Energy Cycle Calculations

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

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

ΔH_latt^θ= ΔH_hyd^θ - ΔH_sol^θ

Remember: the total ΔH_hyd^θ is found by adding the ΔH_hyd^θ 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

Calculate the ΔH^θ of the chloride ion in potassium chloride using the following data:

Answer:

Chemical Energetics - Energy Cycle KCl, downloadable AS & A Level Chemistry revision notes

Step 2: Apply Hess’s law to find ΔH_hyd^θ [Cl^-]
- ΔH_hyd^θ = (ΔH_latt^θ[KCl]) + (ΔH_sol^θ[KCl])
- (ΔH_hyd^θ[K⁺]) + (ΔH_hyd^θ[Cl^-]) = (ΔH_latt^θ[KCl]) + (ΔH_sol^θ[KCl])
- (ΔH_hyd^θ[Cl^-]) = (ΔH_latt^θ[KCl]) + (ΔH_sol^θ[KCl]) - (ΔH_hyd^θ[K⁺])
Step 3: Substitute the values to find ΔH_hyd^ꝋ [Cl^-]
- ΔH_hyd^θ [Cl^-] = (-711) + (+26) - (-322) = -363 kJ mol^-1

Calculate the ΔH^θ_hyd of the magnesium ion in the magnesium chloride using the following data:

Answer:

Chemical Energetics - Energy Cycle MgCl2, downloadable AS & A Level Chemistry revision notes

Step 2: Apply Hess’s law to find ΔH_hyd^ꝋ [Mg²⁺]
- ΔH_hyd^θ = (ΔH_latt^θ[MgCl₂]) + (ΔH_sol^θ[MgCl₂])
- (ΔH_hyd^θ[Mg²⁺]) + (2ΔH_hyd^θ [Cl^-]) = (ΔH_lat^θ [MgCl₂]) + (ΔH_sol^θ[MgCl₂])
- (ΔH_hyd^θ[Mg²⁺]) = (ΔH_latt^θ[MgCl₂]) + (ΔH_sol^θ[MgCl₂]) - (2ΔH_hyd^θ[Cl^-])
Step 3: Substitute the values to find ΔH_hyd^θ[Mg²⁺]
- ΔH_hyd^θ[Mg²⁺] = (-2592) + (-55) - (2 x -363) = -1921 kJ mol^-1

Energy Cycle Calculations (CIE A Level Chemistry)