Worksheet: Gibbs Energy under Nonstandard Conditions

In this worksheet, we will practice using equilibrium constants and reaction quotients to calculate Gibbs free energy changes at nonstandard conditions.

Q1:

During glycolysis, an important biochemical pathway responsible for the generation of energy within a cell, glucose-6-phosphate is converted to fructose-6-phosphate. The standard change in Gibbs free energy, Δ𝐺⦵, for this reaction at 37∘C is 1.70 kJ/mol. This energy is measured at standard reactant and product concentrations of 1.00 M.

At equilibrium, Δ𝐺=0. What is the value of Δ𝐺 to 3 significant figures at 298 K if the concentration of glucose-6-phosphate is 120 μM and the concentration of fructose-6-phosphate is 28.0 μM?

Calculate to 3 significant figures the concentration of glucose-6-phosphate at equilibrium if the ambient temperature is 37∘C and the initial glucose concentration is 1.40 M.

Q2:

The standard change in Gibbs free energy, Δ𝐺⦵, for the evaporation of water at 298 K is 8.58 kJ/mol. This energy is measured under a standard vapor pressure of 1.00 bar.

At equilibrium, Δ𝐺=0. What is the value of Δ𝐺 to 3 significant figures if the partial pressure of water at 298 K is 0.0110 bar?

Calculate to 3 significant figures the partial pressure of water at equilibrium when the ambient temperature is 298 K.

  • A 3 . 2 8 × 1 0   bar
  • B 1 . 0 8 × 1 0   bar
  • C 2 . 9 9 × 1 0   bar
  • D 1 . 8 4 × 1 0   bar
  • E 3 . 1 3 × 1 0   bar

Q3:

Antimony pentachloride decomposes at high temperature into antimony trichloride and chlorine. SbCl()SbCl()+Cl()532ggg

An equilibrium mixture in a 5.000 L flask at 448∘C contains 3.85 g antimony pentachloride, 9.14 g antimony trichloride, and 2.84 g chlorine.

By expressing the partial pressure of each gas as a fraction of the standard gas pressure of 1.000 bar, calculate to 3 significant figures the equilibrium constant 𝐾P for this reaction at 448∘C.

By expressing the partial pressure of each gas as a fraction of the standard gas pressure of 1.000 bar, calculate to 3 significant figures the standard change in Gibbs free energy, Δ𝐺⦵, for this reaction at 448∘C.

Q4:

A diatomic molecule dissociates into single atoms at high temperature. A()2A()2gg

At 975 K and a total equilibrium gas pressure of 1.00 bar, 32.4% of the diatomic molecules dissociate. By expressing the partial pressure of each gas as a fraction of the standard gas pressure of 1.00 bar, calculate to 3 significant figures the standard change in Gibbs free energy, Δ𝐺⦵, for this reaction at 975 K.

Q5:

Under certain conditions, gaseous ammonia can decompose into nitrogen and hydrogen gases: 2NH()3H()+N()322ggg. 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, when a mixture containing 0.100 mol of each gas is heated to 875∘C in a 5.00 L container.

Q6:

Consider a process in which 0.2 mol of liquid acetone is mixed with 0.8 mol of liquid chloroform at a temperature of 35∘C and a pressure of 1 bar. Under these conditions, measurements show that the activity coefficients of the acetone and chloroform constituents of the mixture have the values 0.544 (for acetone) and 0.957 (for chloroform). Given this information, what would be the Δ𝐺 associated with the mixing process?

Q7:

Carbon dioxide decomposes at high temperature into carbon monoxide and oxygen: CO()CO()+O()22ggg12.

The standard entropies and enthalpies of formation for the carbon dioxide and the decomposition products are shown in the table:

Material Standard Molar Entropy 𝑆⦵ (J/K⋅mol) Standard Enthalpy of Formation Δ𝐻⦵f (kJ/mol)
C O ( ) 2 g 213.8 − 3 9 3 . 5
C O ( ) g 197.7 − 1 1 0 . 5
O ( ) 2 g 205.2 0.0

All thermodynamic parameters are measured at standard gas pressures of 1.000 bar.

