How much useful work can be obtained from 1 g of sucrose (C12H22O11) by oxidation with O2 at room temperature? What is the standard potential associated with this reaction?
Useful work is found from the Gibb's energy, so the thermodynamic parameters for the oxidation of sucrose by oxygen must be determined.
A reasonable approximation of the reaction is:
C12H22O11(aq) + O2(g) → CO2(g) + H2O(l)
This can be balanced using the rules for redox reactions or by inspection. Using the rules under acidic conditions:
Oxidation:
C12H22O11(aq) + 13 H2O(l) → 12 CO2(g) + 48 H+(aq) + 48 e–
Reduction:
O2(g) + 4 H+(aq) + 4 e– → 2 H2O(l)
Net:
C12H22O11(aq) + 12 O2(g) → 12 CO2(g) + 11 H2O(l)
Using quantities from the Table of Thermodynamic Quantities the enthalpy change and the entropy change for the reaction can be found:
ΔH° = [12(–393.5) + 11(–285.8)] – [(–2226.1) + 12(0)] = –5639.7 kJ/mol
ΔS° = [12(213.6) + 11(69.9)] – [(360.2) + 12(205.0)] = 511.9 J/mol·K
ΔG° = –5639.7 – (298)(0.5119) = –5792.2 kJ/mol
To find the work per gram, this value must be divided by the molar mass of sucrose (12(12) + 22(1) + 11(16) = 342 g/mol):
Work per gram = –5792.2/342 = –16.9 kJ/g
To find the standard potential for this reaction:
E° = –ΔG°/nF = –[–5792200/(48)(96485)] = 1.25 V