Worksheet: Hess Cycles Using Free Energies

In this worksheet, we will practice using enthalpy and entropy Hess cycles to calculate the free energy changes for chemical reactions.

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:

The standard entropies and enthalpies of formation for manganese(IV) oxide and other materials are shown below:

Material Standard Molar Entropy 𝑆⦵ (J/K·mol) Standard Enthalpy of Formation Δ𝐻⦵f (kJ/mol)
O ( ) 2 g 205.20 0.00
M n ( ) s 32.00 0.00
M n O ( ) s 59.71 − 3 8 5 . 2 0
M n O ( ) 2 s 53.05 − 5 2 0 . 0 3
M n O ( ) 2 3 s 110.46 − 9 5 8 . 9 7
M n O ( ) 3 4 s 155.64 − 1 , 3 7 8 . 8 3

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.

  • A 2 . 1 7 × 1 0  K
  • B 3 . 6 7 × 1 0  K
  • C 3 . 9 3 × 1 0  K
  • D 2 . 8 2 × 1 0  K
  • E 5 . 1 4 × 1 0  K

Q4:

The standard entropies and enthalpies of formation for copper(II) sulfide and other materials are shown below:

Material Standard Molar Entropy 𝑆⦵(J/K·mol) Standard Enthalpy of Formation Δ𝐻⦵f(kJ/mol)
C u S ( ) s 66.5 − 5 3 . 1
C u S ( ) 2 s 120.9 − 7 9 . 5
C u ( ) s 33.2 0.0
C u ( ) 2 + a q − 9 9 . 6 64.8
S ( ) 8 s 256.8 0.0
S ( ) 2 – a q 22.0 41.8

Calculate, to 3 significant figures, the standard Gibbs free energy of formation, Δ𝐺⦵f, for copper(II) sulfide, expressed per mole of copper(II) sulfide produced.

Q5:

The standard entropies and enthalpies of formation for hydrogen bromide and other materials are shown below:

Material Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Standard Enthalpy of Formation Δ𝐻⦵f (kJ/mol)
H B r ( ) g 198.7 − 3 6 . 3
B r ( ) 2 l 152.2 0.0
B r ( ) 2 g 245.5 30.9
B r ( ) g 175.0 111.9
H ( ) 2 g 130.7 0.0
H ( ) g 114.7 218.0

Calculate, to 3 significant figures, the standard Gibbs free energy of formation, Δ𝐺⦵f, for hydrogen bromide, expressed per mole of hydrogen bromide produced.

Q6:

The standard entropies and enthalpies of formation for disulfur dichloride and other materials are shown below:

Material Standard Molar Entropy Δ𝑆⦵ (J/K⋅mol) Standard Enthalpy of Formation Δ𝐻⦵f (kJ/mol)
S C l ( ) 2 2 g 319.45 − 1 9 . 5 0
S O C l ( ) 2 g 309.66 − 2 1 2 . 5 5
C S ( ) 2 l 151.34 89.70
C S ( ) 2 g 238.00 116.89
C C l ( ) 4 l 214.42 − 1 2 8 . 2 3
C C l ( ) 4 g 309.75 − 9 5 . 6 8
C l ( ) 2 g 223.10 0.00

Chlorine and liquid carbon disulfide react to form gaseous disulfur dichloride and carbon tetrachloride. Calculate, to 3 significant figures, the standard change in free energy at 298 K, Δ𝐺⦵, expressed per mole of disulfur dichloride produced.

Q7:

Dinitrogen trioxide decomposes reversibly to produce nitric oxide and nitrogen dioxide: NO()NO()+NO()232ggg. The standard entropies and enthalpies of formation for dinitrogen trioxide and other materials are shown in the table.

Material Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Standard Enthalpy of Formation Δ𝐻⦵f (kJ/mol)
N O ( ) 2 5 g 355.7 11.3
N O ( ) 2 4 g 304.4 11.1
N O ( ) 2 3 g 312.2 83.7
N O ( ) 2 g 220.0 81.6
N O ( ) g 210.8 90.3
N O ( ) 2 g 240.1 33.2

A sample of dinitrogen trioxide is stored under equal standard pressures of its decomposition products. Assuming the thermodynamic parameters in the table do not vary with temperature, calculate, to the nearest degree Celsius, the minimum temperature at which the sample of dinitrogen trioxide would spontaneously decompose.

