Worksheet: Gibbs Free Energy

In this worksheet, we will practice calculating changes in molar Gibbs free energy from standard molar entropy and enthalpy change data.

Q1:

Ethane gas can be produced by the hydrogenation of gaseous ethene. The standard entropies and enthalpies of formation for ethene and other materials are shown in the table.

Material Standard Molar Entropy 𝑆⦵(J/K·mol) Standard Enthalpy of Formation Δ𝐻⦵(kJ/mol)
C H ( ) 2 2 g 200.9 227.4
C H ( ) 2 4 g 219.3 52.4
C H ( ) 2 6 g 229.2 − 8 4 . 0
H ( ) g 114.7 218.0
H ( ) 2 g 130.7 0

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

Q2:

Consider the reaction shown and the table of free energies of formation. BCl()+3HO()B(OH)()+3HCl()323glsg

Substance B C l ( ) 3 g H O ( ) 2 l B ( O H ) ( ) 3 s H C l ( ) g
Δ 𝐺 ⦵ f ( K i l o j o u l e p e r M o l e ) − 3 8 8 . 7 − 2 3 7 . 1 − 9 6 8 . 9 2 − 9 5 . 2 9 9

What is the standard free energy change for the reaction?

Q3:

Consider the reaction shown and the table of free energies of formation. BF()+3HO()B(OH)()+3HF()323glsg

Substance B F ( ) 3 g H O ( ) 2 l B ( O H ) ( ) 3 s H F ( ) g
Δ 𝐺 ⦵ f (kg/mol) − 1 , 1 1 9 . 4 − 2 3 7 . 1 − 9 6 8 . 9 2 − 2 7 5 . 4

What is the standard free energy change for the reaction?

Q4:

Consider the reaction and the table of free energies of formation below. BH()+6HO()2B(OH)()+6H()26232glsg

Substance B H ( ) 2 6 g H O ( ) 2 l B ( O H ) ( ) 3 s H ( ) 2 g
Δ 𝐺 ⦵ f (kJ/mol) 87.6 − 2 3 7 . 1 − 9 6 8 . 9 2 0

What is the standard free energy change for the reaction, to the nearest kilojoule per mole?

Q5:

Consider the following reaction for which Δ𝐺=−70.54⦵rkJ at 298 K. Cu()+4NH()Cu(NH)()2+3342+aqaqaq If the activities of Cu2+, NH3, and Cu(NH)342+ in a reaction mixture at 298 K are all equal to 0.01, what is the value of Δ𝐺r?

Q6:

Fill in the blank: Thermodynamics is to free energy as kinetics is to .

  • Aactivation energy
  • Benthalpy
  • Centropy
  • Dthermal energy
  • Eelectron transfer

Q7:

Acetic acid can form a hydrogen-bonded dimer in the gas phase:

2CH3COOHCH3COOHHOOCCH3
The standard enthalpy change for this reaction at 25.0∘C, Δ𝐻⦵, is −66.5 kJ/mol, expressed per mole of dimer. The equilibrium constant, 𝐾, is 1.30×10. Calculate the standard entropy change at 25.0∘C, Δ𝑆⦵, to 3 significant figures.

Q8:

The standard entropies and enthalpies of formation for two phases of chloroform are shown in the table.

Phase Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Standard Enthalpy of Formation Δ𝐻⦵f (kJ/mol)
C H C l ( ) 3 l 214.4 − 1 2 8 . 2
C H C l ( ) 3 g 309.7 − 9 5 . 7

Assuming that these thermodynamic parameters do not vary with temperature, estimate the boiling point of chloroform to the nearest degree Celsius.

Q9:

The standard entropies and enthalpies of formation for calcium sulfate dihydrate 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 a S O ( ) 4 s 106.5 − 1 , 4 3 4 . 5
C a S O · H O ( ) 3 2 s 184.1 − 1 , 7 5 2 . 7
C a S O · 2 H O ( ) 4 2 s 194.1 − 2 , 0 2 2 . 6
H O ( ) 2 l 70.0 − 2 8 5 . 8
H O ( ) 2 g 188.8 − 2 4 1 . 8

Calculate the standard entropy change Δ𝑆⦵ for the complete dehydration of calcium sulfate dihydrate to form anhydrous calcium sulfate and steam, expressed per mole of reactant.

