Question

Which of the following relation(s) is/are correct?
Here,
$\Delta G=\text{Change in Gibbs' free energy}n=\text{no. of moles of electron transferred in a reaction}F=\text{Faraday constant}{E}_{cell}=\text{Cell potential or emf}$

• A. $\Delta G=\text{Minimum useful work}$
• B. $\Delta G=\text{Maximum useful work}$
• C. $\Delta G=-nF{E}_{cell}$
• D. $-n\Delta G=F{E}_{cell}$

Answer 1

Answer: (B), (C)

$\Delta G=-nF{E}_{cell}$

For a spontaneous reaction
$\Delta G<0$
The free energy change $\Delta G$ (a thermochemical quantity) and the cell potential $E_{cell}$ (an electrochemical quantity),both measure the driving force of a chemical reaction
Larger the decrease in free energy, greater would be the emf.

Mathematically,
$\Delta G=\text{Maximum useful work}$
$\Delta G=W_{\text{electrical}}$
$\Delta G=Q_{total}\times E_{cell}$
Here ,
$Q_{total}=\text{Total charge}$
$Q_{total}=-nF$

$n=\text{no. of moles of electron transferred in a reaction}F=\text{Faraday constant}$

$\text{Faraday constant is the charge on 1 mol of electrons}$

So,
$\Delta G=-nF\times E_{cell}$
$\text{Charge on one electron}=1.6\times {10}^{-19}C$
$\text{Charge on one mol of electrons (F)}=1.6\times {10}^{-19}\times N_{A}CF=1.6\times {10}^{-19}\times 6.022\times {10}^{23}=96487C$