Energy Cycle Calculations
- The energy cycle involving the enthalpy change of solution (ΔHsolθ), lattice energy (ΔHlattθ), and enthalpy change of hydration (ΔHhydθ) 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:
ΔHhydθ = ΔHlattθ + ΔHsolθ
- This equation can be rearranged depending on which enthalpy value needs to be calculated
- For example, ΔHlattθ can be calculated using:
ΔHlattθ = ΔHhydθ - ΔHsolθ
- Remember: the total ΔHhydθ is found by adding the ΔHhydθ 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
Calculate the ΔHθ of the chloride ion in potassium chloride using the following data:
- ΔHlattθ [KCl] = -711 kJ mol-1
- ΔHsolθ [KCl] = +26 kJ mol-1
- ΔHhydθ [K+] = -322 kJ mol-1
Answer:
- Step 1: Draw the energy cycle of KCl
- Step 2: Apply Hess’s law to find ΔHhydθ [Cl-]
- ΔHhydθ = (ΔHlattθ[KCl]) + (ΔHsolθ[KCl])
- (ΔHhydθ[K+]) + (ΔHhydθ[Cl-]) = (ΔHlattθ[KCl]) + (ΔHsolθ[KCl])
- (ΔHhydθ[Cl-]) = (ΔHlattθ[KCl]) + (ΔHsolθ[KCl]) - (ΔHhydθ[K+])
- Step 3: Substitute the values to find ΔHhydꝋ [Cl-]
- ΔHhydθ [Cl-] = (-711) + (+26) - (-322) = -363 kJ mol-1
Worked example
Calculate the ΔHθhyd of the magnesium ion in the magnesium chloride using the following data:
- ΔHlattθ [MgCl2] = -2592 kJ mol-1
- ΔHsolθ [MgCl2] = -55 kJ mol-1
- ΔHhydθ [Cl–] = -363 kJ mol-1
Answer:
- Step 1: Draw the energy cycle of MgCl2
- Step 2: Apply Hess’s law to find ΔHhydꝋ [Mg2+]
- ΔHhydθ = (ΔHlattθ[MgCl2]) + (ΔHsolθ [MgCl2])
- (ΔHhydθ[Mg2+]) + (2ΔHhydθ [Cl-]) = (ΔHlatθ [MgCl2]) + (ΔHsolθ [MgCl2])
- (ΔHhydθ[Mg2+]) = (ΔHlattθ[MgCl2]) + (ΔHsolθ[MgCl2]) - (2ΔHhydθ[Cl-])
- Step 3: Substitute the values to find ΔHhydθ[Mg2+]
- ΔHhydθ[Mg2+] = (-2592) + (-55) - (2 x -363) = -1921 kJ mol-1