Q8:

Iron(III) oxide can be produced by the reaction of iron with gaseous oxygen. The standard entropies and enthalpies of formation for iron(III) oxide and other materials are shown in the table.

Material Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Standard Enthalpy of Formation Δ𝐻⦵f (kJ/mol)
F e ( ) s 27.3 0.0
F e ( ) g 180.5 416.3
F e O ( ) s 60.8 − 2 7 2 . 0
F e O ( ) 2 3 s 87.4 − 8 2 4 . 2
F e O ( ) 3 4 s 146.4 − 1 , 1 1 8 . 4
O ( ) 2 g 205.2 0.0

The standard change in Gibbs free energy, Δ𝐺⦵, for the oxidation of iron at 298 K is expressed per mole of iron reacted. Calculate, to 3 significant figures, the value of Δ𝐺⦵ at 298 K.

Q9:

The standard entropies and enthalpies of formation for yellow mercury(II) oxide and other materials are shown in the table.

Material Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Standard Enthalpy of Formation Δ𝐻⦵f (kJ/mol)
H g O ( ) s , y e l l o w 71.13 − 9 0 . 4 6
H g ( ) l 75.90 0.00
H g ( ) g 175.03 61.40
O ( ) 2 g 205.20 0.00

At 298 K, a sample of yellow mercury(II) oxide decomposes into its constituent elements in their standard states with the standard change in Gibbs free energy Δ𝐺⦵. Calculate to 3 significant figures the value of Δ𝐺⦵, expressed per mole of reactant.

Q10:

Carbon monoxide gas can be produced by the partial combustion of carbon. The standard entropies and enthalpies of formation for carbon monoxide 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 ( ) s , g r a p h i t e 5.7 0.0
C ( ) g 158.1 716.7
O ( ) g 161.1 249.2
O ( ) 2 g 205.2 0.0
C O ( ) g 197.7 − 1 1 0 . 5
C O ( ) 2 g 213.8 − 3 9 3 . 5

The standard change in Gibbs free energy, Δ𝐺⦵, for the partial combustion of carbon at 298 K is expressed per mole of carbon reacted. Calculate, to 3 significant figures, the value of Δ𝐺⦵ at 298 K.

Q11:

Consider the reaction N()+3H()2NH()223ggg, and the following thermodynamic data: standard heat of formation of NH()3g, Δ𝐻=−46.11/⦵fkJmol; standard molar entropy of N(),2mg𝑆⦵ = 191.61 J/K⋅mol; standard molar entropy of H(),2mg𝑆⦵ = 130.684 J/K⋅mol; and standard molar entropy of NH(),3mg𝑆⦵ = 192.45 J/K⋅mol. Calculate Δ𝐻, Δ𝑆, and Δ𝐺 for this reaction at 298.00 K and standard pressure, expressing the values per mole of nitrogen gas reacted.

  • A Δ 𝐻 = − 9 2 . 2 2 / k J m o l ; Δ 𝑆 = − 1 9 8 . 7 6 / ⋅ J K m o l ; Δ 𝐺 = − 3 2 . 9 9 / k J m o l
  • B Δ 𝐻 = 4 6 . 1 / k J m o l ; Δ 𝑆 = 1 2 9 . 8 / ⋅ J K m o l ; Δ 𝐺 = 7 . 4 3 / k J m o l
  • C Δ 𝐻 = − 4 6 . 1 1 / k J m o l ; Δ 𝑆 = − 1 2 9 . 8 / ⋅ J K m o l ; Δ 𝐺 = − 7 . 4 3 / k J m o l
  • D Δ 𝐻 = − 4 6 . 1 1 / k J m o l ; Δ 𝑆 = − 9 9 . 3 8 / ⋅ J K m o l ; Δ 𝐺 = − 1 6 . 4 9 / k J m o l
  • E Δ 𝐻 = 9 2 . 2 2 / k J m o l ; Δ 𝑆 = 1 9 8 . 7 6 / ⋅ J K m o l ; Δ 𝐺 = 3 2 . 9 9 / k J m o l

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