Answer : The value of standard free energy is, -152.4 kJ/mol
Explanation :
The given balanced cell reaction is:
[tex]FADH_2+\frac{1}{2}O_2\rightarrow FAD+H_2O[/tex]
The half reaction will be:
Reaction at anode (oxidation) : [tex]FADH_2\rightarrow FAD+2H^++2e^-[/tex] [tex]E^0_{Anode}=+0.03V[/tex]
Reaction at cathode (reduction) : [tex]\frac{1}{2}O_2+2H^++2e^-\rightarrow H_2O[/tex] [tex]E^0_{Cathode}=+0.82V[/tex]
First we have to calculate the standard electrode potential of the cell.
[tex]E^o=E^o_{cathode}-E^o_{anode}[/tex]
[tex]E^o=(+0.82V)-(+0.03V)=+0.79V[/tex]
Relationship between standard Gibbs free energy and standard electrode potential follows:
[tex]\Delta G^o=-nFE^o_{cell}[/tex]
where,
[tex]\Delta G^o[/tex] = standard free energy = ?
n = number of electrons transferred = 2
F = Faraday constant = [tex]96.48kJ.mol^{-1}V^{-1}[/tex]
[tex]E^o_{cell}[/tex] = standard electrode potential of the cell = 0.79 V
Now put all the given values in the above formula, we get:
[tex]\Delta G^o=-(2)\times (96.48kJ.mol^{-1}V^{-1})\times (0.79V)[/tex]
[tex]\Delta G^o=-152.4kJ/mol[/tex]
Therefore, the value of standard free energy is, -152.4 kJ/mol
