ΔH_latt ^ꝋ = (-437) - [(+90) + (+122) + (+418) + (-349)] = -718 kJ mol^-ane

Worked example: Calculating the lattice free energy of MgO

Chemical Energetics - Worked example_Calculating the lattice energy of MgO, downloadable AS & A Level Chemistry revision notes

Reply

Footstep 1: The corresponding Born-Haber cycle is:

Chemical Energetics - Constructing a Born-Haber cycle for MgO Cycle 2, downloadable AS & A Level Chemistry revision notes

Step two: Applying Hess' law, the lattice energy of MgO is:

ΔH_latt ^ꝋ = ΔH_f ^ꝋ - ΔH₁ ^ꝋ

ΔH_latt ^ꝋ = ΔH_f ^ꝋ - [(ΔH_at ^ꝋ Mg) + (ΔH_at ^ꝋ O) + (IE_one Mg) + (IE₂ Mg) + (EA₁ O) + (EA₂ O)]

Step three: Substitute in the numbers:

ΔH_latt ^ꝋ = (-602) - [(+148) + (+248) + (+736) + (+1450) + (-142) + (+770)]

= -3812 kJ mol^-ane

Test Tip

Make certain you use brackets when carrying out calculations using Born-Haber cycles equally you may forget a +/- sign which volition affect your final answer!