CIE A Level Chemistry

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First teaching 2020

Last exams 2024

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5.1.8 Energy Cycle Calculations

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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

Chemical Energetics - Worked example_Calculating the enthalpy change of hydration of chloride, downloadable AS & A Level Chemistry revision notes

Answer

Step 1: Draw the energy cycle of KCl

 

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

  • 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

Chemical Energetics - Worked example_Calculating the enthalpy change of hydration of magnesium, downloadable AS & A Level Chemistry revision notes

Answer

  • Step 1: Draw the energy cycle of MgCl2

 

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

  • 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

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