Born-Haber cycles and lattice enthalpyAQA A-Level Chemistry: Subtopic test

1. 1
   A student is constructing a Born–Haber cycle for magnesium oxide, MgO, starting from the elements in their standard states. The cycle contains the enthalpy of formation of MgO, the enthalpies of atomisation of magnesium and oxygen, the first and second ionisation energies of magnesium, the first and second electron affinities of oxygen, and the lattice enthalpy of MgO.

   (a)

   Which equation represents the enthalpy of lattice formation of magnesium oxide?

   [1 mark]

   • AMg²⁺(g) + O²⁻(g) → MgO(s)
   • BMgO(s) → Mg²⁺(g) + O²⁻(g)
   • CMg(s) + ½O₂(g) → MgO(s)
   • DMg²⁺(aq) + O²⁻(aq) → MgO(s)

   (b)

   Which equation represents the second electron affinity of oxygen?

   [1 mark]

   • AO(g) + 2e⁻ → O²⁻(g)
   • BO⁻(g) → O(g) + e⁻
   • CO⁻(g) + e⁻ → O²⁻(g)
   • D½O₂(g) + 2e⁻ → O²⁻(g)

   (c)

   The second electron affinity of oxygen is endothermic. Explain why.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Born–Haber data are used to find the lattice enthalpy of magnesium chloride, MgCl₂. Standard enthalpy changes (kJ mol⁻¹): enthalpy of formation of MgCl₂ = −641; enthalpy of atomisation of Mg = +148; first ionisation energy of Mg = +738; second ionisation energy of Mg = +1451; enthalpy of atomisation of Cl = +122 (per mole of Cl atoms); first electron affinity of Cl = −349.

   (a)

   Calculate the enthalpy of lattice formation of magnesium chloride.

   [1 mark]

   • A+2524 kJ mol⁻¹
   • B−2524 kJ mol⁻¹
   • C−2751 kJ mol⁻¹
   • D−1242 kJ mol⁻¹

   (b)

   Which one of these changes in the cycle for magnesium chloride is exothermic?

   [1 mark]

   • AThe enthalpy of atomisation of magnesium
   • BThe first ionisation energy of magnesium
   • CThe second ionisation energy of magnesium
   • DThe first electron affinity of chlorine

   (c)

   Write an equation, including state symbols, for the second ionisation energy of magnesium. Explain why it is larger than the first ionisation energy.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The enthalpy of formation of calcium oxide, CaO, is −635 kJ mol⁻¹. Other standard enthalpy changes (kJ mol⁻¹): atomisation of Ca = +178; first ionisation energy of Ca = +590; second ionisation energy of Ca = +1145; atomisation of oxygen, ½O₂(g) → O(g) = +249; first electron affinity of oxygen = −141. The enthalpy of lattice formation of CaO is −3401 kJ mol⁻¹.

   (a)

   Calculate the second electron affinity of oxygen. Show your working.

   [3 marks]

   (b)

   Barium oxide has the same structure as calcium oxide. Predict how the enthalpy of lattice formation of barium oxide compares with that of calcium oxide, and explain your answer.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A chemist compares lattice enthalpies from Born–Haber cycles with values calculated using the perfect ionic model, in which ions are treated as perfect spheres with charge spread evenly over them. Enthalpies of lattice formation (kJ mol⁻¹): NaCl, Born–Haber −787 and perfect ionic model −766; AgI, Born–Haber −889 and perfect ionic model −778. Further data for NaCl (kJ mol⁻¹): atomisation of Na = +107; first ionisation energy of Na = +496; atomisation of Cl = +122; first electron affinity of Cl = −349.

   (a)

   For both NaCl and AgI, the Born–Haber value of the lattice enthalpy is compared with the perfect ionic model value. Explain what the data show about the bonding in each compound.

   [6 marks]

   (b)

   Calculate the enthalpy of formation of sodium chloride using the Born–Haber lattice enthalpy. Repeat the calculation using the perfect ionic model value, and state what the two results suggest about the bonding in sodium chloride.

   [6 marks]

   Total for question 4: 12 marks

End of questions