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# Chapter 05: Chemical Energetics

Chapter 5
Chemical Energetics Hess’ law

ΔHfθ = ∑ BE (bonds broken) - ∑BE (bonds formed)
Must remember to multiply the bond energies with the number of bonds broken or formed.

Worked Example 1:

What is the value of the ΔH for the reaction NH3(g) + 3F2(g) → NF3(g) + 3HF(g)
Consider the bonds broken and formed.
(Bond energies/ kJ mol-1: N-H = 390; F-F = 158; H-F = 562; N-F =272)

Step 1
Draw out the bonds of every reactant and product. This is to make sure you do not miss out any bonds. Step 2
Count the number of each bond.

N-H F-F N-F H-F
3(+390) 3(+158) 3(+272) 3(+562)

Step 3
Apply the formula:

ΔHθ = ∑ BE (bonds broken) - ∑BE (bonds formed)
= [ 3(+390) + 3(+158) ] - [ 3(+272) + 3(+562) ]
= -858 kJ mol-1

Note: Even if the answer is endothermic, the positive ‘+’ sign must still be written. Bond cycles

Worked Example 2:

Given the following enthalpy changes

I₂(g) + 3Cl₂(g) → 2ICl₃(s)

ΔHθ = -214 kJ mol⁻¹

I₂(s) → l₂(g)

ΔHθ = +38 kJ mol⁻¹

By drawing a suitable energy cycle, what is the enthalpy change of formation of ICI₃?

1. Always start by writing an equation for the reaction that the question is asking for. Hence in this question, we construct an equation for the enthalpy change of formation of ICI₃.
¹/² l₂(s) + ³/² Cl₂(g) → ICI₃(s)

2. Assess why the equation l₂(g) + 3Cl₂(g) → 2ICl₃(s) does not represent the enthalpy change of formation of ICI₃(s).
It does not since l₂ is solid at standard conditions. Enthalpy change of formation is the energy change when 1 mole of a compound is formed from its constituent elements in their standard states under standard conditions.

3. Hence connect the equations at hand to form a cycle. Answer: ΔHfӨ = (38-214) ÷ 2

= -88 kJ mol-1  Born-Haber cycles

Checklist for Born-Haber cycles

Equation are balanced with state symbol included

All Arrows are labelled with enthalpy changes

Label y-axis “ energy/kJ mol-¹ ” and “zero” for elements at standard states.

↓ arrow for exothermic reaction; ↑ arrow for endothermic reaction

Worked Example 3:

Construct a Born-Haber cycle for the formation of CaF from its elements. For ionic compounds like CaF₂ above, we can use the acronym FAIEL to check if we have included the necessary equations. Hopefully by using this acronym, you will “fail” to get such questions wrong again.

F Standard enthalpy change of Formation Ca(s) + F₂(g) → CaF₂(s) Standard enthalpy change of Atomisation Ca(s) → Ca(g) F₂(g) → 2F(g) Ionisation energy Ca(g) → Ca²⁺(g) = 2e⁻ Electron affinity 2F(g) + 2e⁻ → 2F⁻(g) Lattice energy Ca²⁺(g) + 2F⁻(g) → CaF₂(s)
F A Standard enthalpy change of Formation Ca(s) + F₂(g) → CaF₂(s) Standard enthalpy change of Atomisation Ca(s) → Ca(g) F₂(g) → 2F(g) Ionisation energy Ca(g) → Ca²⁺(g) + 2e⁻ Electron affinity 2F(g) + 2e⁻ → 2F⁻(g) Lattice energy Ca²⁺(g) + 2F⁻(g) → CaF₂(s)

Do note that this acronym is only applicable to ionic compounds. Solubility

Ever wondered why salt dissolves in water? The short answer is that although the ΔHsolθ of salt dissolving in water is endothermic, it is still relatively small enough for salt to be soluble in water. Required heat from the surroundings can be absorbed such that salt dissolves into water.
Generally, the more exothermic the  ΔHsolθ , the more soluble a solute is in a solvent. So, how do we determine the  ΔHsolθ and  hence solubility of an ionic compound in water?

Two stages are involved in the dissolution of ionic compounds,
Stage 1 : The ions are pulled far apart to form separate gaseous ions.
The heat change would be the reverse of lattice energy  -ΔHlattθ since ionic bonds are breaking to form the constituent gaseous ions of the ionic compound. Since energy is taken in to break bonds, this stage is always endothermic.

Stage 2: Solvent molecules, HO, form bonds to the gaseous ions to form a solution of aqueous ions. The heat change would be the enthalpy change of hydration, ΔHhydθ. Since energy is released to form ion-dipole interactions between HO molecules and ions, this stage is always exothermic. Thus, we can conclude that  ΔHsolθ = ΔHhydθ - ΔHlattθ

Generally, entropy, ΔS, increases when an ionic compound dissolves in water.
In stage 1, As the number of particles increases, the number of ways to arrange the gaseous particles increases too, thus disorder of the system increases and entropy increases.
In stage 2, as water molecules form bonds around the ions, their positions become more fixed and the number of ways to rearrange the particles decreases. Thus, disorder of the system decreases and entropy decreases.
Since overall entropy depends on both stages, and usually the disordering process in stage 1 is dominant, thus ΔS increases overall. Gibbs Free Energy and  Entropy

ΔGӨ = ΔHӨ - TΔSӨ
You can remember this equation using a mnemonic aid, which is the acronym Go Home To Sleep.
Do note that SI units for ΔGӨ and ΔHӨ are in kJ mol-1 while units for ΔSӨ are in JK-1mol-1 and T is in K.

ΔGӨ < 0 Forward reaction is spontaneous Reaction is not spontaneous Reaction is in equilibrium

Examples where reaction is in equilibrium and ΔGӨ = 0 would be when a phase change is taking place.

There are limits to ΔGӨ, however.
The spontaneity of a reaction using ΔGӨ is only possible under standard conditions. Also, a reaction might be spontaneous as ΔGӨ < 0, but kinetically too slow for an observable reaction.

Checklist for answering entropy change questions

Describe the change

State if there are more or less ways of arranging the particles/ distribute energy “packets” among particles

Hence state if there is greater or less disorder of the system

Thus entropy increases or decreases.

Using the above checklist,

Worked Example 4:

Describe and explain how the entropy of the following system will change during the stated process. Assume the pressure remains constant throughout.

1 mol of Cl2(g) at 298 K is heated to 373 K

Solution:

1. As temperature increases,
2. The system possesses more kinetic energy, hence there are more ways to arrange the particles.
3. This leads to greater disorder of the system,
4. Thus, entropy increases.

Continue Reading on Chapter 06: Reaction Kinetics