Worksheet: Equilibrium Constants and Gibbs Free Energies

In this worksheet, we will practice converting between Gibbs free energies of equilibria and equilibrium constants by applying the equation ΔG = –RTlnK.

Q1:

Under certain conditions, gaseous ammonia can decompose into nitrogen and hydrogen gases: 2NH()3H()+N()322ggg. The partial pressures of NH3, H2, and N2 are denoted 𝑃(NH)3, 𝑃(H)2, and 𝑃(N)2 respectively. When the initial partial pressure of each gas is equal to the standard value of 1.00 atm and the temperature is fixed at 298 K, the change in Gibbs free energy for the reaction, Δ𝐺⦵, is 33.00 kJ/mol. Calculate, to 3 significant figures, the change in Gibbs free energy, Δ𝐺, at 298 K when 𝑃=(NH)12.9atm3, 𝑃=(H)0.250atm2, and 𝑃=(N)0.870atm2.

Q2:

Which of the following is the best definition of Δ𝐺⦵, the standard change in Gibbs free energy for a reversible process?

  • A Δ 𝐺 ⦵ is the difference in free energy between the pure products in their stoichiometric ratio and the equilibrium mixture of reactants and products.
  • BWhen the concentrations or partial pressures of reactants and products are all equal to the standard value, Δ𝐺⦵ is the energy that must be absorbed for equilibrium to be reached.
  • C Δ 𝐺 ⦵ is the difference in free energy between the pure reactants in their stoichiometric ratio and the equilibrium mixture of reactants and products.
  • DWhen the concentrations or partial pressures of reactants and products are all equal to the standard values, Δ𝐺⦵ is the energy that must be released for equilibrium to be reached.
  • EWhen the sum of the concentrations or partial pressures of reactants and products is equal to the standard value, Δ𝐺⦵ is the energy that must be released for equilibrium to be reached.

Q3:

The standard change in Gibbs free energy for a reversible process, Δ𝐺⦵, is measured for a standard solution of reactants and products. What are the initial concentrations of the reactants and products in this solution?

  • AReactants are present in the stoichiometric ratio and the sum of the reactant concentrations is 1 M. Product concentrations are defined in the same way.
  • BReactants and products are present in the stoichiometric ratio and the sum of the reactant concentrations is 1 M.
  • CReactants and products are present in the equilibrium ratio and the sum of the reactant and product concentrations is 1 M.
  • DThe concentration of each reactant and product is 1 M.
  • EReactants and products are present in the stoichiometric ratio and the sum of the reactant and product concentrations is 1 M.

Q4:

The equilibrium constant (𝐾) for the hydrolysis of adenosine triphosphate (ATP) to adenosine diphosphate (ADP) and phosphate is 1.67×10/moldm at 37∘C, and the Δ𝐻⦵ for this reaction has a value of −20.1 kJ/mol. Given this information, what is the value of Δ𝑆⦵ for the reaction?

Q5:

Consider the reaction shown. Glycerol()+HPO()DL-glycerol--phosphate+HO()aqaql42–21(𝑎𝑞) The equilibrium constant for this reaction at 37∘C is 0.0120, and the value of Δ𝐺⦵r at 25∘C is 9.37 kJ. Given this information, what is the equilibrium constant (𝐾)eq for the reaction at 25∘C, and what is the value of Δ𝐻⦵r for the reaction? (You may assume that the Δ𝐻⦵r of the reaction is independent of temperature.)

  • A 𝐾 = 0 . 0 2 3 e q at 25∘C; Δ𝐻=−41.2⦵rkJ
  • B 𝐾 = 0 . 0 0 3 e q at 25∘C; Δ𝐻=−21.2⦵rkJ
  • C 𝐾 = 0 . 4 6 2 e q at 25∘C; Δ𝐻=41.2⦵rkJ
  • D 𝐾 = 0 . 0 4 6 e q at 25∘C; Δ𝐻=21.2⦵rkJ

Q6:

Consider the two reactions shown. Glutamate+NHglutaminekJmolatC(1)4+,Δ𝐺=15.7/37⦵∘ATPADP+PikJmolatC(2),Δ𝐺=−31.0/37⦵∘ Note that, in reaction (2), ATP denotes adenosine triphosphate, ADP denotes adenosine diphosphate, and Pi represents inorganic phosphate. These two reactions can be coupled by an enzyme catalyst (glutamine synthetase), which leads to the following reaction. Glutamate+NH+ATPglutamine+ADP+Pi(3)4+ What is the equilibrium constant for reaction (3) at a temperature of 37∘C?

