Worksheet: Hess Cycles Using Standard Entropies

In this worksheet, we will practice calculating reaction entropies by applying Hess's law to energy cycles based on tabulated standard entropies.

Q1:

The standard entropies of water and other materials are shown in the table.

Material H O ( ) 2 g H O ( ) 2 l H O ( ) 2 2 l H ( ) 2 g H ( ) g O ( ) 2 g O ( ) g
Standard Molar Entropy 𝑆 2 9 8 (J/K⋅mol) 188.8 70.0 109.6 130.7 114.7 205.2 161.1

Calculate, to 3 significant figures, the standard entropy change Δ 𝑆 2 9 8 for the formation of liquid water from its constituent elements in their standard states, expressed per mole of water.

Calculate, to 3 significant figures, the maximum value of Δ 𝐻 2 9 8 , the standard molar enthalpy change per mole of water, at which this reaction would occur spontaneously at 298 K.

Q2:

Lead reacts with hydrogen chloride gas to form lead(II) chloride and hydrogen. The standard entropies of these and other materials are shown in the table.

Material P b ( ) s P b ( ) g P b C l ( ) 2 s H C l ( ) g H ( ) g H ( ) 2 g
Standard Molar Entropy 𝑆 2 9 8 (J/K⋅mol) 64.8 175.4 136.0 186.9 114.7 130.7

Calculate, to 3 significant figures, the standard entropy change for this reaction, Δ 𝑆 2 9 8 , expressed per mole of lead consumed.

Calculate, to 3 significant figures, the maximum value of Δ 𝐻 2 9 8 , the standard molar enthalpy change per mole of lead, at which this reaction would occur spontaneously at 298 K.

Q3:

The standard entropies of methanol and other materials are shown in the table:

Material C H O H ( ) 3 l C H O H ( ) 3 g O ( ) g O ( ) 2 g C ( 𝑔 𝑟 𝑎 𝑝 𝑖 𝑡 𝑒 ) C O ( ) g C O ( ) 2 g H O ( ) 2 g
Standard Molar Entropy, 𝑆 ( J / K · m o l ) 126.8 239.9 161.1 205.2 5.7 197.7 213.8 188.8

Calculate the standard entropy change, Δ 𝑆 , for the complete combustion of methanol in the gas phase, expressed per mole of methanol reacted.

Q4:

The standard entropies of calcium hydroxide and other materials are shown in the table:

Material C a ( O H ) ( ) 2 s C a ( ) s C a O ( ) s O ( ) 2 g H O ( ) 2 g H ( ) 2 g
Standard Molar Entropy, 𝑆 ( J / K · m o l ) 83.4 41.6 38.1 205.2 188.8 130.7

Calculate the standard entropy change, Δ 𝑆 , for the conversion of solid calcium hydroxide to solid calcium oxide and gaseous by-products, expressed per mole of reactant.

Q5:

Ethane gas can be produced by the hydrogenation of gaseous ethene. The standard molar entropy, 𝑆 2 9 8 , for ethane is 229.2 J/K⋅mol, the value for ethene is 219.3 J/K⋅mol, and the value for hydrogen is 130.7 J/K⋅mol.

Give a balanced chemical equation for this process including state symbols.

  • A C H ( ) + 2 H ( ) C H ( ) 2 4 2 2 8 g g g
  • B C H ( ) + 2 H ( ) C H ( ) 2 4 2 6 g l g
  • C C H ( ) + H ( ) C H ( ) 2 4 2 2 8 g l g
  • D C H ( ) + H ( ) C H ( ) 2 4 2 2 6 g g g
  • E C H ( ) + 4 H ( ) C H ( ) 2 4 2 8 g g g

Calculate the standard molar entropy change for this process, Δ 𝑆 2 9 8 .

Q6:

The standard entropies of nitric oxide and other materials are shown below:

Material N O ( ) 2 g N O ( ) g N O ( ) 2 g O ( ) g O ( ) 2 g N ( ) g N ( ) 2 g
Standard Molar Entropy 𝑆 ( J / K · m o l ) 240.1 210.8 220.0 161.1 205.2 153.3 191.6

Calculate, to 1 decimal place, the standard entropy change, Δ 𝑆 , for the formation of nitric oxide from the constituent elements in their standard states, expressed per mole of nitric oxide produced.

Q7:

The standard molar entropy changes for four reactions are given below:

Reaction 2 H O ( ) + O ( ) 2 H O ( ) 2 2 2 2 g g g 2 H ( ) + O ( ) 2 H O ( ) 2 2 2 g g g H ( ) 2 H ( ) 2 g g O ( ) 2 O ( ) 2 g g
Standard Molar Entropy Change Δ 𝑆 (J/K⋅mol) 3 6 3 . 6 8 9 . 0 98.7 117.0

Calculate, to 3 significant figures, Δ 𝑆 for the reaction 2 H ( ) + 2 O ( ) H O ( ) g g g 2 2 .

Q8:

In the Haber-Bosch process, gaseous ammonia is produced from nitrogen and hydrogen gases. The standard entropies of these and other materials are shown below:

Material H ( ) 2 g H ( ) + a q H ( ) g N ( ) 2 g N ( ) g N H ( ) 3 g N H ( ) 2 4 g
Standard Molar Entropy 𝑆 2 9 8 (J/K⋅mol) 130.7 0.0 114.7 191.6 153.3 192.8 238.5

Calculate, to 3 significant figures, the standard entropy change Δ 𝑆 2 9 8 for this reaction, expressed per mole of nitrogen reacted.

