# 5.1.8 Energy Cycle Calculations

### Energy Cycle Calculations

• The energy cycle involving the enthalpy change of solution (ΔHsol ), lattice energy (ΔHlatt), and enthalpy change of hydration (ΔHhyd) 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:

ΔHhyd= ΔHlatt + ΔHsol

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

ΔHlatt= ΔHhyd – ΔHsol

• Remember: the total ΔHhyd is found by adding the ΔHhyd 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

Step 1: Draw the energy cycle of KCl

• Step 2: Apply Hess’s law  to find ΔHhyd [Cl]

ΔHhyd = (ΔHlatt[KCl]) + (ΔHsol[KCl])

Hhyd[K+]) + (ΔHhyd[Cl])   =  (ΔHlatt[KCl]) + (ΔHsol[KCl])

Hhyd[Cl])   = (ΔHlatt[KCl]) + (ΔHsol[KCl]) – (ΔHhyd[K+])

• Step 3: Substitute the values to find ΔHhyd [Cl]

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

#### Worked example: Calculating the enthalpy change of hydration of magnesium

• Step 1: Draw the energy cycle of MgCl2

• Step 2: Apply Hess’s law  to find ΔHhyd [Mg2+]

ΔHhyd = (ΔHlatt[MgCl2]) + (ΔHsol[MgCl2])

Hhyd[Mg2+]) + (2ΔHhyd [Cl])   = (ΔHlatt [MgCl2]) + (ΔHsol[MgCl2])

Hhyd[Mg2+])   = (ΔHlatt[MgCl2]) + (ΔHsol[MgCl2]) – (2ΔHhyd[Cl])

• Step 3: Substitute the values to find ΔHhyd [Mg2+]

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

### Author: Francesca

Fran has taught A level Chemistry in the UK for over 10 years. As head of science, she used her passion for education to drive improvement for staff and students, supporting them to achieve their full potential. Fran has also co-written science textbooks and worked as an examiner for UK exam boards.
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