• The energy cycle involving the enthalpy change of solution (ΔH_sol^??), lattice energy (ΔH_latt^?), and enthalpy change of hydration (ΔH_hyd^?) can be used to calculate the different enthalpy values
• According to Hess’s law, the enthalpy change of the direct and of the indirect route will be the same, such that:

ΔH_hyd^??= ΔH_latt^??+ ΔH_sol^?

• This equation can be rearranged depending on which enthalpy value needs to be calculated
• For example, ΔHlatt??can be calculated using:

ΔH_latt^??= ΔH_hyd^??- ΔH_sol^?

• Remember: the total ΔH_hyd^??is found by adding the ΔH_hyd^??values of both anions and cations together
• Remember:?take into account the number of each ion when completing calculations
  • For example, MgCl₂?has?two chloride ions, so when completing calculations this will need to be accounted for
  • In this case, you would need to double the value of the hydration enthalpy, since you are hydrating?2 moles?of chloride ions instead of 1

Worked example: Calculating the enthalpy change of hydration of chloride

Answer

Step 1:?Draw the energy cycle of KCl

• Step 2:?Apply Hess’s law? to find ΔH_hyd^??[Cl^-]

ΔH_hyd^??= (ΔH_latt^?[KCl]) + (ΔH_sol^?[KCl])

(ΔH_hyd^?[K⁺]) + (ΔH_hyd?[Cl^-])?? =? (ΔHlatt^?[KCl]) + (ΔH_sol^?[KCl])

(ΔH_hyd^?[Cl^-])?? = (ΔH_latt?[KCl]) + (ΔH_sol^?[KCl]) - (ΔH_hyd^?[K+])

• Step 3:?Substitute the values to find ΔH_hyd^??[Cl^-]

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

Worked example: Calculating the enthalpy change of hydration of magnesium

Answer

• Step 1:?Draw the energy cycle of MgCl₂

• Step 2:?Apply Hess’s law? to find ΔH_hyd^?[Mg²⁺]

ΔH_hyd^??= (ΔH_latt^?[MgCl₂]) + (ΔH_sol^??[MgCl₂])

(ΔH_hyd^?[Mg²⁺]) + (2ΔH_hyd^??[Cl^-])?? = (ΔH_latt^??[MgCl₂]) + (ΔH_sol^??[MgCl₂])

(ΔH_hyd^?[Mg²⁺])?? = (ΔH_latt^?[MgCl₂]) + (ΔH_sol^?[MgCl₂]) - (2ΔH_hyd^?[Cl^-])

• Step 3:?Substitute the values to find ΔH_hyd^??[Mg²⁺]

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