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Chemistry LibreTexts

Lattice Enthalpies and Born Haber Cycle (Worksheet)

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    96819
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    Q1.1

    Define the terms

    • lattice dissociation enthalpy
    • lattice formation enthalpy.

    Q1.25a57df6ca4340c198c6f07477dd93ad2.jpg

    \(\ce{NaCl}\), \(\ce{NaBr}\) and \(\ce{MgO}\) all have the same crystal structure.

    • Explain why the lattice dissociation enthalpy of \(\ce{NaBr}\) is a bit less than that of \(\ce{NaCl}\).
    • Explain why the lattice dissociation enthalpy of \(\ce{MgO}\) is about 5 times greater than that of \(\ce{NaCl}\).

    Q1.3

    • Define the term standard atomization enthalpy.
    • The standard atomization enthalpy of bromine is +112 kJ mol-1, and for sodium is +107 kJ mol-1. Write equations for the reactions that these figures relate to.

    Q1.4

    The Born-Haber cycle for the formation of sodium chloride is:

    • The +107 transition in the figure is the atomization enthalpy of sodium. Explain what all the other transitions represent.
    • Use the figures on the diagram to calculate the lattice formation enthalpy of \(\ce{NaCl}\).
    • Draw the equivalent diagram which would enable you to calculate the lattice formation enthalpy of magnesium chloride, \(\ce{MgCl2}\). Write the names of the enthalpy changes against each arrow rather than using actual values.

    Q1.5

    Lattice enthalpies can be calculated from figures obtained experimentally using Born-Haber cycles. They can also be calculated theoretically. The Table 1 gives experimental and theoretical values for the silver halides. (The values are listed as lattice dissociation energies. Don't worry about the difference between lattice energy and lattice enthalpy. All I am asking you to do is to compare the values without worrying about the exact difference between the two terms.)

    experimental (kJ mol-1) theoretical (kJ mol-1)
    AgF +967 +953
    AgCl +915 +864
    AgBr +904 +830
    AgI +889 +808
    • For AgF, the experimental and theoretical values are very close. What does that show?
    • For AgI, there is a much greater difference between the two values. What does that suggest?
    • Why do you think the difference between the two values increases as you go from AgF to AgI?

    Q1.6

    Two of the biggest enthalpy changes during a Born-Haber cycle are the energy needed to ionize the metal, and the energy released when the positive and negative ions come together to make the lattice - the lattice formation enthalpy. In terms of these energy changes, explain why magnesium forms a chloride with the formula \(\ce{MgCl2}\) and not \(\ce{MgCl}\) or \(\ce{MgCl3}\). (You do not have to quote any numbers here - you can discuss it perfectly well in general terms.)