Born-Haber cycles & lattice enthalpy

A value for enthalpy of solution can be determined from the results of a calorimetry experiment or by the application of Hess’s law.

Give the equation, including state symbols, for the process that occurs when the enthalpy of solution of potassium hydroxide is determined.

A student does an experiment to determine a value for the enthalpy of solution of potassium hydroxide.

The student uses this method.

• Add some distilled water to a measuring cylinder and record the volume.

• Pour the water into a polystyrene cup.

• Record the temperature of the water in the cup.

• Add 3.00 g of solid KOH to the water in the cup.

• Stir the solution and record the maximum temperature reached.

Table 1 shows the student’s results.

The student calculated the enthalpy of solution of potassium hydroxide

The specific heat capacity of the solution, c = 4.18 J K^–1 g^–1

Assume the density of the solution = 1.00 g cm^–3

Calculate the volume of water that the student added to the cup.

Table 2 shows some enthalpy change data.

Use the data in Table 2 to calculate the enthalpy of solution for potassium hydroxide.

Suggest why the value calculated in Question 01.3 is different from the experimental value given in Question 01.2.

This question is about enthalpy changes.

Theoretical values for enthalpies of lattice dissociation can be calculated using a perfect ionic model.

State the meaning of the term perfect ionic model.

Enthalpies of lattice dissociation can also be obtained from Born–Haber cycles.

Figure 3 shows an incomplete Born–Haber cycle for the formation of sodium oxide.

Complete Figure 3 by writing formulas, including state symbols, of the appropriate species on each of the two blank lines.

Table 4 shows some enthalpy changes.

Use the data in Table 4 to calculate the enthalpy of lattice dissociation of sodium oxide.

Explain why the second electron affinity of oxygen has a positive value.

Explain why the enthalpy of lattice dissociation for sodium oxide is greater than the enthalpy of lattice dissociation for sodium chloride.

Sodium chloride dissolves in water.

Table 5 shows some more enthalpy changes.

Use the data in Table 5 to calculate the enthalpy of solution for sodium chloride.

Give a reason why data books do not contain a value for the enthalpy of solution of sodium oxide.

Calculate the temperature, in °C, at which this reaction becomes feasible.

This question is about metal chlorides.

Table 2 shows some enthalpy change data.

Use the data in Table 2 to calculate the molar enthalpy change when calcium chloride dissolves in water.

Molar enthalpy change
kJ mol^–1

Use your answer to Question 05.1 to deduce how the temperature changes when calcium chloride dissolves in water.

Explain why the enthalpy of hydration of fluoride ions is more negative than the enthalpy of hydration of chloride ions.

Figure 2 shows an incomplete Born–Haber cycle for calcium chloride.

Complete the Born–Haber cycle by writing the formulas of the missing species on each of the two blank lines.

Table 3 shows some enthalpy change data.

Use Figure 2 and data from Table 3 to calculate the second ionisation energy of calcium.

Second ionisation energy
kJ mol^–1

Explain why the second ionisation energy of calcium is greater than the first ionisation energy of calcium.

Table 4 shows lattice enthalpies based on a perfect ionic model and lattice enthalpies from Born–Haber cycles for three metal chlorides.

Discuss the values in Table 4.

In your answer you should

compare the three values based on a perfect ionic model

compare the values based on a perfect ionic model to the values from a Born–Haber cycle for each compound.

A value for enthalpy of solution can be determined in two ways:

• from a cycle, using lattice enthalpy and enthalpies of hydration

• from the results of a calorimetry experiment.

Define the term enthalpy of lattice dissociation.

The enthalpy of solution for ammonium nitrate is the enthalpy change for the reaction shown.

Draw a suitably labelled cycle and use it, with data from Table 1, to calculate the enthalpy of lattice dissociation for ammonium nitrate.

A student does an experiment to determine a value for the enthalpy of solution for ammonium nitrate.

The student uses this method.

• Measure 25.0 cm³ of distilled water in a measuring cylinder.

• Pour the water into a beaker.

• Record the temperature of the water in the beaker.

• Add 4.00 g of solid NH₄NO₃ to the water in the beaker.

• Stir the solution and record the lowest temperature reached.

Table 2 shows the student’s results.

