# 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 Standard Molar Entropy 𝑆⦵ (J/K⋅mol) HO()2g HO()2l HO()22l H()2g H()g O()2g O()g 188.8 70.0 109.6 130.7 114.7 205.2 161.1

Calculate, to 3 significant figures, the standard entropy change 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 , 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 Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Pb()s Pb()g PbCl()2s HCl()g H()g H()2g 64.8 175.4 136.0 186.9 114.7 130.7

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

Calculate, to 3 significant figures, the maximum value of , 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 Standard Molar Entropy, 𝑆⦵(J/K·mol) CHOH()3l CHOH()3g O()g O()2g C()graphite CO()g CO()2g HO()2g 126.8 239.9 161.1 205.2 5.7 197.7 213.8 188.8

Calculate the standard entropy change, , 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 Standard Molar Entropy, 𝑆⦵ (J/K⋅mol) Ca(OH)()2s Ca()s CaO()s O()2g HO()2g H()2g 83.4 41.6 38.1 205.2 188.8 130.7

Calculate the standard entropy change, , 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, , 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
• B
• C
• D
• E

Calculate the standard molar entropy change for this process, .

Q6:

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

 Material Standard Molar Entropy 𝑆⦵(J/K·mol) NO()2g NO()g NO()2g O()g O()2g N()g N()2g 240.1 210.8 220.0 161.1 205.2 153.3 191.6

Calculate, to 1 decimal place, the standard entropy change, , 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 Standard Molar Entropy Change Δ𝑆⦵ (J/K⋅mol) 2HO()+O()2HO()2222ggg 2H()+O()2HO()222ggg H()2H()2gg O()2O()2gg −363.6 −89.0 98.7 117.0

Calculate, to 3 significant figures, for the reaction .

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 Standard Molar Entropy 𝑆⦵ (J/K⋅mol) H()2g H()+aq H()g N()2g N()g NH()3g NH()24g 130.7 0.0 114.7 191.6 153.3 192.8 238.5

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

Calculate, to 3 significant figures, the maximum value of , 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 Standard Molar Entropy 𝑆⦵ (J/K⋅mol) CHOH()25g CH()38g CO()g CO()2g O()2g O()g HO()2l HO()2g 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, , expressed per mole of propane combusted.

Q10:

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

 Material Standard Molar Entropy 𝑆⦵(J/K·mol) C()diamond C()graphite C()g O()g O()2g CO()g CO()2g 2.4 5.7 158.1 161.1 205.2 197.7 213.8

Calculate, to 1 decimal place, the standard entropy change, , 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 Standard Molar Entropy 𝑆⦵ (J/K⋅mol) O()2g O()g O()3g N()2g N()g NO()23g NO()24g NO()25g 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 for this reaction, expressed per mole of nitrogen reacted.

Calculate, to 3 significant figures, the maximum value of , 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 Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Fe()s Fe()g FeO()34s FeO()s FeO()23s Al()s Al()g AlO()23s 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, expressed per mole of iron(III) oxide reacted.

Calculate, to 3 significant figures, the maximum value of , 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 Standard Molar Entropy 𝑆⦵ (J/K⋅mol) CuS()s CuS()2s Cu()g Cu()s S()8s S()g 66.5 120.9 166.4 33.2 256.8 167.8

Calculate the standard entropy change 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 Standard Molar Entropy 𝑆⦵ (J/K⋅mol) FeO()s FeO()23s FeO()34s Fe()s C(𝑔𝑟𝑎𝑝ℎ𝑖𝑡𝑒) CO()g CO()2g 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 Standard Molar Entropy 𝑆⦵ (J/K⋅mol) NH()3g BH()26g NH()24l NH()24g HO()22l HO()22g KClO()3s N()2g H()2g O()2g B()g HO()2g KCl()s 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
• B
• C
• D
• E