  • A 3 . 8 × 1 0 
  • BThere is not enough information provided to answer this question.
  • C 2 . 3 × 1 0  
  • D1.1

Q7:

Carbon tetrachloride is formed by the chlorination of methane at high temperature: CH()+4Cl()CCl()+4HCl()424gggg. The standard entropies and enthalpies of formation for the reactants and products are shown in the table.

Material Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Standard Enthalpy of Formation Δ𝐻⦵f (kJ/mol)
C C l ( ) 4 l 214.4 − 1 2 8 . 2
C C l ( ) 4 g 309.7 − 9 5 . 7
C H ( ) 4 g 186.3 − 7 4 . 6
C l ( ) 2 g 223.1 0.0
H C l ( ) g 186.9 − 9 2 . 3

Assuming the thermodynamic parameters do not vary with temperature, calculate, to 1 significant figure, the equilibrium constant for this reaction at 250∘C.

  • A 7 × 1 0  
  • B 7 × 1 0  
  • C 9 × 1 0  
  • D 1 × 1 0  
  • E 1 × 1 0  

Q8:

Hydrogen sulfide reacts reversibly with sulfur dioxide to form sulfur and water: 2HS()+SO()S()+2HO()2282ggsl38. The standard free energies of formation, Δ𝐺⦵, for hydrogen sulfide and other materials are shown in the table. These energies are measured at 25∘C.

Material H S ( ) 2 g S O ( ) 2 g S O ( ) 3 g S ( ) 8 s S ( ) g H O ( ) 2 g H O ( ) 2 l
Standard Gibbs Free Energy of Formation Δ𝐺⦵ (kJ/mol) − 3 3 . 4 − 3 0 0 . 1 − 3 7 1 . 1 0.0 238.3 − 2 2 8 . 6 − 2 3 7 . 1

Calculate, to 2 significant figures, the equilibrium constant for this reaction at 25∘C.

  • A 6 . 6 × 1 0  
  • B 6 . 3 × 1 0  
  • C 4 . 5 × 1 0  
  • D 2 . 3 × 1 0 
  • E 1 . 4 × 1 0 

A student uses the values of Δ𝐺⦵ at 25∘C to calculate the equilibrium constant for this reaction at 90∘C. Why are the results of this calculation likely to be inaccurate?

  • AThe equation Δ𝐺=−𝑅𝑇𝐾⦵ln is only true at a standard temperature of 25∘C.
  • B Δ 𝐺 ⦵  values change with temperature.
  • CThe products of the reaction have different phases at the higher temperature.
  • DThe reaction may not occur at the higher temperature.
  • EThe standard pressure changes with temperature.

Q9:

What is the equilibrium constant for the following reaction at 575∘C, to three significant figures? 2SO()+O()2SO()223ggg

Substance Δ 𝐻 ⦵ f ( k J / m o l ) 𝑆 ⦵    ( J / m o l )
O ( ) 2 g 205.2
S O ( ) 2 g − 2 9 6 . 8 3 248.2
S O ( ) 3 g − 3 9 5 . 7 2 256.76

Q10:

What is the equilibrium constant for the following process at 80∘C, to three significant figures? CS()CS()22gl

Substance Δ 𝐻 ⦵ f ( k J / m o l ) Δ 𝑆 ⦵    ( J / m o l )
C S ( ) 2 g 116.9 238.0
C S ( ) 2 l 89.70 151.34

Q11:

Consider the following reaction. 2LiOH()+CO()LiCO()+HO()sgsg2232

Substance Δ 𝐻 ⦵ f ( k J / m o l ) 𝑆 ⦵    ( J / m o l )
C O ( ) 2 g − 3 9 3 . 5 1 213.8
H O ( ) 2 g − 2 4 1 . 8 2 188.8
L i O H ( ) s − 4 8 7 . 5 42.8
L i C O ( ) 2 3 s − 1 , 2 1 6 . 0 4 90.17

What is Δ𝐺 for the reaction at 575∘C? Assume that the entropy and enthalpy change of formation for a substance do not vary with temperature.

