 Welcome to the next part of our discussion on thermodynamics. So, so far we have discussed mostly the concept and fundamentals of thermodynamics, where we have gone through the basic properties of a thermodynamic system, the work, energy and heat, how they are all connected together with respect to the first law of thermodynamics. Then we have defined two important terms enthalpy and entropy and we have described the second law of thermodynamics and third law of thermodynamics with respect to entropy. Then we have derived the two important energy functions the Helmholtz free energy and Gibbs free energy and to find out with respect to them how we can define a spontaneous reaction. Now, we will go further and look how this thermodynamic parameters and understanding can be used for different chemical and physical processes. This will be the application portion of thermodynamics. So, let us begin. So, from the first law of thermodynamics, we have defined delta E is equal to Q minus W. Again Q is positive when the heat is coming to the system and W is negative when system is doing a work and then we can write Q is delta E plus W and now we are going to expand a little bit further and expanding what kind of work I am talking about. If I am talking about P delta V the expansion work plus W the useful work that means without the mechanical or expansion work. As we just know delta E plus P delta V is nothing, but delta H and enthalpy change becomes this particular equation Q equal to delta H plus useful work. Now, for a reversible process occurring at a constant temperature, we know delta S is equal to Q by T or we can say Q is nothing, but T delta S. So, now if I use this particular equation and these two equations and exchange the values of Q's, we can easily write T delta S is equal to delta H plus W useful or we can write delta H minus T delta S is equal to useful we are just multiplying with minus 1 on both sides. So, over there we can say this is nothing, but delta G at a constant temperature and pressure is nothing, but minus U useful or taking the negative side on this side negative delta G T P it is going to give me the idea about how much useful work I can do for a particular system. So, it is another elongated discussion of what is the useful work and how it is connected with the Gibbs free energy that we are continuing from the discussion of the last segment. Now, with that thing in our mind this is very critical because now different kind of system we can consider to find out what is the useful amount of work. So, for the first system of this one we are going to consider is the electrochemical cells. Now, what is an electrochemical cell? Electrochemical cell is a particular vessel where we have two electrodes present there which are connected to each other and over here either a chemical energy or a chemical transformation I should say chemical change can trigger an electron movement in the form of electricity or vice versa. A electrical potential applied on the system creates a chemical change or a chemical transformation. So, either the chemical change creating the electricity or the electricity is actually doing the chemical change either way it is possible and depending on which side of the thing we are doing. So, there is a chemical reaction happening and it is actually creating a movement in electron which can be given as electricity. Now, if the first system is happening a chemical change is happening first and that is creating the electricity movement that is known as a galvanic cell and if the second thing is happening where the electricity is actually bringing the chemical change it is known as a electrolytic cell. So, these are the two different variations of electrochemical cells we talk about and it all depends on the directionality of the system like it is a chemical change bringing the electricity or the electricity is bringing the chemical change and depending on that we can differentiate them with galvanic cell and electrolytic cell. Now I am drawing the electrochemical cell one more time now what kind of reaction is happening in these two particular electrodes present in the electrochemical cell. So, in one of the electrode happens the reduction and that is known as the cathode and the other one happens the opposite reaction the oxidation which actually completes the overall cycle this is known as anode and these two reactions happen at a particular energy and that energy we can measure with respect to the potential or the voltage we have applied. And say this is happening as E cathode or reduction and this is happening as E anode or oxidation and the difference between this cathode and the anodic potential gives me the overall E or sometime as is written E cell the overall capacity of this electrochemical cell in galvanic stage or electrolytic stage to do the maximum amount of work. So, this is the overall amount of work we can do which is given by this value of E which is known as the electromotive force. So, this is the potential which actually is the driving force behind this chemical reactions to be happening. So, this is actually a measure of the overall chemical reaction is possible in this particular cell. Now, how to connect that with delta G that gives free energy value. So, now if we look into a chemical reaction which is happening say we are taking an oxidant molecule we are giving him N electrons and then this system is producing the reduced equivalent. Now over here what is the maximum work possible for this redox reaction in a electrochemical cell. So, the maximum work possible over here is going to be number of coulombs of charge flowing