Calculate the standard enthalpy change, Δ𝐻⦵, for the complete dehydration of calcium sulfate dihydrate to form anhydrous calcium sulfate and steam, expressed per mole of reactant.

A sample of calcium sulfate dihydrate is stored under a standard pressure of water vapor. Assuming the thermodynamic parameters in the table do not vary with temperature, calculate, to the nearest degree Celsius, the minimum temperature at which dehydration of this sample would be spontaneous.

Q10:

The standard entropies and enthalpies of formation for red 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 S ( ) r e d 82.40 − 5 8 . 1 6
H g O ( ) r e d 70.29 − 9 0 . 8 3
H g O ( ) 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
S ( ) g 167.82 278.81

Calculate the standard entropy change Δ𝑆⦵ for the decomposition of red mercury(II) oxide into its constituent elements in their standard states, expressed per mole of reactant.

Calculate the standard enthalpy change Δ𝐻⦵ for the decomposition of red mercury(II) oxide into its constituent elements in their standard states, expressed per mole of reactant.

A sample of red mercury(II) oxide is stored under equal standard pressures of its gaseous 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 red mercury(II) oxide would spontaneously decompose into its constituent elements in their standard states.

Q11:

The standard entropies and enthalpies of formation for two phases of carbon disulfide are shown in the table.

Phase Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Standard Enthalpy of Formation Δ𝐻⦵f (kJ/mol)
C S ( ) 2 l 151.34 89.70
C S ( ) 2 g 238.00 116.90

Assuming that these thermodynamic parameters do not vary with temperature, estimate the boiling point of carbon disulfide to the nearest degree Celsius.

Q12:

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

Material Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Standard Enthalpy of Formation Δ𝐻⦵ (kJ/mol)
C a ( O H ) ( ) 2 s 83.4 − 9 8 5 . 2
C a O ( ) s 38.1 − 6 3 4 . 9
C a C O ( ) 3 s 110.0 − 1 , 2 2 0 . 0
C a ( ) s 41.6 0.0
H O ( ) 2 l 70.0 − 2 8 5 . 8
H O ( ) 2 g 188.8 − 2 4 1 . 8

Calculate the standard entropy change Δ𝑆⦵ for the formation of calcium hydroxide from calcium oxide and liquid water, expressed per mole of calcium hydroxide produced.

Calculate the standard enthalpy change Δ𝐻⦵ for the formation of calcium hydroxide from calcium oxide and liquid water, expressed per mole of calcium hydroxide produced.

Assuming the thermodynamic parameters do not vary with temperature, calculate, to 3 significant figures, the maximum temperature in kelvins at which calcium hydroxide would form spontaneously from calcium oxide and liquid water.

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

Q13:

The standard entropies and enthalpies of formation for the phases of water are shown in the table.

Phase Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Standard Enthalpy of Formation Δ𝐻⦵ (kJ/mol)
H O ( ) 2 s 41.0 − 2 9 1 . 8 3
H O ( ) 2 l 70.0 − 2 8 5 . 8 3
H O ( ) 2 g 188.8 − 2 4 1 . 5 8

Assuming that these thermodynamic parameters do not vary with temperature, estimate the boiling point of water in ∘C to 1 decimal place.

Q14:

The dissolution of silver(I) sulfide in water is represented by the following equation. AgS()2Ag()+S()2+2–saqaq The standard changes in Gibbs free energy, Δ𝐺⦵, for the formation of silver(I) sulfide and aqueous silver(I) ions at 298 K are −39.5 kJ/mol and 77.1 kJ/mol respectively. The solubility product for silver(I) sulfide is 8.00×10 at 298 K. All thermodynamic parameters are calculated using standard concentrations of 1.00 M. Calculate to 3 significant figures the value of Δ𝐺⦵ for the formation of aqueous sulfide ions at 298 K.

