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.

MaterialHO()2gHO()2lHO()22lH()2gH()gO()2gO()g
Standard Molar Entropy 𝑆 (J/K⋅mol)188.870.0109.6130.7114.7205.2161.1

Calculate, to 3 significant figures, the standard entropy change Δ𝑆 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 Δ𝐻, 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.

MaterialPb()sPb()gPbCl()2sHCl()gH()gH()2g
Standard Molar Entropy 𝑆 (J/K⋅mol)64.8175.4136.0186.9114.7130.7

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

Calculate, to 3 significant figures, the maximum value of Δ𝐻, 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:

MaterialCHOH()3lCHOH()3gO()gO()2gC()graphiteCO()gCO()2gHO()2g
Standard Molar Entropy, 𝑆(J/K·mol)126.8239.9161.1205.25.7197.7213.8188.8

Calculate the standard entropy change, Δ𝑆, 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:

MaterialCa(OH)()2sCa()sCaO()sO()2gHO()2gH()2g
Standard Molar Entropy, 𝑆 (J/K⋅mol)83.441.638.1205.2188.8130.7

Calculate the standard entropy change, Δ𝑆, 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, 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.

  • ACH()+H()CH()24228glg
  • BCH()+2H()CH()2426glg
  • CCH()+4H()CH()2428ggg
  • DCH()+2H()CH()24228ggg
  • ECH()+H()CH()24226ggg

Calculate the standard molar entropy change for this process, Δ𝑆.

Q6:

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

MaterialNO()2gNO()gNO()2gO()gO()2gN()gN()2g
Standard Molar Entropy 𝑆(J/K·mol)240.1210.8220.0161.1205.2153.3191.6

Calculate, to 1 decimal place, the standard entropy change, Δ𝑆, 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:

Reaction2HO()+O()2HO()2222ggg2H()+O()2HO()222gggH()2H()2ggO()2O()2gg
Standard Molar Entropy Change Δ𝑆 (J/K⋅mol)363.689.098.7117.0

Calculate, to 3 significant figures, Δ𝑆 for the reaction 2H()+2O()HO()ggg22.

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:

MaterialH()2gH()+aqH()gN()2gN()gNH()3gNH()24g
Standard Molar Entropy 𝑆 (J/K⋅mol)130.70.0114.7191.6153.3192.8238.5

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

Calculate, to 3 significant figures, the maximum value of Δ𝐻, 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.

MaterialCHOH()25gCH()38gCO()gCO()2gO()2gO()gHO()2lHO()2g
Standard Molar Entropy 𝑆 (J/K⋅mol)281.6270.3197.7213.8205.2161.170.0188.8

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

Q10:

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

MaterialC()diamondC()graphiteC()gO()gO()2gCO()gCO()2g
Standard Molar Entropy 𝑆(J/K·mol)2.45.7158.1161.1205.2197.7213.8

Calculate, to 1 decimal place, the standard entropy change, Δ𝑆, 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.

MaterialO()2gO()gO()3gN()2gN()gNO()23gNO()24gNO()25g
Standard Molar Entropy 𝑆 (J/K⋅mol)205.2161.1238.9191.6153.3312.2304.4355.7

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

Calculate, to 3 significant figures, the maximum value of Δ𝐻, 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:

MaterialFe()sFe()gFeO()34sFeO()sFeO()23sAl()sAl()gAlO()23s
Standard Molar Entropy 𝑆 (J/K⋅mol)27.3180.5197.7213.8205.228.3164.550.9

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

Calculate, to 3 significant figures, the maximum value of Δ𝐻, 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.

MaterialCuS()sCuS()2sCu()gCu()sS()8sS()g
Standard Molar Entropy 𝑆 (J/K⋅mol)66.5120.9166.433.2256.8167.8

Calculate the standard entropy change Δ𝑆 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.

MaterialFeO()sFeO()23sFeO()34sFe()sC(𝑔𝑟𝑎𝑝𝑖𝑡𝑒)CO()gCO()2g
Standard Molar Entropy 𝑆 (J/K⋅mol)60.887.4146.427.35.7197.7213.8

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.

MaterialNH()3gBH()26gNH()24lNH()24gHO()22lHO()22gKClO()3sN()2gH()2gO()2gB()gHO()2gKCl()s
Standard Molar Entropy 𝑆 (J/K⋅mol)192.8232.1121.2238.5109.6232.7143.0191.6130.7205.2153.4188.883.0

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

  • ABH()2B()+3H()262ggg
  • B2HO()2HO()+O()2222lgg
  • C2NH()N()+3H()322ggg
  • D2KClO()3O()+2KCl()32sgs
  • ENH()N()+2H()2422ggg

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