Questions on enthalpies of solution and hydration

Question 1

Explain, in terms of lattice enthalpy and hydration enthalpy, why magnesium sulfate is soluble in water and barium sulfate is almost insoluble.

Accepted Answer

Indicative content

the enthalpy of solution is the lattice enthalpy of dissociation plus the hydration enthalpies of the two ions
the sulfate ion is large, so the distance between the ions is dominated by the sulfate and changes little from Mg²⁺ to Ba²⁺
the lattice enthalpy of dissociation therefore falls only slightly from MgSO₄ to BaSO₄
Ba²⁺ is much larger than Mg²⁺, so its charge density is lower and its hydration enthalpy much less exothermic, −1360 against −1920 kJ mol⁻¹
the hydration enthalpy falls by much more than the lattice enthalpy, so the enthalpy of solution is much more endothermic for BaSO₄
the more endothermic the enthalpy of solution, the less soluble the salt, so MgSO₄ dissolves and BaSO₄ does not

Levels

Level 3 (5–6 marks) the enthalpy of solution is set out as the sum of the two terms for both salts, the lattice enthalpy is shown to change little because the large sulfate ion dominates the spacing, the hydration enthalpy is shown to fall much more because of the lower charge density of Ba²⁺, and the more endothermic enthalpy of solution is linked to insolubility
Level 2 (3–4 marks) both terms are used and Ba²⁺ is said to hydrate less exothermically because of its size; why the lattice enthalpy hardly changes, or how the enthalpy of solution decides solubility, is not explained
Level 1 (1–2 marks) lattice or hydration enthalpy is mentioned on its own; barium sulfate is often said to be insoluble because its lattice is the stronger one

Question 2

State what is meant by the terms enthalpy of hydration and enthalpy of solution, and state how the starting states of the two differ.

Accepted Answer

B1 enthalpy of hydration: the enthalpy change when one mole of gaseous ions B1 dissolves in water to form one mole of aqueous ions; reject 'one mole of compound' for the hydration enthalpy B1 enthalpy of solution: the enthalpy change when one mole of an ionic solid dissolves in enough water that the ions are well separated and do not interact B1 hydration starts from separate gaseous ions, whereas solution starts from the solid lattice

Question 3

Describe how water molecules are arranged around a sodium ion and around a chloride ion in aqueous solution, and explain why every enthalpy of hydration is negative.

Accepted Answer

B1 around Na⁺ the water molecules point their δ− oxygen atoms towards the ion B1 around Cl⁻ the water molecules point a δ+ hydrogen atom towards the ion B1 the gaseous ion attracts the oppositely charged end of each polar water molecule, an ion–dipole attraction; reject 'covalent bonds form between the ion and water' B1 attractions form and none are broken, so energy is released and the enthalpy change is negative

Question 4

Calculate the enthalpy of solution of strontium chloride from the data in the table, and state whether dissolving it warms or cools the water.

Accepted Answer

M1 ΔsolH = ΔLEH(dissociation) + ΔhydH(Sr²⁺) + 2 × ΔhydH(Cl⁻) M1 the hydration enthalpies sum to −1480 + 2 × (−364) = −2208 kJ mol⁻¹ A1 ΔsolH = +2156 − 2208 = −52 kJ mol⁻¹, two significant figures; error carried forward from M2 if the chloride was not doubled, which gives +312 B1 the enthalpy of solution is negative, so dissolving is exothermic and the water warms; allow ecf from a positive answer to 'cools'

Question 5

Calculate the enthalpy of solution of magnesium chloride. The lattice enthalpy of dissociation of MgCl₂ is +2525 kJ mol⁻¹; the enthalpies of hydration are −1920 kJ mol⁻¹ for Mg²⁺ and −364 kJ mol⁻¹ for Cl⁻.

Accepted Answer

M1 ΔsolH = ΔLEH(dissociation) + ΔhydH(Mg²⁺) + 2 × ΔhydH(Cl⁻) M1 the chloride value is doubled: 2 × (−364) = −728 kJ mol⁻¹ M1 the hydration enthalpies sum to −1920 − 728 = −2648 kJ mol⁻¹; error carried forward from M2 if the chloride was not doubled A1 ΔsolH = +2525 − 2648 = −123 kJ mol⁻¹, three significant figures, negative sign required

Question 6

Evaluate this claim: 'The enthalpy of solution of sodium chloride is positive, so sodium chloride cannot dissolve in water at room temperature.'

