Question

: The rusting of iron takes place as follows:
\[2{H^ + } + 2{e^ - } + \dfrac{1}{2}{O_2} \to {H_2}O\];\[{E^O} = + 1.23V\]
\[F{e^{2 + }} + 2{e^ - } \to Fe\] ;\[{E^O} = - 044V\]
Calculate \[\vartriangle {G^O}\]for the net process.
(A) \[ - 322KJ/mol\]
(B) \[ - 152KJ/mol\]
(C) \[ - 76KJ/mol\]
(D) \[ - 161KJ/mol\]

Answer 1

Hint:Standard cell potential of both reactions is given. Standard cell potential is represented by \[{E^o}\]. Gibbs free energy is the energy that is available to do useful work. Gibbs free energy is represented by \[\Delta G\].

Complete step by step answer:
Reaction at cathode: \[2{H^ + } + 2{e^ - } + \frac{1}{2}{O_2} \to {H_2}O\] (\[{E^O} = + 1.23V\])
Use this formula to calculate Standard Gibbs free energy is- \[\vartriangle {G^O} = - nF{E^o}\]
Here \[\vartriangle {G^O}\]= Standard Gibbs free energy
\[n = \]Moles of electron from balanced redox reaction
\[F = \]Faraday constant whose value is \[96458C/mol\]
\[{E^O}\]= Standard cell potential
Reaction at cathode in which \[n = 2\] and \[{E^O} = + 1.23V\] F=\[96458C/mol\]
\[\vartriangle {G^O}_1 = - 2.46F\]
Now at anode: \[F{e^{2 + }} + 2{e^ - } \to Fe\]
Here \[n = 2\]and \[{E^O} = - 044V\]
\[\vartriangle {G^O}_2 = - 0.88F\]
Now on applying formula \[\vartriangle {G^O}_{net} = \vartriangle {G^O}_1 + \vartriangle G_2^O\]
\[\vartriangle G_{net}^o\]= $[-2.46F] + [-0.88F]$
\[\vartriangle G_{net}^o\]= $-3.34F$
\[\vartriangle G_{net}^o\]= $-322169.72\[J/mol\]$
We know that
\[\vartriangle G_{net}^o\]=\[ - 322.169KJ/mol\]

Hence, option A is the correct option.

Additional information:
Gibbs free energy is the energy that is available to do useful work.
A reaction spontaneously occurs when \[\Delta G\] is negative.
A reaction is nonspontaneous when \[\Delta G\] is positive.
Gibbs free energy related to entropy by using this formula \[\left( {\vartriangle G = \vartriangle H - \ T\vartriangle S} \right)\] in which \[\vartriangle H\] is the change in enthalpy, \[\vartriangle T\] is the change in temperature and \[\vartriangle S\] is the change in entropy.

Note:
\[\Delta G\] is negative in spontaneous reaction. It means that the products of the reaction have less free energy than the reactants because they lose some free energy during the reaction. So this type of reaction is called an exothermic reaction.
\[\Delta G\] Is positive in nonspontaneous reaction it means that the product of the reaction has more free energy than the reactants because they gain some free energy during the reaction. So this type of reaction is called an endothermic reaction.
Gibbs free energy is used to calculate maximum reversible work.