Question

What is $ \Delta G $ , if $ n = 2 $ and cell potential is $ 2.226{\text{ V}} $ ?

Answer 1

Hint : $ \Delta G $ is the change in the free energy. It is a state function which determines whether a reaction is favorable or not. The relation between the Gibbs energy and the cell potential is $ \Delta G = - nF{E_{(cell)}} $ This equation of Gibbs free energy is used only for redox reactions so $ \Delta G $ gives the spontaneity of redox reactions.

Complete Step By Step Answer:
The Gibbs free energy (G) of a system is a measure of the amount of usable energy (energy that can do work) in that system. $ \Delta G $ Is the change in the Gibbs free energy of a system from initial state to the final state. It can be positive or negative according to whether the reaction is spontaneous or nonspontaneous. For thermodynamics $ \Delta G = \Delta H - T\Delta S $
In electrochemical reactions, $ \Delta G $ is the change in free energy which is equal to the electrochemical potential also called as cell potential times the electrical charge q (equals to nF) transferred in a redox reaction. The equation of free energy change is given by:
  $ \Delta G = - nF{E_{(cell)}} $ where $ \Delta G $ is the change in Gibbs free energy, n is the number of electrons transferred , F is Faraday’s constant having value $ {96485_{}}J/{V_{}}mol $ (for calculations it is approximately taken as $ {96500_{}}J/{V_{}}mol $ )and $ {E_{(cell)}} $ is the cell potential.
It is asked in the question to find out $ \Delta G $ ; we are going to use the above formula:
 $ \Rightarrow $ $ \Delta G = - nF{E_{(cell)}} $
Given that the number of electrons transferred ‘n’ $ = 2 $ and cell potential $ {E_{(cell)}} = {2.226_{}}V $
Thus $ \Rightarrow $ $ \Delta G = - nF{E_{(cell)}} $
 $ \Delta G = - 2 \times 96500 \times 2.226 $
 $ \Delta G = - 2 \times 96500 \times 2.226 $
 $ \Delta G = - 429618 $
 $ \Rightarrow $ $ \Delta G = - {42.9618_{}}Kjmo{l^{ - 1}} $
Therefore the Gibbs free energy change $ \Delta G = - {42.9618_{}}Kjmo{l^{ - 1}} $ .

Note :
Under standard experimental conditions the formula $ \Delta G = - nF{E_{(cell)}} $ changes to $ \Delta {G^0} = - nF{E^0}_{(cell)} $ where $ \Delta {G^0} $ is the standard Gibbs free energy and $ {E^0}_{(cell)} $ is standard cell potential. This usually happens when the reactants and the products are combining at the standard conditions of temperature and pressure.