Lesson: Hess Cycles Using Free Energies

In this lesson, we will learn how to use enthalpy and entropy Hess cycles to calculate the free energy changes for chemical reactions.

Worksheet: 11 Questions

Q1:

The standard entropies and enthalpies of formation for methane and other materials are shown in the table.

Material Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Standard Enthalpy of Formation Δ𝐻⦵f (kJ/mol)
C H ( ) 4 g 186.3 − 7 4 . 6
C ( ) g 158.1 716.7
C ( ) 𝑑 𝑖 𝑎 𝑚 𝑜 𝑛 𝑑 2.4 1.9
C ( ) 𝑔 𝑟 𝑎 𝑝 ℎ 𝑖 𝑡 𝑒 5.7 0.0
O ( ) 2 g 205.2 0.0
H O ( ) 2 l 70.0 − 2 8 5 . 8
H O ( ) 2 g 188.8 − 2 4 1 . 8

The incomplete combustion of methane generates graphite and steam as the only products. Calculate, to the nearest kilojoules per mole, the standard change in free energy for this reaction, Δ𝐺⦵, expressed per moles of methane reacted.

Q2:

The standard entropies and enthalpies of formation for lithium carbonate and other materials are shown in the table.

Material Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Standard Enthalpy of Formation Δ𝐻⦵ (kJ/mol)
L i C O ( ) 2 3 s 90.2 − 1 , 2 1 6 . 0
L i O H ( ) s 42.8 − 4 8 7 . 5
C O ( ) g 197.7 − 1 1 0 . 5
C O ( ) 2 g 213.8 − 3 9 3 . 5
H O ( ) 2 l 70.0 − 2 8 5 . 8
H O ( ) 2 g 188.8 − 2 4 1 . 8

Calculate Δ𝐺⦵, the standard change in free energy at 298 K, for the reaction of lithium hydroxide with carbon dioxide to form lithium carbonate and steam, expressed per moles of lithium carbonate produced.

Q3:

Manganese(IV) oxide decomposes into manganese and oxygen. Calculate, to 3 significant figures, the standard change in free energy at 298 K, Δ𝐺⦵, expressed per mole of manganese produced.

Assuming the thermodynamic parameters do not vary with temperature, calculate the minimum temperature at which the decomposition of manganese(IV) oxide into manganese and oxygen would be spontaneous.

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