through the interface that means from the solution to the electrode through the circuit that is how much coulombs of charge is actually exchanging into the energy available per coulombs per coulomb of charge. If you combine them together that is the maximum work we can do that is totally how many charge how much charge is actually converting over there and for each amount of charge how much work can be done. So, the number of coulombs transforming over there is equal to N is the number of electrons involved into Faraday. Faraday is a unit which is equivalent to 96485 coulomb. So, that gives us the overall charge flowing into the energy available per coulomb of charge which is nothing but the E the electromotive force that we have discussed just in the initial part which is the overall energy the difference between the anodic and cathodic section and that is the overall energy available for this particular reaction to happen for one unit of charge and it is totally doing for NF unit of charge. So, it all multiplies together to NFE. So, the overall maximum work doable in this system is NFE and now we have already described the minus delta G at constant temperature and pressure is equal to double max the maximum work possible without the non-expansion work and over there the most non-expansion work possible for the electrochemical cell is NFE. So, now we can combine them together and we can say minus delta G Tp is equal to NFE and this gives us the famous equation delta G is equal to nothing but minus NFE. So, for a electrochemical cell we can easily find out what is the overall Gibbs free energy change which is nothing but minus NFE n is the number of electrons involved in this reaction for this redox change. F is the unit Faraday which take care of the overall coulombs of charge available and E is the energy available for this particular reaction per unit of coulomb. So, this is the factor it is coming into the picture. Now, we can go a little bit further to expand it a little bit more. So, now say you are still looking the same reaction oxidant plus an electron is giving me the reduction product. Now, using Vantz-Hoff equations that is out of the ambit of this particular segment, but I encourage you to go and look into the Vantz-Hoff equation and how it is connected. That actually says a equilibrium constant of a system can be given by the concentration of the products and concentration of the reactant. In this case it is a product is reduced and oxidant concentration. From the Vantz-Hoff equation I can write this one delta G is equal to delta G naught that means the Gibbs free energy we calculated at the standard state plus RT natural log of product divided by oxidant. So, that is what is given by the Vantz-Hoff equation. Now, using this factor I can write it out delta G as we already know is is equal to minus nfe. Similarly, delta G naught will be equal to nfe naught which is nothing but this is measured at any particular condition whereas this superscript 0 defines that it is measured at standard states or standard condition. What is the standard conditions as we defined again earlier 298 Kelvin or 25 degree centigrade temperature, 1 atmospheric pressure and for solid state it is always in the standard state 1. So, all these things if we combine them together and replace these two values over here and there what we are actually going to get is the following minus nfe is equal to minus nfe naught plus RT ln reduced the product and oxidized the reactant system that is we are actually getting. Now, if we divide everything by minus nf we are going to get E equal to E naught minus RT by nf ln R divided by oxidant. We go a little bit further E equal to E naught minus 2.303 RT by nf and I am changing this to the log to the best 10 from the natural log this factor and over here this value can be further simplified by putting this R is nothing but the universal gas constant T is the absolute temperature and if we consider at a 25 degree centigrade the T is nothing but 298 Kelvin we all bring it together to this particular value by n where we also use F equal to 1 Faraday which is also a constant to log of R divided by oxidant. So, over there you can see by using the Gibbs free energy and is expansion is connection to the potential of a system delta is equal to minus nfe and using the Vance of equation we require we arrive to this particular equation where we can define the potential of any particular condition connected to the standard potential with respect to the how much oxidant and reduct and is particularly present in that particular condition and this equation is nothing but known as the Nernst equation and this Nernst equation is very important because by looking into the change of the potential from the standard state we can actually find out how much reduced and oxidized species is present what is their equilibrium why it is actually lies. So, from there we can actually find out what is the concentration of different analyte and this particular function has been used not to find only particular chemicals but also to measure even the pH of a solution where proton is one of the reactant. So, pH meter calculation is also based on the Nernst equation. So, Nernst equation is actually an application of the thermodynamics of Gibbs free energy of Vance of equation and their interaction and over there we arrive to this Nernst equation which actually gives us a very clear idea how to measure the different concentration of reactants and products with respect to a change in the equilibrium potential. So, that will be the conclusion of this particular segment of the application. Thank you.