Accepted Answer

B1 the claim is contradicted by observation: sodium chloride dissolves readily in water at room temperature B1 the enthalpy change alone does not decide whether a change is feasible B1 dissolving increases entropy, because ions spread through the water are more disordered than ions in a lattice B1 the TΔS term is larger than the small positive ΔH, so ΔG = ΔH − TΔS is negative and dissolving is feasible; the claim is wrong

Question 7

Calculate the enthalpy of hydration of the fluoride ion, given that the enthalpy of solution of sodium fluoride is +1 kJ mol⁻¹, its lattice enthalpy of dissociation is +913 kJ mol⁻¹, and the enthalpy of hydration of Na⁺ is −406 kJ mol⁻¹.

Accepted Answer

M1 ΔsolH = ΔLEH(dissociation) + ΔhydH(Na⁺) + ΔhydH(F⁻), so ΔhydH(F⁻) = ΔsolH − ΔLEH(dissociation) − ΔhydH(Na⁺) M1 ΔhydH(F⁻) = +1 − 913 − (−406) A1 ΔhydH(F⁻) = −506 kJ mol⁻¹, three significant figures, negative sign required

Question 8

Explain why the enthalpy of hydration of Mg²⁺, −1920 kJ mol⁻¹, is much more exothermic than that of Na⁺, −406 kJ mol⁻¹.

Accepted Answer

B1 Mg²⁺ has a larger charge than Na⁺ B1 Mg²⁺ is also smaller than Na⁺, so it has a much higher charge density B1 it attracts the δ− oxygen atoms of the water molecules more strongly, so more energy is released when the ion is hydrated

Question 9

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

Accepted Answer

B1 the ions all have a charge of +1 but the ionic radius increases down the group B1 the water molecules cannot get as close to the centre of the charge, so the charge density falls B1 the attraction between the ion and the δ− oxygen of the water is weaker, so less energy is released

Question 10

Calculate the enthalpy of solution of potassium bromide. The lattice enthalpy of dissociation of KBr is +689 kJ mol⁻¹; the enthalpies of hydration are −322 kJ mol⁻¹ for K⁺ and −348 kJ mol⁻¹ for Br⁻.

Accepted Answer

M1 ΔsolH = ΔLEH(dissociation) + ΔhydH(K⁺) + ΔhydH(Br⁻) M1 the hydration enthalpies sum to −322 + (−348) = −670 kJ mol⁻¹ A1 ΔsolH = +689 − 670 = +19 kJ mol⁻¹, two significant figures; accept 19 with 'endothermic' in place of the + sign

Question 11

Calculate the lattice enthalpy of dissociation of lithium chloride. Its enthalpy of solution is −37 kJ mol⁻¹; the enthalpies of hydration are −519 kJ mol⁻¹ for Li⁺ and −364 kJ mol⁻¹ for Cl⁻.

Accepted Answer

M1 ΔLEH(dissociation) = ΔsolH − ΔhydH(Li⁺) − ΔhydH(Cl⁻), from rearranging the cycle M1 ΔLEH(dissociation) = −37 − (−519) − (−364) A1 ΔLEH(dissociation) = +846 kJ mol⁻¹, three significant figures, positive sign shown

Question 12

Calculate the enthalpy of solution of ammonium chloride from the results of the experiment given in the table.

Accepted Answer

M1 q = mcΔT = 50.0 × 4.18 × 7.1 = 1484 J M1 amount of NH₄Cl = 5.35 ÷ 53.5 = 0.100 mol A1 ΔsolH = +1.484 ÷ 0.100 = +15 kJ mol⁻¹, to two significant figures to match the 7.1 °C, positive because the temperature fell

Question 13

Suggest why the Group 2 hydroxides become more soluble down the group, in terms of lattice enthalpy and hydration enthalpy.

Accepted Answer

B1 the hydroxide ion is small, so the distance between the ions depends strongly on the size of the cation B1 as the cation gets larger down the group, the lattice enthalpy falls quickly, and the hydration enthalpy of the cation also falls B1 the lattice enthalpy falls faster than the hydration enthalpy, so the enthalpy of solution becomes less endothermic and the hydroxides more soluble

Question 14

Suggest why the enthalpy of hydration of Al³⁺ is far more exothermic than that of Mg²⁺, using the data in the table.