Q15:

The standard entropies and enthalpies of formation for the phases of water are shown in the table.

Phase Standard Molar Entropy 𝑆⦵(J/K·mol) Standard Enthalpy of Formation Δ𝐻⦵(kJ/mol)
H O ( ) 2 s 41.0 − 2 9 1 . 8 3
H O ( ) 2 l 70.0 − 2 8 5 . 8 3
H O ( ) 2 g 188.8 − 2 4 1 . 5 8

Using the values in the table, calculate, to 3 significant figures, the standard molar change in Gibbs free energy, Δ𝐺⦵, for the boiling of water at 298 K.

Q16:

The equilibrium constant for the shown dimerization reaction has a value of 6.75 at a temperature of 298 K. What is the value of Δ𝐺⦵r for this reaction at 298 K? 2NO()NO()224gg

  • A4.73 kJ
  • B9.46 kJ
  • C − 2 . 8 5 kJ
  • D2.85 kJ
  • E − 4 . 7 3 kJ

Q17:

The equilibrium constant for the given reaction is reported to have a value of 3.5×10 at a temperature of 298 K. H()⁄O()HO()222ggl+12 Given this information, calculate to 3 significant figures the value of Δ𝐺⦵r for this reaction at 298 K.

  • A − 2 3 7 kJ
  • B − 2 3 7 J
  • C − 1 1 6 kJ
  • D237 J
  • E237 kJ

Q18:

What is the equilibrium pressure of NH()3g over a sample of NHCl()4s as a result of decomposition at 25∘C, given that Δ𝐺=91.12⦵rkJ for the shown reaction? NHCl()NH()+HCl()43sgg

  • A 1 . 0 3 × 1 0   bar
  • B0.81 bar
  • C 1 . 0 6 × 1 0    bar
  • D0.65 bar

Q19:

What is the equilibrium pressure of O()2g over a sample of NiO()s at 298 K, given that Δ𝐺=211.7⦵rkJ for the reaction NiO()Ni()+⁄O()ssg122?

  • A 2 . 1 5 × 1 0    bar
  • B 8 . 0 5 × 1 0   bar
  • C 7 . 7 8 × 1 0    bar
  • D 6 . 0 5 × 1 0    bar
  • E0.843 bar

Q20:

What is the pressure of CO()2g over a sample of CaCO()3s at a temperature of 1,000 K, given that Δ𝐺=22.9⦵rkJ for the following reaction? CaCO()CaO()+CO()32ssg

  • A 6 . 3 6 × 1 0   bar
  • B 6 . 3 6 × 1 0   bar
  • C 2 . 7 4 5 × 1 0   bar
  • D 6 . 3 6 × 1 0   bar
  • E 2 . 7 4 5 × 1 0   bar

Q21:

Consider the following reaction between glycine and nitrous acid in an aqueous solution. NHCHCOOH()+HNO()HOCHCOOH()+N()+HO()222222aqaqaqgl What would the difference be between the Δ𝐺⦵r and Δ𝐴⦵r for this reaction at 298 K, assuming that the N()2g product can be treated as an ideal gas?

Q22:

Among the following statements, which one is incorrect?

  • AThe entropy of a molecular system depends on the spacings between the rotational and vibrational energy levels of the constituent molecules.
  • BThe molar entropy of a molecular gas depends on the molar mass of the constituent molecules.
  • CThe molar entropy of a substance always increases with an increase in temperature.
  • DThe entropy has a positive value for nonspontaneous reactions.
  • EThe molar entropy of a substance is an extensive property.

Q23:

Among the following processes, which would have a Δ𝐺 value greater than 0?

  • ALiquid water vaporized at 1 bar pressure and a temperature of 110∘C.
  • BSolid water (ice) melting at 1 bar pressure and a temperature of 0∘C.
  • CLiquid water vaporized at 1 bar pressure and a temperature of 105∘C.
  • DLiquid water vaporized at 1 bar pressure and a temperature of 95∘C.
  • ESolid water (ice) melting at 1 bar pressure and a temperature of 5∘C.

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