Calculate the enthalpy of solution, in kJ mol¹, for ammonium nitrate in this experiment.

Assume that the specific heat capacity of the solution, c = 4.18 J K¹ g¹

Assume that the density of the solution = 1.00 g cm³

The uncertainty in each of the temperature readings from the thermometer used in this experiment is ±0.1°C

Calculate the percentage uncertainty in the temperature change in this experiment.

Percentage uncertainty

Suggest a change to the student’s method, using the same apparatus, that would reduce the percentage uncertainty in the temperature change.

Give a reason for your answer.

Another student obtained a value of +15 kJ mol¹ using the same method.

Suggest the main reason for the difference between this experimental value for the enthalpy of solution and the correct value of +26 kJ mol¹

Table 3 shows some entropy data at 298 K

	Entropy S / J K1mol1
NH4NO3(s)	151
NH4(aq)	113
NO3(aq)	146

Calculate a value for the Gibbs free-energy change (G), at 298 K, for the reaction when ammonium nitrate dissolves in water.

Use data from Table 3 and the value of H from the equation. Assume for the solvent, water, that the entropy change, S = 0

Explain what the calculated value of G indicates about the feasibility of this reaction at 298 K

Ammonium nitrate decomposes as shown.

The entropy change (S) for this reaction is +144 J K^–1 mol¹

Calculate the temperature at which this reaction becomes feasible.

This question is about enthalpy changes for calcium chloride and magnesium chloride.

State the meaning of the term enthalpy change.

Figure 1 shows an incomplete Born–Haber cycle for the formation of calcium chloride.

Complete Figure 1 by writing the formulas, including state symbols, of the appropriate species on each of the three blank lines.

Table 1 shows some enthalpy data.

Use Figure 1 and the data in Table 1 to calculate a value for the enthalpy of lattice dissociation of calcium chloride.

Magnesium chloride dissolves in water.

Give an equation, including state symbols, to represent the process that occurs when the enthalpy of solution of magnesium chloride is measured.

Table 2 shows some enthalpy data.

Use your answer to Question 01.4 and the data in Table 2 to calculate a value for the enthalpy of solution of magnesium chloride.

The enthalpy of hydration of Ca²⁺(g) is –1650 kJ mol^–1

Suggest why this value is less exothermic than that of Mg²⁺(g)

This question is about enthalpy changes.

Figure 1 shows a Born–Haber cycle for the formation of strontium chloride, SrCl₂

Table 1 shows some thermodynamic data.

Use the data in Table 1 to calculate a value for the electron affinity of chlorine.

State why there is a difference between the theoretical and experimental values.

Table 3 shows enthalpy of hydration values for ions of some Group 1 elements.

Explain why the enthalpy of hydration becomes less exothermic from Li⁺ to K⁺

Calcium bromide dissolves in water.

Table 4 shows some enthalpy data.

Use the data in Table 4 to calculate the enthalpy of hydration, in kJ mol^–1, of bromide ions.

Figure 1 shows an incomplete Born–Haber cycle for the formation of caesium iodide. The diagram is not to scale.

Figure 1

Table 1 gives values of some standard enthalpy changes.

Complete Figure 1 by writing the formulas, including state symbols, of the appropriate species on each of the two blank lines.

Use Figure 1 and the data in Table 1 to calculate the standard enthalpy of atomisation of iodine.

The enthalpy of lattice formation for caesium iodide in Table 1 is a value obtained by experiment. The value obtained by calculation using the perfect ionic model is –582 kJmol^–1

Deduce what these values indicate about the bonding in caesium iodide.

Use data from Table 2 to show that this reaction is not feasible at 298 K

This question is about lattice enthalpies.

Figure 1 shows a Born–Haber cycle for the formation of magnesium oxide.

Complete Figure 1 by writing the missing symbols on the appropriate energy levels.

Table 1 contains some thermodynamic data.

Calculate a value for the enthalpy of lattice formation for magnesium oxide.

Which equation represents the process that occurs when the standard enthalpy of atomisation of iodine is measured?

Lattice enthalpy values can be obtained from Born–Haber cycles and by calculations based on a perfect ionic model.

Which compound shows the greatest percentage difference between these two values?