How to calculate lattice energy of magnesium sulfide?

Question

I am trying to calculate the lattice energy of magnesium sulfide (MgS) but am encountering some confusion due to the stoichiometry involved. Here are the relevant thermodynamic equations:

Mg(s) → Mg(g)  ΔH° = 148 kJ/mol
Mg(g) → Mg²⁺(g) + 2e⁻  ΔH° = 2186 kJ/mol
S₈(s) → 8S(g)  ΔH° = 2232 kJ/mol
S(g) + 2e⁻ → S²⁻(g)  ΔH° = 450 kJ/mol
8Mg(s) + S₈(s) → 8MgS(s)  ΔH°f = -2744 kJ/mol

I need to find the lattice energy of magnesium sulfide, represented as ΔH°MgS. However, I am unsure how to adjust the calculations since the reaction involves 8 moles of magnesium and 1 mole of sulfur. Could someone please guide me through the process? Thank you for your assistance!

Annalise Metz V · Accepted Answer

Take the second equation and flip it around. This changes the sign of ΔH°
Mg2+(g) + 2e- → Mg(g) ΔH°=-2186 KJ/mol
flip the fourth equation around. Again only the sign of ΔH° changes
S2-(g) → S(g) + 2e- ΔH°=-450 KJ/mol
Divide the fifth equation by 8. This also divides the value of ΔH° by 8
Mg(s) + 1/8S8(s) → MgS(s) ΔH°=-343 KJ/mol
flip the first equation
Mg(g) → Mg(s) ΔH°=-148 KJ/mol
flip the third equation and divide by 8
S(g) → 1/8S8(s) ΔH°=-279 KJ/mol
Now combine all the equations and you should get the desired equation. Add all the values for ΔH° and you get the lattice energy for MgS.
Mg2+(g) + S2-(g) → MgS(s) ΔH°MgS=-3406 KJ/mol

Anonymous · Answer

Lattice Energy Of Magnesium Sulfide

Anonymous

How to calculate lattice energy of magnesium sulfide?

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