# 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: The partial pressures of , , and are denoted , , and 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, , is 33.00 kJ/mol. Calculate, to 3 significant figures, the change in Gibbs free energy, , at 298 K when , , and .

Q2:

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

• A 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, is the energy that must be absorbed for equilibrium to be reached.
• C 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, 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, is the energy that must be released for equilibrium to be reached.

Q3:

The standard change in Gibbs free energy for a reversible process, , 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 for the hydrolysis of adenosine triphosphate (ATP) to adenosine diphosphate (ADP) and phosphate is at , and the for this reaction has a value of kJ/mol. Given this information, what is the value of for the reaction?

Q5:

Consider the reaction shown. The equilibrium constant for this reaction at is 0.0120, and the value of at is 9.37 kJ. Given this information, what is the equilibrium constant for the reaction at , and what is the value of for the reaction? (You may assume that the of the reaction is independent of temperature.)

• A at ;
• B at ;
• C at ;
• D at ;

Q6:

Consider the two reactions shown. 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. What is the equilibrium constant for reaction (3) at a temperature of ?

• A
• BThere is not enough information provided to answer this question.
• C
• D1.1

Q7:

Carbon tetrachloride is formed by the chlorination of methane at high temperature: The standard entropies and enthalpies of formation for the reactants and products are shown in the table.

MaterialStandard Molar Entropy (J/K⋅mol)Standard Enthalpy of Formation (kJ/mol)
214.4
309.7
186.3
223.10.0
186.9

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

• A
• B
• C
• D
• E

Q8:

Hydrogen sulfide reacts reversibly with sulfur dioxide to form sulfur and water: The standard free energies of formation, , for hydrogen sulfide and other materials are shown in the table. These energies are measured at .

 Material Standard Gibbs Free Energy of Formation Δ𝐺⦵ (kJ/mol) HS()2g SO()2g SO()3g S()8s S()g HO()2g HO()2l −33.4 −300.1 −371.1 0.0 238.3 −228.6 −237.1

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

• A
• B
• C
• D
• E

A student uses the values of at to calculate the equilibrium constant for this reaction at . Why are the results of this calculation likely to be inaccurate?

• AThe equation is only true at a standard temperature of .
• B 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 , to three significant figures?

Substance
205.2
248.2
256.76

Q10:

What is the equilibrium constant for the following process at , to three significant figures?

Substance
116.9238.0
89.70151.34

Q11:

Consider the following reaction.

Substance
213.8
188.8
42.8
90.17

What is for the reaction at ? 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 , to 2 significant figures?

• A
• B
• C
• D
• E

Q12:

Consider the following reaction.

Substance
83.72312.17
90.25210.8
33.2240.1

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

Q13:

Consider the following process.

Substance
365.8
258.6

What is for the process at ? 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 , to three significant figures?

Q14:

What is the equilibrium constant for the following reaction at , to 3 significant figures?

Substance
223.1
116.14
17.78247.44
• A
• B
• C
• D
• E

Q15:

What is the equilibrium constant for the following reaction at , to three significant figures?

Substance
130.7
26.48206.59
116.14
• A
• B
• C27.5
• D
• E

Q16:

What is the equilibrium constant for the following reaction at to three significant figures?

Substance
309.7
116.9238.0
223.1
319.45
• A
• B
• C
• D
• E

Q17:

Consider the following reaction.

Substance
202.8
24.7247.43
205.2

What is for the reaction at ? 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 , to three significant figures?

• A
• B
• C
• D
• E

Q18:

Consider the following reaction.

Substance
152.23
116.14
40.84258.66

What is for the reaction at ? 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 , to three significant figures?

• A
• B
• C
• D413
• E

Q19:

Sulfur dioxide and oxygen react to form sulfur trioxide when heated.

The standard Gibbs free energy change for this reaction, , is kJ/mol. Calculate to 2 significant figures the equilibrium constant, , for this reaction at .

• A
• B
• C
• D
• E

Q20:

Carbon disulfide and chlorine react reversibly to form carbon tetrachloride and disulfur dichloride. The standard Gibbs free energy change for this reaction, , is kJ/mol. Calculate to 2 significant figures the equilibrium constant, , for this reaction at .

• A
• B
• C
• D
• E

Q21:

Hydrogen and iodine react reversibly to form hydrogen iodide, as shown in the equation. The standard Gibbs free energy change for this reaction, , is 3.40 kJ/mol. Calculate the equilibrium constant, , for this reaction at , giving your answer to 2 significant figures.

Q22:

Iodine and chlorine react reversibly to form iodine(I) chloride, as shown. The standard Gibbs free energy change for this reaction, , is kJ/mol. Calculate the equilibrium constant, , for this reaction at .

Q23:

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

• A3.2
• B
• C
• D25
• E0.96

Q24:

Dinitrogen trioxide decomposes reversibly to produce nitric oxide and nitrogen dioxide, as shown. The standard Gibbs free energy change for this reaction, , is kJ/mol. Calculate to 2 significant figures the equilibrium constant, , for this reaction at .

Q25:

Lithium hydroxide reacts with carbon dioxide to form lithium carbonate and water, as shown. The standard Gibbs free energy change for this reaction, , is kJ/mol. Calculate to 2 significant figures the equilibrium constant, , for this reaction at .

• A
• B
• C
• D
• E