Understanding points
Reactivity 1.2.3—Standard enthalpy changes of combustion, ΔHc⦵, and formation, ΔHf⦵, data are used in thermodynamic calculations. (AHL)
Reactivity 1.2.4—An application of Hess’s law uses enthalpy of formation data or enthalpy of
combustion data to calculate the enthalpy change of a reaction. (AHL)
Reactivity 1.2.5—A Born–Haber cycle is an application of Hess’s law, used to show energy changes in the formation of an ionic compound. (AHL)
Standard enthalpy change of formation
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The enthalpy change when 1 mole of a substance is made from its elements in their standard states
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∆H⊖ = 𝜮 ∆H⊖f (products) - 𝜮 ∆H⊖f (reactants)
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Elements in their standard states (most pure form at 298K and 100kPa, e.g. H2 (g) , O2 (g) ) have a standard enthalpy of formation of 0
Standard enthalpy change of combustion
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The enthalpy change when 1 mole of a substance is completely burnt in excess oxygen
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∆H⊖ = 𝜮 ∆H⊖c (reactants) - 𝜮 ∆H⊖c (products)
Born-Haber cycle
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Energy cycle of steps in ionic compound formation
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Used to determine lattice enthalpy (experimental lattice enthalpies cannot be directly determined)
Born- Haber cycle of MgCl2(s) | Born- Haber cycle of Na2O(s) |
∆Hθlat [MgCl2] : +642+148+244+738+1451-698 = +2525kJmol-1 | ∆Hθlat [Na2O] : +414.2+216+249+992-141+753= +2483.2 kJmol-1 |
*the -ve enthalpy of formation value becomes positive as the lattice enthalpy is going the opposite direction |
Common calculation pitfalls
1.
Halving bond enthalpy (atomisation of non-metal)
a.
ΔH value of 242 kJ mol-1 for Cl2(g) → 2Cl(g) for compounds like MgCl2
b.
But ΔH value of only 121 kJ mol-1 for ½Cl2(g) → Cl(g) for compounds like NaCl ˙.˙ only 1 Cl(g) needed.
2.
Doubling electron affinity (ionization of non-metal)
a.
ΔH value of -349 kJ mol-1 for Cl(g) + e- → Cl-(g) for compounds like NaCl
b.
But ΔH value of -698 kJ mol-1 of 2Cl(g) + 2e- → 2Cl-(g) for compounds like MgCl2 ˙.˙ 2 Cl(g) needed.
Lattice enthalpy: energy required to separate 1 mole of crystalline compound into its constituent gaseous ions
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NaCl(s) → Na+(g) + Cl-(g)
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MgCl2(s) → Mg2+(g) + 2Cl-(g)
Reaction Step | Definition | Metal | Non-metal | ΔH |
1. Atomization
“State change to gas” | Enthalpy change when 1 mole of gaseous atoms is formed from the element in its standard state
X(s or l) → X(g)
X2(g) → 2X(g) | Vapourization
1 mole of gaseous atoms | Breakage of bond (if diatomic/ polyatomic) | > 0 |
2. Ionization
“Transfer of electron(s)” | 1st Ionization Energy: Energy required to remove 1 mole of electrons from 1 mole of gaseous atoms to produce 1 mole of ions
X(g) → X+(g) + e- | Enthalpy of ionization | — | > 0 |
1st Electron Affinity: Energy released when 1 mole of gaseous atoms each gain 1 electron to form an ion with -1 charge
X(g) + e- → X-(g) | — | Electron affinity | < 0 generally | |
3. Lattice
“Electrostatic attraction” | The standard lattice enthalpy is the energy required to separate 1 mole of crystalline compound into its constituent gaseous ions | Electrostatic attraction between gaseous ions to form ionic lattice | < 0* |
Essentially, lattice enthalpy is how strong the lattice is, which is how strong the ionic bonds are
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Lattice enthalpy depends on the size and charge of the ions
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The smaller the ion and the greater the charge, the higher (more endothermic) the lattice enthalpy
1. Effect of Size
LiCl | NaCl | KCl | |
cation | Li+ | Na+ | K+ |
No. of occupied shells | 1 | 2 | 3 |
no. of electrons | 2 | 10 | 18 |
no. of protons | 3 | 11 | 19 |
Lattice Enthalpy (kJmol-1) | 1049 | 930 | 829 |
↳ most charge dense as 1+ charge is spread over the smallest radius
most endothermic
Lattice enthalpy | ↳ least charge dense as 1+ charge is spread over the largest radius
least endothermic
Lattice enthalpy |
2. Effect of Charge
NaCl | MgCl2 | CaCl2 | |
cation | Na+ | Mg2+ | Ca2+ |
No. of occupied shells | 2 | 2 | 3 |
no. of electrons | 10 | 10 | 18 |
no. of protons | 11 | 12 | 20 |
Lattice Enthalpy (kJmol-1) | 1049 | 2540 | 2271 |
↳ Cation has a charge of 1+, lower electrostatic interaction
Less endothermic lattice enthalpy | ↳ Cation has higher charge of 2+, stronger electrostatic interaction
More endothermic lattice enthalpy | ↳ Same 2+ charge as Ca2+ but is spread over a larger ionic radius
Less endothermic lattice enthalpy than MgCl2 |
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if the cation is the control variable, then we compare the anions
Enthalpy of hydration: enthalpy change when 1 mole of a gaseous ion is dissolved completely in water
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Na+(g) → Na+(aq)
Enthalpy of solution : enthalpy change when 1 mole of a solute is dissolved completely in excess solvent
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NaCl(s) → Na+(aq) + Cl-(aq)
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MgCl2(s) → Mg2+(aq) + 2Cl-(aq)
Scenario 1 | Scenario 2 |
When the sum of the enthalpy of hydrations is a greater magnitude than the lattice enthalpy, then the will ∆Hθsolution always be exothermic
This means that the ionic compound will almost always be soluble because the hydrated ions are more stable compared to when they are found within a lattice | When the sum of the enthalpy of hydrations is of less magnitude than of the lattice enthalpy, then the ∆Hθsolution will always be endothermic
This means that the ionic compound will most likely be not soluble because the hydrated ions are less stable than when they are found within a lattice |
Factors that affect Hydration Enthalpies
Mg2+ | Ca2+ | K+ | |
Charge of cation | 2+ | 2+ | 1+ |
no. of energy levels | 2 energy levels | 3 energy levels | 3 energy levels |
no. of electrons | 10e- | 18e- | 18e- |
no. of protons | 12p | 20p | 19p |
↳smallest ionic radius, greatest charge, greatest charge density
Largest, most exothermic, enthalpy of hydration | ↳ largest ionic radius, smallest charge, largest charge density
Smallest, least exothermic, enthalpy of hydration |