 So, before solving this question, let's take a quick recap of what Raoult's law is. Now Raoult's law states that for a solution of volatile liquids, the partial pressure of each component of the solution is directly proportional to its mole fraction. For instance, if this is what our solution is, our solution contains two components let's say A and B, both are volatile liquids, then the partial vapor pressure of component A, that is P A, is proportional to its mole fraction in the solution, that is P A is proportional to X A. Similarly, the partial vapor pressure of component B, P B is directly proportional to X B. Now if you remove the proportionality, it becomes P A is equal to P A naught into X A and P B is equal to P B naught into X B. Now the proportionality constants P A naught and P B naught refer to the vapor pressure of the pure liquids A and B at the same temperature. Now the total pressure exerted on the solution phase would simply be the sum of the partial pressure of both the components of the solution, correct? So P total would be P A plus P B and what do we know is P and P B here? P A is P A naught X A and P B is P B naught X B. Now we also know that sum of the mole fractions of all the components in a mixture would be equal to 1. So X A plus X B should be equal to 1. Basically it's not X X B, the actual sign for mole fraction as we all know is chi. So for simplicity let's just assume it is X, okay? Then we can rephrase this as P A naught into 1 minus X B plus P B naught into X B. So finally we get P A naught plus P B naught minus P A naught into X B. So you can express the total pressure in terms of the mole fraction of one of the components of the liquid mixture. Now this is very very powerful tool. Now just as we can find the composition in the liquid phase which is X A and X B, the mole fractions of both the components, we can similarly find the composition in the vapor phase. So for that let's assume Y A and Y B are the mole fractions of components A and B in the vapor phase. Then the composition vapor phase Y A can be obtained from P A by P total because this is from directly from Dalton's law of partial pressures and Y B can be obtained from P B by P total because we know that partial pressure A in vapor phase is nothing but mole fraction of the component of the vapor phase multiplied by the total pressure. So from here you can get the composition of the vapor phase which is Y A and Y B. Okay so although I wanted to keep it really short, I have explained way too much about Raoult's law here. So let's now directly jump to the question. Okay. Alright so we are given vapor pressure of pure liquids A and B which are 300 and 600 mmHg and also the total vapor pressure of the liquid mixture which is 500 mmHg. Alright so let's now find out the composition of the liquid mixture. So let's quickly write down whatever details is given in the question just for a reference. Now we know that the total pressure exerted over the solution phase P total is equal to some of the vapor pressure of the individual components which is P A plus P B. Now this can be further written as P A naught x A plus P B naught x B. Now we have information P A naught and P B naught and we also know that some of the mole fractions of the individual components in a mixture is equal to 1 so x A plus x B is equal to 1. So using this we can easily rearrange this equation in the following way. Now this is nothing but P A naught plus P B naught minus P A naught into x B. By substituting these values you will get 300 plus 300 into x B and what is the P total here? It is 500. So on solving this we get x B is finite minus 3 into 2 by 3 and x A is what? 1 minus x B and that is 1 by 3. Therefore the composition in the liquid mixture x A is to x B is 1 is to 2. Now to find out the composition in the vapor phase we can use Dalton's law of partial pressures. It states that the total pressure exerted by a mixture of gases is the sum of the pressures that each gas would exert if it were alone. So let's assume that the mole fractions of A and B in vapor phase are y A and y B. Now y A is nothing but partial pressure of A divided by the total pressure and y B will be 1 minus y A because of course it's mole fraction. Now how do we arrive at P A here? P A is nothing but P A naught into x A. I'm sorry this does not look like P. By substituting the values of P A naught which is 300 mm Hg and x A here what we have is 1 by 3. So 300 into 1 by 3 gives you P A which is 100 mm Hg. Alright so we have to simply substitute this value here which is 100 divided by P total. P total is 500. So y A is 1 by 5 and y B becomes 1 minus 1 by 5 which is 4 by 5. So this is the composition in vapor phase. Y A is to y B is equal to 1 is to 4. So this is the liquid phase. This is the liquid composition and this is the composition in the vapor phase.