Calculate, to 3 significant figures, the maximum value of Δ 𝐻 2 9 8 , the standard enthalpy change per mole of nitrogen, at which this reaction would occur spontaneously at 298 K.

Q9:

The complete combustion of propane produces carbon dioxide and steam. The standard entropies of these and other materials are shown in the table.

Material C H O H ( ) 2 5 g C H ( ) 3 8 g C O ( ) g C O ( ) 2 g O ( ) 2 g O ( ) g H O ( ) 2 l H O ( ) 2 g
Standard Molar Entropy 𝑆 (J/K⋅mol) 281.6 270.3 197.7 213.8 205.2 161.1 70.0 188.8

Calculate, to 3 significant figures, the standard entropy change for this reaction, Δ 𝑆 , expressed per mole of propane combusted.

Q10:

The standard entropies of graphite and other materials are shown below:

Material C ( ) d i a m o n d C ( ) g r a p h i t e C ( ) g O ( ) g O ( ) 2 g C O ( ) g C O ( ) 2 g
Standard Molar Entropy 𝑆 ( J / K · m o l ) 2.4 5.7 158.1 161.1 205.2 197.7 213.8

Calculate, to 1 decimal place, the standard entropy change, Δ 𝑆 , for the complete combustion of graphite, expressed per mole of carbon dioxide produced.

Q11:

Dinitrogen pentoxide can be produced from nitrogen and oxygen gases. The standard entropies of these and other materials are shown in the given table.

Material O ( ) 2 g O ( ) g O ( ) 3 g N ( ) 2 g N ( ) g N O ( ) 2 3 g N O ( ) 2 4 g N O ( ) 2 5 g
Standard Molar Entropy 𝑆 2 9 8 (J/K⋅mol) 205.2 161.1 238.9 191.6 153.3 312.2 304.4 355.7

Calculate, to 3 significant figures, the standard entropy change Δ 𝑆 2 9 8 for this reaction, expressed per mole of nitrogen reacted.

Calculate, to 3 significant figures, the maximum value of Δ 𝐻 2 9 8 , the standard enthalpy change per mole of nitrogen, at which this reaction would occur spontaneously at 298 K.

Q12:

In the thermite reaction, solid iron(III) oxide reacts with aluminum to produce aluminum oxide and iron. The standard entropies of these and other materials are shown in the following table:

Material F e ( ) s F e ( ) g F e O ( ) 3 4 s F e O ( ) s F e O ( ) 2 3 s A l ( ) s A l ( ) g A l O ( ) 2 3 s
Standard Molar Entropy 𝑆 2 9 8 (J/K⋅mol) 27.3 180.5 197.7 213.8 205.2 28.3 164.5 50.9

Calculate, to 3 significant figures, the standard entropy change for this reaction, Δ 𝑆 2 9 8 expressed per mole of iron(III) oxide reacted.

Calculate, to 3 significant figures, the maximum value of Δ 𝐻 2 9 8 , the standard enthalpy change per mole of iron(III) oxide, at which this reaction would occur spontaneously at 298 K.

Q13:

The standard entropies of copper(I) sulfide and other materials are shown in the table.

Material C u S ( ) s C u S ( ) 2 s C u ( ) g C u ( ) s S ( ) 8 s S ( ) g
Standard Molar Entropy 𝑆 (J/K⋅mol) 66.5 120.9 166.4 33.2 256.8 167.8

Calculate the standard entropy change Δ 𝑆 for the formation of copper(I) sulfide from the constituent elements in their standard states, expressed per mole of copper(I) sulfide produced.

Q14:

The standard entropies of iron(III) oxide and other materials are shown in the table.

Material F e O ( ) s F e O ( ) 2 3 s F e O ( ) 3 4 s F e ( ) s C ( 𝑔 𝑟 𝑎 𝑝 𝑖 𝑡 𝑒 ) C O ( ) g C O ( ) 2 g
Standard Molar Entropy 𝑆 (J/K⋅mol) 60.8 87.4 146.4 27.3 5.7 197.7 213.8

Calculate the standard entropy change for the reduction of iron(III) oxide to iron by carbon monoxide, expressed per mole of iron(III) oxide reacted.

Q15:

The standard entropies for a range of fuels and their decomposition products are shown in the table.

Material N H ( ) 3 g B H ( ) 2 6 g N H ( ) 2 4 l N H ( ) 2 4 g H O ( ) 2 2 l H O ( ) 2 2 g K C l O ( ) 3 s N ( ) 2 g H ( ) 2 g O ( ) 2 g B ( ) g H O ( ) 2 g K C l ( ) s
Standard Molar Entropy 𝑆 (J/K⋅mol) 192.8 232.1 121.2 238.5 109.6 232.7 143.0 191.6 130.7 205.2 153.4 188.8 83.0

Which of the following reactions produces the smallest increase in entropy per mole of reactant under standard conditions?

  • A N H ( ) N ( ) + 2 H ( ) 2 4 2 2 g g g
  • B B H ( ) 2 B ( ) + 3 H ( ) 2 6 2 g g g
  • C 2 H O ( ) 2 H O ( ) + O ( ) 2 2 2 2 l g g
  • D 2 N H ( ) N ( ) + 3 H ( ) 3 2 2 g g g
  • E 2 K C l O ( ) 3 O ( ) + 2 K C l ( ) 3 2 s g s

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