Cyclopentane 1C5H102 and cyclohexane 1C6H122 are vola- tile, nonpolar hydrocarbons. At 30.0 °C, the vapor pres- sure of cyclopentane is 385 mm Hg, and the vapor pressure of cyclohexane is 122 mm Hg. What is Xpentane in a mixture of C5H10 and C6H12 that has a vapor pressure of 212 mm Hg at 30.0 °C?

Video transcript

Hello. In this problem we are told at 40 degrees Celsius, the vapor pressure of ethyl acetate and chloroform, which are volatile and non polar hydrocarbons are 100 and 88 millimeters of mercury and 360 60 millimeters of mercury. Respectfully If a mixture of ethyl acetate and chloroform has a vapor pressure of 283 mm mercury at 40°C. We are asked what is the full fraction of chloroform when finding the vapor pressure of a solution. Then we make use of rails Law. In this case we have two volatile components that alas it eight and four form rails law then says that the total vapor pressure above the solution is equal to the vapor pressure due to component A. Plus the vapor pressure due to component B. The vapor pressure due to component A. Is equal to the mole fraction of a. Times vapor pressure of pure A. And the vapor pressure of B is equal to the mole fraction of B times the vapor pressure of peer B. So in this case we are we have one equation and two unknowns. So we don't know our mole fractions but we do know that some of the mole fractions Has to Equal one. And so we can then write the mole fraction of B. In terms of A. So the mole fraction of B is equal to then one minus the mole fraction of A. And in this problem we are told the vapor pressure for the solution and we are told the vapor pressure for the pure um chloroform and the pure ethyl acetate. So let's take the equation above. So the vapor pressure above the solution then is equal to the mole fraction of component A. Times the vapor pressure Pure A. We're now gonna substitute in for the mole fraction of B. One minus the mole fraction of A. And multiply that times the vapor pressure of pure B. So we're going to then carry out the foil method. So we have one times the vapor pressure of pure B. Which is equal to the end of a pressure peer B. Times or sorry, minus the mole fraction of a. Times the vapor pressure of pure B. We're going to move the vapor pressure of peer B. To the other side of the equation. So we subtract it from both sides, get the vapor pressure then above the solution minus the vapor pressure of peer B is equal to the mole fraction of a. Times the vapor pressure of Puree minus the mole fraction of eight times the vapor pressure of pure B. We can factor out then the mole fraction of A. We get then the vapor pressure of Puree minus the vapor pressure of pure be isolating mole fraction of a. By itself. We're gonna divide both sides by vapor pressure of Puree minus that of Pure B. So we get more fraction of A. Then is equal to that vapor pressure above the solution minus the day pressure. Pier B divided by the vapor pressure of pure A minus the vapor pressure of pure B. And so generally it's easier if you simplify the equation as we've done here in terms of what we are after. So in this case we're after the mole fraction of chloroform. So we're gonna call a chloroform and we'll call B then ethyl acetate. So it's easier to simplify the equation, solve what we're after and then plug in our vapor pressures. So we are told that the vapor pressure of pure chloroform is 360 millimeters of mercury and that the vapor pressure of peer B Is 188 Where B is state there in mm of Mercury. And we were told that the vapor pressure above the solution was equal to 283 millimeters of mercury. So we're gonna plug in our known values into the equation. So we get the mole fraction of chloroform then Is equal to vapor pressure above the solution which is two and 83 mm of mercury minus the vapor pressure of ethyl acetate, which was 188 millimeters of mercury. All over the vapor pressure of pure chloroform, which was 360 of mercury minus the vapor pressure of pure B, which is ethyl acetate, which was 188 millimeters of mercury. And This then works out 2.552. So our mole fraction of law reform Is equal to 0.552. Where we have a mixture of two volatile components, ethyl acetate and chloroform. Again, given the mole fraction of one, we can find out of the other mole fraction of both of them have to sum to one, so we can make use of this so that we simplify our equation as we did above to have one equation and one unknown which was the mole fraction of a, which we termed chloroform. In doing so, then we plugged in what we knew about the vapor pressures for the solution and that of the peer components and found that the mole fraction of core form was .552. Thanks for watching. Hope this is helpful.