What is the equilibrium constant for the reaction, at 575∘C, to 2 significant figures?

  • A 3 . 7 × 1 0  
  • B 2 . 7 × 1 0 
  • C 1 . 2 × 1 0  
  • D 3 . 5 × 1 0 
  • E 2 . 9 × 1 0  

Q12:

Consider the following reaction. NO()NO()+NO()232ggg

Substance Δ 𝐻 ⦵ f ( k J / m o l ) 𝑆 ⦵    ( J / m o l )
N O ( ) 2 3 g 83.72 312.17
N O ( ) g 90.25 210.8
N O ( ) 2 g 33.2 240.1

What is the equilibrium constant for the reaction at −10.0∘C to two significant figures? Assume that the entropy and enthalpy change of formation for a substance do not vary with temperature.

What is the equilibrium constant for the reaction, at −10.0∘C, to three significant figures?

Q13:

Consider the following process. SnCl()SnCl()44lg

Substance Δ 𝐻 ⦵ f ( k J / m o l ) 𝑆 ⦵    ( J / m o l )
S n C l ( ) 4 g − 4 7 1 . 5 365.8
S n C l ( ) 4 l − 5 1 1 . 3 258.6

What is Δ𝐺 for the process at 200∘C? Assume that the entropy and enthalpy change of formation for a substance do not vary with temperature.

What is the equilibrium constant for the process, at 200∘C, to three significant figures?

Q14:

What is the equilibrium constant for the following reaction at 100∘C, to 3 significant figures? I()+Cl()2ICl()22sgg

Substance Δ 𝐻 ⦵ f ( k J / m o l ) 𝑆 ⦵    ( J / m o l )
C l ( ) 2 g 223.1
I ( ) 2 s 116.14
I C l ( ) g 17.78 247.44
  • A 5 . 7 7 × 1 0  
  • B 1 . 4 2 × 1 0 
  • C 1 . 8 1 × 1 0 
  • D 1 . 7 3 × 1 0   
  • E 7 . 0 5 × 1 0  

Q15:

What is the equilibrium constant for the following reaction at 0∘C, to three significant figures? H()+I()2HI()22gsg

Substance Δ 𝐻 ⦵ f ( k J / m o l ) 𝑆 ⦵    ( J / m o l )
H ( ) 2 g 130.7
H I ( ) g 26.48 206.59
I ( ) 2 s 116.14
  • A 5 . 0 3 × 1 0 
  • B 3 . 6 4 × 1 0  
  • C27.5
  • D 3 . 1 6 × 1 0  
  • E 4 . 8 6 × 1 0  

Q16:

What is the equilibrium constant for the following reaction at 90∘C to three significant figures? CS()+3Cl()CCl()+SCl()22422gggg

Substance Δ 𝐻 ⦵ f ( k J / m o l ) 𝑆 ⦵    ( J / m o l )
C C l ( ) 4 g − 9 5 . 7 309.7
C S ( ) 2 g 116.9 238.0
C l ( ) 2 g 223.1
S C l ( ) 2 2 g − 1 9 . 5 0 319.45
  • A 1 . 2 1 × 1 0  
  • B 7 . 1 7 × 1 0  
  • C 2 . 6 1 × 1 0  
  • D 8 . 2 9 × 1 0   
  • E 1 . 4 0 × 1 0   

Q17:

Consider the following reaction. O()+2F()2FO()(1)222ggg

Substance Δ 𝐻 ⦵ f ( k J / m o l ) 𝑆 ⦵    ( J / m o l )
F ( ) 2 g 202.8
F O ( ) 2 g 24.7 247.43
O ( ) 2 g 205.2

What is Δ𝐺 for the reaction at 100∘C? Assume that the entropy and enthalpy change of formation for a substance do not vary with temperature.

What is the equilibrium constant for the reaction, at 100∘C, to three significant figures?