The initial pressure of a sample of carbon dioxide at 1,000∘C is 1.150 bar. Assuming the thermodynamic parameters do not vary with temperature, calculate, to 3 significant figures, the equilibrium partial pressure of oxygen in this sample at 1,000∘C.

  • A 1 . 6 3 × 1 0   bar
  • B 2 . 0 5 × 1 0   bar
  • C 1 . 0 3 × 1 0   bar
  • D 2 . 3 8 × 1 0   bar
  • E 1 . 2 9 × 1 0   bar

By what factor does the equilibrium constant for this reaction change if 𝑆⦵ and Δ𝐻⦵f are expressed using standard gas pressures of 1.000 Pa?

  • A 1 0 
  • B 1 0  
  • C 1 0     
  • D 1 0    
  • E1

The change in Gibbs free energy for the reaction under nonstandard conditions, Δ𝐺, is calculated using values of 𝑆⦵ and Δ𝐻⦵f measured under standard conditions. Calculate, to 3 significant figures, the change in Δ𝐺 for the decomposition of carbon dioxide if values of 𝑆⦵ and Δ𝐻⦵f are expressed using standard gas pressures of 1.000 Pa.

When the standard change in Gibbs free energy, Δ𝐺⦵, for the decomposition of carbon dioxide is expressed per mole of carbon dioxide reacted, the equilibrium constant for the reaction is 𝐾. Determine the new value of the equilibrium constant in terms of 𝐾 if Δ𝐺⦵ is instead expressed per mole of oxygen produced.

  • A 𝐾 2
  • B 𝐾 
  • C 𝐾
  • D 2 𝐾
  • E 𝐾    

Q8:

Dinitrogen tetroxide decomposes reversibly to produce nitrogen dioxide. NO()2NO()242gg

The equilibrium constant for this reaction, 𝐾P, is 0.142 at 25∘C. The standard pressure for all gases is 1.000 bar.

Calculate the standard change in Gibbs free energy, Δ𝐺⦵, for this reaction.

What is the value of the reaction quotient 𝑄 when the reactant and products are in their standard states?

Calculate the partial pressure of NO2 if the initial pressure of dinitrogen tetroxide at 25∘C is 1.00×10 Pa.

How do the reaction quotient, 𝑄, and partial pressure of NO2, 𝑝(NO)2, change if a mixture of dinitrogen tetroxide and nitrogen oxide in their standard states is allowed to reach equilibrium?

  • A 𝑄 increases and 𝑝(NO)2 decreases.
  • BBoth 𝑄 and 𝑝(NO)2 remain constant.
  • C 𝑄 decreases and 𝑝(NO)2 increases.
  • DBoth 𝑄 and 𝑝(NO)2 increase.
  • EBoth 𝑄 and 𝑝(NO)2 decrease.

Q9:

Calcium carbonate can exist in two distinctly different crystalline forms, called calcite and aragonite. The standard Gibbs free energy of formation for calcite at 298 K is Δ𝐺=−1,128.79/⦵kJmol, and the standard Gibbs free energy of formation for aragonite at 298 K is Δ𝐺=−1,127.75/⦵kJmol. Which crystalline form is the more thermodynamically stable at a temperature of 298 K and a pressure of 1 bar, and what would be the value of Δ𝐺⦵ for the calcite → aragonite transformation at 298 K?

  • ACalcite is more stable; Δ𝐺=−1.04/⦵kJmol
  • BCalcite is more stable; Δ𝐺=1.04/⦵kJmol
  • CAragonite is more stable; Δ𝐺=1.04/⦵kJmol
  • DAragonite is more stable; Δ𝐺=−1.04/⦵kJmol

Q10:

Consider a process in which 1.00 mol of an ideal gas is isothermally expanded from 0.0100 m3 to 0.1000 m3 at a temperature of 25∘C. What is Δ𝐺 for this process to 3 significant figures?

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