Chapter 19, Problem 19.38QP

Interpretation Introduction

Interpretation:

The standard emf of the propane fuel using standard free energy change has to be calculated.

Concept introduction:

In a propane-oxygen fuel cell electric current is generated by the oxidation of propane at anode and reduction of oxygen at cathode. The cell reaction was given below.

  $\begin{array}{l}\text{Anode (Oxidation)}{\text{C}}_{\text{3}}{\text{H}}_{\text{8}}{}_{\text{(g)}}{\text{+6H}}_{\text{2}}{\text{O}}_{\text{(l)}}\stackrel{}{\to }3{\text{CO}}_{\text{2}}{}_{\text{(g)}}{\text{+20H}}^{\text{+}}{}_{\text{(g)}}{\text{+20e}}^{\text{-}}\\ \text{Cathode (Reduction)}5{\text{O}}_{\text{2}}{}_{\text{(g)}}{\text{+ 20H}}^{\text{+}}{}_{\text{(aq)}}{\text{+20e}}^{\text{-}}\stackrel{}{\to }10{\text{H}}_{\text{2}}{\text{O}}_{\text{(aq)}}\\ \text{Overall}\text{Reaction}{\text{C}}_{\text{3}}{\text{H}}_{\text{8}}{}_{\text{(g)}}{\text{+5O}}_{\text{2}}{}_{\text{(g)}}\stackrel{}{\to }3{\text{CO}}_{\text{2}}{}_{\text{(g)}}+{\text{4H}}_{\text{2}}{\text{O}}_{\text{(l)}}\end{array}$

Since change in free energy of the reaction is directly related to the emf of the cell it can be calculated using the below equation.

  $\begin{array}{l}{\text{ΔG}}^{\text{o}}{\text{=-nFE}}^{\text{o}}{}_{\begin{array}{l}\text{cell}\\ \end{array}}\\ {\text{E}}^{\text{o}}{}_{\begin{array}{l}\text{cell}\\ \end{array}}\text{=-}\frac{{\text{ΔG}}^{\text{o}}}{\text{nF}}\\ {\text{ΔG}}^{\text{o}}\text{=Standard Gibbs}\text{free}\text{energy}\text{change}\\ \text{n}\text{=}\text{number}\text{of}\text{electrons}\text{transferred}\text{during}\text{the}\text{reaction}\\ \text{F=}\text{Faraday}{\text{constant (96500C/mole e}}^{\text{-}}\text{)}\end{array}$

  $\begin{array}{l}{\text{ΔG}}_{\text{rxn}}{}^{\text{o}}={\text{ΔG}}^{\text{o}}{}_{\text{f}}(\text{product})-{\text{ΔG}}^{\text{o}}{}_{\text{f}}(\text{reactant})\\ {\text{ΔG}}_{\text{rxn}}{}^{\text{o}}{\text{=(3ΔG}}^{\text{o}}{}_{\text{f}}{\text{(CO}}_{\text{2(g)}}{\text{)+4ΔG}}^{\text{o}}{}_{\text{f}}{\text{(HO}}_{\text{2(l)}}{\text{))-((ΔG}}^{\text{o}}{}_{\text{f}}{\text{(C}}_{\text{3}}{\text{O}}_{\text{8}}{}_{\text{(g)}}{\text{)+5ΔG}}^{\text{o}}{}_{\text{f}}{\text{(O}}_{\text{2(g)}}\text{))}\end{array}$

  ${\text{ΔG}}^{\text{o}}{}_{\text{f}}=\text{free}\text{energy}\text{of}\text{formation}$

Free energy of formation for the common reactant and product were used from the data base.