In today's class, we will derive a quantitative relationship between free energy change and potential for an electrode by using thermodynamic concept. That is nest equation and its applications. Derivation of nest equation. Let us consider a metal rod depredinit solution. For example, zinc rod depredin, zinc sulphate or copper rod depredin, copper sulphate or any metal rod depredinit solution. As a result, an electrode system develops. For such an electrode assembly, spontaneous reaction can be given as it is. Metal ion will come in with N number of electron is reversible with metal, called as the question number 1. As this system is an equilibrium by using law of mass action, we can calculate the equilibrium constant. Equal to K equals to concentration of the product divided by concentration of the reactant. That is K is equal to concentration of the metal divided by concentration of metal ion called as equation number 2. As the reaction proceeds, there is a formation of electrical double layer. That is Helmholtz electrical double layer HED. This arises due to the potential difference between metal and the solution at the contact or at the intersurface. It is called as electrode potential. This electrode potential can be defined as the potential that exists between the metal and its ions in solution at the equilibrium when they are in contact with each other. Because of formation of electrical double layer, some sort of electrical work done at the contact position. At the equilibrium, it is called as double maximum. This double maximum mainly depends upon two factors. We do not know how many charges flowing across the intersurface and where the energy available for each couloum. That is NF and E also. Double maximum is given as multiplication of NF and E. This equation can be rearranged as double maximum is equal to N into E into F. This is based on according to FADESLA. One mole of electrons is equal to 1 third F charge. As the reaction is spontaneous, there is a decrease in frequency. This decrease in frequency is equal to Magzou electrical work done. Delta G is equal to W Magzou. But Delta G is negative first spontaneous reaction. We know that W Magzou is equal to N E F. By substituting this value, Delta G is equal to minus N E F, Delta G equation number 4. Similarly, we can write Delta G in our relation also. Delta G equation number 5, where Delta G and E are the change in free energy and electrode potential under standard conditions respectively. Delta G, change in free energy, it varies with the temperature and constant pressure of the product as well as reactant. It is given by one relation called Wantov's reaction isotherm. Delta G is equal to Delta G naught plus RT ln K, Delta G equation number 6. Substitute the value of Delta G and Delta G naught in the equation number 6. We will get this equation. K value, concentration of the metal divided by the concentration of the metal ion. Delta G value minus N E F and Delta G naught value minus N E F. On rearranging and converting, natural algorithm to base 10, we can get final equation like this. This equation is called as NERS equation. At two-mentary at Kelvin, by substituting the value of R and F, we can get the final equation. It is also a NERS equation E is equal to E naught minus 0.059, 1 divided by N, log of 1 over metal ion concentration. This NERS equation is useful in calculating the potential of electrode and E M F of the cell at any temperature and concentration. Knowing the potential of electrode, the concentration of the reactant can be calculated. The concentration of a solution in the galvanic cell is also measured by using NERS equation. With the help of NERS equation, we can calculate the pH of unknown solution by measuring the E M F of a cell also. In this equation, E naught is standard electro-pollensial. It is defined as the potential that exists between metal and its solution of unit concentration at two-mentary at Kelvin, when some of partial process of gas is reactant and produce is equal to one atmosphere pressure.