  • A 9 . 3 5 × 1 0  
  • B 2 . 5 2 × 1 0  
  • C 8 . 6 9 × 1 0  
  • D 3 . 9 7 × 1 0   
  • E 1 . 0 7 × 1 0   

Q18:

Consider the following reaction. I()+Br()2IBr()22slg

Substance Δ 𝐻 ⦵ f ( k J / m o l ) 𝑆 ⦵    ( J / m o l )
B r ( ) 2 l 152.23
I ( ) 2 s 116.14
I B r ( ) g 40.84 258.66

What is Δ𝐺 for the reaction at 0.00∘C? Assume that the entropy and enthalpy change of formation for a substance do not vary with temperature.

What is the equilibrium constant for the reaction, at 0.00∘C, to three significant figures?

  • A 9 . 2 1 × 1 0  
  • B 4 . 0 1 × 1 0 
  • C 2 . 4 2 × 1 0  
  • D413
  • E 1 . 3 3 × 1 0  

Q19:

Sulfur dioxide and oxygen react to form sulfur trioxide when heated. 2SO()+O()2SO()223ggg

The standard Gibbs free energy change for this reaction, Δ𝐺⦵, is −141.82 kJ/mol. Calculate to 2 significant figures the equilibrium constant, 𝐾P, for this reaction at 85∘C.

  • A 2 . 1 × 1 0  
  • B 2 . 2 × 1 0  
  • C 4 . 3 × 1 0  
  • D 4 . 8 × 1 0  
  • E 4 . 2 × 1 0  

Q20:

Carbon disulfide and chlorine react reversibly to form carbon tetrachloride and disulfur dichloride. CS()+3Cl()CCl()+SCl()22422gggg The standard Gibbs free energy change for this reaction, Δ𝐺⦵, is −39.0 kJ/mol. Calculate to 2 significant figures the equilibrium constant, 𝐾P, for this reaction at 50∘C.

  • A 7 . 1 × 1 0 
  • B 3 . 3 × 1 0  
  • C 2 . 0 × 1 0 
  • D 5 . 0 × 1 0 
  • E 7 . 4 × 1 0  

Q21:

Hydrogen and iodine react reversibly to form hydrogen iodide, as shown in the equation. H()+I()2HI()22ggg The standard Gibbs free energy change for this reaction, Δ𝐺⦵, is 3.40 kJ/mol. Calculate the equilibrium constant, 𝐾P, for this reaction at 100∘C, giving your answer to 2 significant figures.

Q22:

Iodine and chlorine react reversibly to form iodine(I) chloride, as shown. I()+Cl()2ICl()22ggg The standard Gibbs free energy change for this reaction, Δ𝐺⦵, is −10.88 kJ/mol. Calculate the equilibrium constant, 𝐾p, for this reaction at 40∘C.

Q23:

The standard Gibbs free energy change for the vaporization of tin(IV) chloride, Δ𝐺⦵, is 8.00 kJ/mol. Calculate, to 2 significant figures, the equilibrium constant, 𝐾C, for this reaction at 25∘C.

  • A3.2
  • B 5 . 9 × 1 0  
  • C 4 . 0 × 1 0  
  • D25
  • E0.96

Q24:

Dinitrogen trioxide decomposes reversibly to produce nitric oxide and nitrogen dioxide, as shown. NO()NO()+NO()232ggg The standard Gibbs free energy change for this reaction, Δ𝐺⦵, is −1.65 kJ/mol. Calculate to 2 significant figures the equilibrium constant, 𝐾P, for this reaction at 25∘C.

Q25:

Lithium hydroxide reacts with carbon dioxide to form lithium carbonate and water, as shown. 2LiOH()+CO()LiCO()+HO()sgsg2232 The standard Gibbs free energy change for this reaction, Δ𝐺⦵, is −79.00 kJ/mol. Calculate to 2 significant figures the equilibrium constant, 𝐾C, for this reaction at 25.0∘C.

  • A 1 . 4 × 1 0  
  • B 2 . 4 × 1 0  
  • C 7 . 4 × 1 0  
  • D 6 . 9 × 1 0  
  • E 6 . 0 × 1 0  

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