Lecture 10: Enthalpy and Born-Haber Cycles

Quick Recap on Enthalpy

  • Symbol: ( \Delta H ) - Enthalpy Change measured under standard conditions.
  • Standard Conditions:
    • Room Temperature: 298 K (25°C)
    • Room Pressure: 100 kPa (1 atm)

Types of Enthalpy

  1. Enthalpy of Formation (( \Delta_f H ))

    • Change when 1 mole of a compound forms from its elements in standard states.
    • Example: ( 2C(s) + 3H2(g) + \frac{1}{2}O2(g) \rightarrow C2H5OH(l) )

  2. Enthalpy of Combustion (( \Delta_c H ))

    • Change when 1 mole of a substance is completely burned in oxygen.
    • Example: ( C2H5OH(l) + O2(g) \rightarrow CO2(g) + H_2O(g) )

  3. Enthalpy of Bond Dissociation (( \Delta_{diss} H ))

    • Change when all same type bonds in 1 mole of gaseous molecules are broken.
    • Example: ( Cl_2(g) \rightarrow 2Cl(g) )

  4. Enthalpy of Atomization (( \Delta_{atm} H ))

    • Change when 1 mole of gaseous atoms formed from an element in standard state.
    • Example: ( Na(s) \rightarrow Na(g) )

  5. Enthalpy of Ionization (1st and 2nd)

    • 1st: ( \Delta_{1stIE} H ) - Change to form 1 mole of gaseous 1+ ions from gaseous atoms.
      • Example: ( Li(g) \rightarrow Li^+(g) + e^- )
    • 2nd: ( \Delta_{2ndIE} H ) - Change to form 1 mole of gaseous 2+ ions from gaseous +1 ions.
      • Example: ( Li^+(g) \rightarrow Li^{2+}(g) + e^- )

  6. Enthalpy of Electron Affinity (1st and 2nd)

    • 1st: ( \Delta_{1st ea} H ) - Change to form 1 mole of gaseous 1- ions from gaseous atoms.
      • Example: ( O(g) + e^- \rightarrow O^-(g) )
    • 2nd: ( \Delta_{2nd ea} H ) - Change to form 1 mole of gaseous 2- ions from gaseous 1- ions.
      • Example: ( O^-(g) + e^- \rightarrow O^{2-}(g) )

  7. Enthalpy of Hydration (( \Delta_{hyd} H ))

    • Change when 1 mole of aqueous ions formed from 1 mole of gaseous ions.
      • Example: ( Na^+(g) \rightarrow Na^+(aq) )

  8. Enthalpy of Solution (( \Delta_{solution} H ))

    • Change when 1 mole of solute dissolves in enough solvent at constant enthalpy.
      • Example: ( NaCl(s) \rightarrow NaCl(aq) )

Lattice Enthalpy (( \Delta_{lattice} H ))

  • Measure of Ionic Bond Strength.
  • Types:
    1. Lattice Enthalpy of Formation: Change when 1 mole of solid ionic compound forms from gaseous ions.
      • Example: ( Na^+(g) + Cl^-(g) \rightarrow NaCl(s) )
    2. Lattice Enthalpy of Dissociation: Change when 1 mole of solid ionic compound dissociates into gaseous ions.
      • Example: ( NaCl(s) \rightarrow Na^+(g) + Cl^-(g) )
  • Lattice enthalpies can’t be calculated directly; use Hess’s Law to build a Born-Haber Cycle.

Constructing a Born-Haber Cycle

  • For the general reaction: ( X + Y \rightarrow XY )
  • Includes changes like:
    • Enthalpy of atomization, ionization, electron affinity, and lattice enthalpy.
  • Use the derived formula to find any missing enthalpy values using:
    ( \Delta Hf = \Delta H{atm} + \Delta H{1stIE} + \Delta H{1st ea} + \Delta H{lattice} + \Delta H{2ndIE} + \Delta H_{2nd ea} )

General Rules for Born-Haber Cycle

  1. ( \Delta H_f ) values are usually NEGATIVE (arrow down).
  2. ( \Delta H_{atm} ) values are usually POSITIVE (arrow up).
  3. ( \Delta H_{IE} ) values are always POSITIVE (arrow up).
  4. 1st ( \Delta H_{ea} ) values are usually NEGATIVE (arrow down).
  5. 2nd ( \Delta H_{ea} ) values are usually POSITIVE (arrow up).
  6. 1st ( \Delta H_{ea} ) values are usually NEGATIVE (arrow down).
  7. ( \Delta H_{lattice} ) values are always NEGATIVE (arrow down).

Example Calculations using Born-Haber Cycle

  1. Lithium Fluoride (LiF):

    • Reaction: ( Li(s) + \frac{1}{2}F_2(g) \rightarrow LiF(s) )
    • Steps:
      • Construct cycle, insert values (found in a table), derive formula, and calculate enthalpy of formation.

  2. Magnesium Chloride (MgCl2):

    • Reaction: ( Mg(s) + Cl2(g) \rightarrow MgCl2(s) )
    • Follow similar methodology as with LiF to find enthalpies using the Born-Haber cycle.

  3. Sodium Oxide (Na2O):

    • Reaction: ( 2Na(s) + \frac{1}{2}O2(g) \rightarrow Na2O(s) )
    • Again, follow steps as stated for the Born-Haber cycle.

  4. Magnesium Oxide (MgO):

    • Reaction: ( Mg(s) + O_2(g) \rightarrow MgO(s) )
    • Follow the same process to obtain necessary values.