Energy Cycle Calculations (CIE A Level Chemistry)

• The energy cycle involving the enthalpy change of solution (ΔH_sol^ꝋ ), lattice energy (ΔH_latt^ꝋ), and enthalpy change of hydration (ΔH_hyd^ꝋ) 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^ꝋ = ΔH_latt^ꝋ + ΔH_sol^ꝋ

• This equation can be rearranged depending on which enthalpy value needs to be calculated
• For example, ΔH_latt^ꝋ can be calculated using:

 ΔH_latt^ꝋ = ΔH_hyd^ꝋ - ΔH_sol^ꝋ

• Remember: the total ΔH_hyd^ꝋ is found by adding the ΔH_hyd^ꝋ 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^ꝋ [Cl^-]

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

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

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

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

ΔH_hyd^ꝋ [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^ꝋ [Mg²⁺]

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

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

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

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

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