 We are going to be looking at Faraday's second law of electrolysis and Faraday's second law follows from the first law. So before we proceed, I'm going to give you a quick recap of Faraday's first law and the idea of the first law is that if we have an electrolysis setup like this where there is some deposition that is happening on any of the electrodes, we can say that the weight of the material deposited will be proportional to the charge passing through the circuit and we can write this Q as the current I times the time for which the current passes that is T and so we know that the weight deposited is proportional to the current times the time for which the current passes. Now if we were to get rid of this proportionality, we can write this as W is Z times I T where Z is the constant which is called electrochemical equivalent. Now if we just rearrange this and look at the units of Z, we realize that Z has the units of some mass by coulombs because Z is essentially W by Q. So we know that Z will have some units like kg per coulomb or grams per coulomb. So if we consider the reaction at one of the electrodes and we say that let's say one mole of deposition happens. So we know that the weight of one mole will be equal to the molar mass of the material and we also know the charge for one mole and so we can simplify this Z and write it in terms of molar mass and the number of moles of electrons involved and we can plug in everything to get this relationship that is the weight of the substance deposited in grams will be equal to the molar mass of the substance divided by the number of moles of electrons involved divided by this number 96500 which is an approximate value of the charge of one mole of electrons also called one faraday times the current in the circuit and the time for which the current is passed. So if we know the values of these quantities we can plug them in to calculate how much of the substances deposited at the electrode and this was the expression for Faraday's first law. If you want to know more about how we got to this expression you can check out the other video which was exclusively on the first law. Now there is one more piece of information that we need to understand the second law and that is the definition of equivalent weight. So this m by n is defined as equivalent weight that is the molar mass of the substance divided by the number of moles of electrons involved. So this was the background that we needed to understand the second law the expression for Faraday's first law and the definition of equivalent weight and as you see Faraday's second law is just a rearrangement of this expression. So let's see how that happens. To understand Faraday's second law let's take this setup where we have two similar electrolytic cells and let's say that in one of them metal A is deposited and in the other metal B is deposited and we're going to assume that the current I through this circuit is the same for both of these cells and the current is passing in the circuit for the same time T in both of these cases and the electrolyte and the electrodes are different in both of these cases because different metals A and B are deposited in each of them but other than that the current and the time are same for both of these. So let's say that the weight deposited in the first case is WA and the equivalent weight of A is EA and in case of B the weight deposited is WB and the equivalent weight of B is EB. What Faraday's second law says is that the ratio of the weights deposited that is WA is to WB will be equal to the ratio of the equivalent weights of A and B that is EA and EB and as I told you before this relationship between the weights and the equivalent weights can be sort of derived from the expression of the first law. So we saw earlier how this M by N was the equivalent weight of the substance deposited. So if we just take this M by N to the left hand side we can write W by E where E is the equivalent weight is equal to whatever was remaining on the right hand side that is I multiplied by T divided by 96500 which is one Faraday. Now we took the condition that the current I in both of these is the same and we also said that the current is passing through these circuits for the same amount of time T. So if you look at the right hand side of this equation the I is the same in both cases the time T is also the same and this is a constant. So what follows from here is that W by E is a constant. So in that case for both of these setups this constant will be the same. So we can write that WA by EA will be equal to WB by EB and now if we just rearrange both of these we can write WA by WB is equal to EA by EB or in other words we can say that the ratio of the weights deposited of metal A and metal B will be the same as the ratio of their equivalent weights which is Faraday's second law. So as you can see this relationship can be derived by just rearranging these terms. So we can say that Faraday's second law actually just follows from Faraday's first law.