Enthalpy of solution

• The?standard enthalpy change of solution (ΔHsol?)?is the enthalpy change when?1 mole?of an ionic substance?dissolves?in sufficient water to form an?infinitely?dilute solution
• The symbol?(aq)?is used to show that the solid is dissolved in?sufficient water
  • For example, the enthalpy changes of solution for potassium chloride are described by the following equations:

   

KCl(s) + aq → KCl(aq)

OR

KCl(s) + aq → K+(aq) + Cl-(aq)

• ΔHsol??can be?exothermic?(negative) or?endothermic?(positive)

Enthalpy of hydration

• The?standard enthalpy change of hydration?(ΔHhyd?)?is the enthalpy change when?1 mole?of a specified?gaseous ion dissolves?in sufficient water to form an infinitely dilute?solution
  • For example, the enthalpy change of hydration for magnesium ions is described by the following equation:

   

Mg2+(g) + aq → Mg2+(aq)

• • Hydration enthalpies are the measure of the energy that is released when there is an attraction formed between the ions and water molecules
  • Hydration enthalpies are?exothermic

   

• When an?ionic solid?dissolves in water, positive and negative ions are formed
• Water is a?polar?molecule with a δ- oxygen (O) atom and δ+ hydrogen (H) atoms which will form?ion-dipole attractions?with the ions present in the solution
• The oxygen atom in water will be attracted to the?positive ions?and the hydrogen atoms will be attracted to the?negative?ions

The polar water molecules will form ion-dipole bonds with the ions in solution causing the ions to become hydrated

How are enthalpy of solution and hydration enthalpies related?

The relationship between lattice enthalpy, hydration enthalpies and enthalpy of solution

• From the diagram we can see that the relationship is

Enthalpy of solution = reverse lattice enthalpy* + hydration enthalpy

• The hydration enthalpy is the?sum?of the hydration enthalpies of each ion
• If there is more than one cation or anion, such as in MgCl2, then you must multiply by the appropriate coefficient for that ion

*To be consistent with lattice?formation?enthalpy

• Questions in this topic typically ask you to calculate the hydration enthalpy of one of the ions, given the lattice enthalpy, enthalpy of solution and hydration enthalpy of the other ion.
• This can be done by constructing an appropriate energy cycle and using Hess's Law to find the unknown energy value
• The energy cycle above shows that there are two routes to go from the gaseous ions to the ions in an aqueous solution:
  • • Route 1: going from gaseous ions → ionic solid → ions in aqueous solution (this is the?indirect route)
    • Route 2: going from gaseous ions? →? ions in aqueous solution (this is the?direct route)

     

   

• According to?Hess’s law,?the enthalpy change for both routes is the same, such that:

ΔHhyd??= ΔHlatt??+ ΔHsol?

• Each ion will have its own enthalpy change of hydration, ΔHhyd?, which will need to be taken into account during calculations
  • The total ΔHhyd??is found by adding the? ΔHhyd??values of both anions and cations together

   

Answer

Step 1:?Draw the energy cycle and make ΔHhyd??[Cl-] the subject of the formula:

Step 2:?Substitute the values to find ΔHhyd??[Cl-]

ΔHhyd??[Cl-]?? = (-711) + (+26) - (-322) = -363 kJ mol-1

Alternative Diagram

• You can also draw a Born-Haber cycle as an alternative approach to the same problem

Energy level diagram:

Answer

Step 1:?Draw an energy cycle:

Step 2:?Substitute the values to find ΔHhyd??[Mg2+]

ΔHhyd?[Mg2+]? = (-2592) + (-55) - (2 x -363) = -1921 kJ mol-1

Alternative route to find ΔHhyd?[Mg2+]

• Here is the same solution using a Born-Haber cycle