Born-Haber Cycle Notes

Born-Haber Cycle

Overview

• The Born-Haber Cycle was developed by Max Born and Fritz Haber to analyze reaction enthalpies by examining individual reactions.

The Born-Haber Cycle

• Max Born and Fritz Haber used known thermodynamic data to develop a simplified, cyclic method for determining unknown lattice energies of ionic crystals.

Definition of the Born-Haber Cycle

• The Born-Haber Cycle calculates lattice enthalpy by comparing the standard enthalpy change of formation of an ionic compound to the enthalpy required to create gaseous ions from its elements.
• It's primarily used to calculate lattice enthalpies, which are hard to measure directly.

Born-Haber Cycle Components

• The cycle involves transforming elements (metal and non-metal) into an ionic compound via gaseous ions.
• Process:
  • Break bonds to form gaseous ions.
    • Metals lose electrons and become positively charged (+ve).
    • Non-metals gain electrons and become negatively charged (-ve).
  • Lattice Energy:
    • Is the attraction between the positive and negative ions.
• It is a specific type of Hess’ Cycle.
• $\Delta H_f$ represents the enthalpy of formation.

Example: Sodium Chloride (NaCl)

• The formation of NaCl(s) from Na(s) and Cl2(g) can be broken down into intermediate steps:
  • $Na(s) + \frac{1}{2} Cl_2(g) \rightarrow NaCl(s)$
  • (i) Metallic sodium into gaseous sodium atom
  • (ii) Dissociation of chlorine molecule into chlorine atoms
  • (iii) Gaseous sodium atom into gaseous cation
  • (iv) Gaseous chlorine atom into gaseous anion
  • (v) Combination of oppositely charged gaseous ions to form solid crystal

Step 1: Metallic Sodium to Gaseous Sodium

• The energy required to convert 1 mole of sodium metal into gaseous sodium atoms is the enthalpy of sublimation ($\Delta H_s$).
• This step is energy-consuming.
• $Na(s) + \Delta H_s \rightarrow Na(g)$
• $\Delta H_s = 108.5 \frac{kJ}{mol}$

Step 2: Dissociation of Chlorine Molecule

• The energy required to form 1 mole of chlorine atoms from chlorine molecules is the enthalpy of dissociation ($\Delta H_d$).
• $Cl<em>2(g) + 2\Delta H</em>d \rightarrow 2Cl(g)$
• $\frac{1}{2} Cl<em>2(g) + \Delta H</em>d \rightarrow Cl(g)$
• $\Delta H_d = 121.0 \frac{kJ}{mol}$

Step 3: Gaseous Sodium Atom to Gaseous Cation

• The energy required to remove 1 mole of electrons from 1 mole of gaseous atoms is the First Ionization Energy (IE).
• $Na(g) + IE \rightarrow Na^+(g) + e^-$
• $IE = 495.8 \frac{kJ}{mol}$

Step 4: Gaseous Chlorine Atom to Gaseous Anion

• The energy released when 1 mole of gaseous atoms accepts 1 mole of electrons is the First Electron Affinity (EA).
• This process releases energy.
• $Cl(g) + e^- \rightarrow Cl^-(g) + EA$
• $EA = -349 \frac{kJ}{mol}$

Step 5: Combination of Oppositely Charged Gaseous Ions

• The energy released when oppositely charged gaseous ions combine to form 1 mole of an ionic compound is the lattice energy (U).
• $Na^+(g) + Cl^-(g) \rightarrow NaCl(s) + U$
• $U = -769.8 \frac{kJ}{mol}$

Calculating ΔHf (Enthalpy of Formation)

• According to Hess’s Law, the sum of the energy changes during the various steps equals the enthalpy of formation ($\Delta H_f$) of NaCl(s).
• $\Delta H<em>f = \Delta H</em>s + \Delta H_d + IE + EA + U$
• $\Delta H_f = 108.5 + 121.0 + 495.8 + (-349) + (-769.8) = -393.5 \frac{kJ}{mol}$

Calculating Lattice Enthalpy

• The Born-Haber Cycle can calculate the lattice energy of an ionic solid if other thermodynamic data are known.
• Example: Magnesium Fluoride (MgF2)
  • Sublimation Energy (S) of Mg = $146.4 \frac{kJ}{mol}$
  • IE1 of Mg = $737 \frac{kJ}{mol}$
  • IE2 of Mg = $1449 \frac{kJ}{mol}$
  • Dissociation energy (D) of F = $158.8 \frac{kJ}{mol}$
  • EA of F = $-328 \frac{kJ}{mol}$
  • $\Delta H_f$ of MgF2 = $-1096.5 \frac{kJ}{mol}$