   Chapter 18, Problem 66GQ

Chapter
Section
Textbook Problem

Yeast can produce ethanol by the fermentation of glucose (C6H12O6), which is the basis for the production of most alcoholic beverages.C6H12O6(aq) → 2 C2H5OH(ℓ) + 2 CO2(g)Calculate ΔrH°, ΔrS°, and ΔrG° for the reaction at 25 °C. Is the reaction product- or reactant-favored at equilibrium? In addition to the thermodynamic values in Appendix L, you will need the following data for C6H12O6(aq):ΔfH° = −1260.0 kl/mol; S° = 289 J/K · mol; and ΔfG° = −918.8 kl/mol.

Interpretation Introduction

Interpretation:

The values of ΔrH°, ΔrS° and ΔrG for the fermentation of glucose should be calculated using the given data.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔrG. It is related to entropy and entropy by the following expression,

ΔrG=ΔrHTΔrS

Here, ΔrH is the change in enthalpy and ΔrS is the change in entropy.

Explanation

The value of ΔrH°, ΔrS° and ΔrG for the fermentation of glucose is calculated below.

The Appendix L referred for the values of standard entropies and enthalpies.

C6H12O6(aq)2C2H5OH(l)+2CO2(g)ΔfH°(kJ/mol)1260.0277393.509S(J/Kmol)289160.7213.74

ΔrH°=nΔfH°(products)nΔfH°(reactants)=[[(2 mol C2H5OH(l)/mol-rxn)ΔfH°[C2H5OH(l)]+(2 mol CO2(g)/mol-rxn)ΔfH°[CO2(g)]] (1 mol C6H12O6(aq)/mol-rxn)ΔfH°[C6H12O6(aq)]]

Substituting the enthalpy values,

ΔrH°=[[(2 mol C2H5OH(l)/mol-rxn)(277 kJ/mol)+(2 mol CO2(g)/mol-rxn)(393.509 kJ/mol)] (1 mol C6H12O6(aq)/mol-rxn)(1260

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