Accepted Answer

B1 Al³⁺ has a 3+ charge against the 2+ of Mg²⁺ B1 Al³⁺ is also smaller, so its charge density is much higher B1 it attracts the δ− oxygen atoms of the water molecules much more strongly, so much more energy is released on hydration

Question 15

Compare the hydration of a sodium ion, radius 102 pm, with the hydration of a chloride ion, radius 181 pm.

Accepted Answer

B1 both are exothermic, because each ion attracts polar water molecules by ion–dipole attractions B1 the water molecules face Na⁺ with their δ− oxygen atoms, but face Cl⁻ with a δ+ hydrogen atom B1 Na⁺ is the smaller ion with the higher charge density, so its hydration enthalpy is the more exothermic, −406 kJ mol⁻¹ against −364 kJ mol⁻¹

Question 16

Outline how the enthalpy of solution of a salt can be measured in a school laboratory.

Accepted Answer

B1 a measured volume or mass of water is placed in a polystyrene cup and its starting temperature recorded B1 a weighed mass of the salt is added and stirred until it dissolves, and the highest or lowest temperature is recorded B1 q = mcΔT is calculated and divided by the amount of salt in moles, with a positive sign if the temperature fell and a negative sign if it rose

Question 17

Calculate the temperature rise when anhydrous magnesium sulfate dissolves in water, using the data in the table.

Accepted Answer

M1 amount of MgSO₄ = 3.01 ÷ 120.4 = 0.0250 mol M1 heat released, q = 0.0250 × 91000 = 2275 J; error carried forward from M1 A1 ΔT = 2275 ÷ (50.0 × 4.18) = 11 °C (10.9), a rise, two significant figures to match the enthalpy of solution

Question 18

Explain why the entropy change when magnesium sulfate dissolves in water is negative, although its ions leave an ordered lattice.

Accepted Answer

B1 breaking up the lattice and spreading the ions through the water increases the disorder of the ions B1 Mg²⁺ is small and doubly charged, with a high charge density, so it holds a shell of water molecules very tightly B1 those water molecules lose much of their freedom to move, and this increase in order outweighs the disorder gained, so the overall entropy change is negative

Question 19

Suggest why hydrated calcium chloride, CaCl₂·6H₂O, dissolves in water endothermically, although anhydrous calcium chloride dissolves exothermically.

Accepted Answer

B1 in the hydrate the ions are already surrounded by water molecules within the crystal B1 much of the hydration enthalpy was released when the hydrate formed, so far less is released when it dissolves B1 the energy needed to break up the hydrated crystal is then greater than the energy released, so the enthalpy of solution is positive

Question 20

Explain why sodium chloride dissolves in water but not in hexane.

Accepted Answer

B1 water is polar, and its δ− oxygen and δ+ hydrogen atoms are attracted to the cations and anions, releasing hydration enthalpy close in size to the lattice enthalpy B1 hexane is non-polar, so it has no partial charges to attract the ions and almost no energy is released when ions are surrounded by it B1 in hexane nothing repays the large lattice enthalpy of dissociation, so the lattice does not break up

Question 21

Give equations, with state symbols, for the enthalpy of hydration of the magnesium ion and for the enthalpy of solution of calcium chloride.

Accepted Answer

B1 Mg²⁺(g) → Mg²⁺(aq), starting from the gaseous ion B1 CaCl₂(s) → Ca²⁺(aq) + 2Cl⁻(aq), with two chloride ions

Enthalpy change	Value / kJ mol⁻¹
Lattice enthalpy of dissociation of SrCl₂	+2156
Enthalpy of hydration of Sr²⁺	−1480
Enthalpy of hydration of Cl⁻	−364

Quantity	Value
Mass of NH₄Cl dissolved	5.35 g
Mr of NH₄Cl	53.5
Mass of water	50.0 g
Temperature change	a fall of 7.1 °C
Specific heat capacity of the solution	4.18 J g⁻¹ K⁻¹

Ion	Ionic radius / pm	Enthalpy of hydration / kJ mol⁻¹
Mg²⁺	72	−1920
Al³⁺	54	−4690

Quantity	Value
Mass of anhydrous MgSO₄ dissolved	3.01 g
Mr of MgSO₄	120.4
Mass of water	50.0 g
Enthalpy of solution of MgSO₄	−91 kJ mol⁻¹
Specific heat capacity of the solution	4.18 J g⁻¹ K⁻¹