welcome to a brief discussion of the fundamental concepts behind simple distillation in order to properly understand how it is that simple distillation can allow us to purify one liquid from a mixture we need to go back to general chemistry and think about several of the important laws that we use during that course the first of these is routs law which predicts that the vapor pressure exerted by a liquid in a mixture is equal to the vapor pressure of that liquid when it is pure times its mole fraction within the mixture the second is dalton's law which predicts that the total pressure in any system is equal to the sum of the vapor pressures of each component regardless of the identity of that component and finally we need to think about ideal gas law for a moment PV equals NRT is the most commonly shown arrangement of this particular equation but we need to rearrange this to PV over NT equals R giving us an equation which has a constant result for all gases at all times because of this we could say the pressure of compound a and the number of moles of compound a can be related to the pressure in the system overall and the total amount within there notice that in this case when we arrange the equations this way for two different sets of gases if they're contained within the same space volumes will cancel and of course if they're within the same space they must be at the same temperature meaning the temperatures will also cancel from this equation leaving us with a more simple equality we can rearrange this equality to arrive at an expression where the number of moles of a over the total number of moles is equal to the partial pressure of a over the total pressure in other words the mole fraction of any compound is simply equal to is partial pressure in the system divided by the total pressure within the system now let's take a look at how we can use these three observations to predict how a distillation will behave shown here is a beaker filled with a liquid it's a binary mixture of two different compounds in this case we're going to say that the blue spheres represent molecules of toluene and that the red spheres represent molecules of benzene so the depiction here would be of a mixture which is about 50 mole percent benzene and toluene we go to the data tables we find that at the boiling point of this mixture the partial pressure of toluene or pure at this temperature it was 300 Torr well the partial pressure exerted by benzene would be 1200 Torr if we apply rounds law to this system what we find is that the partial pressure exerted by the toluene is actually 150 tor because it's mole fraction is 0.5 and similarly benzene is expected to exert a vapor pressure equal to half that of pure benzene at this temperature or 600 Torr relying on ideal gas law to convert these partial pressures to a mole fraction we arrive at the conclusion that the vapor above this liquid is in fact not 50 mole percent benzene but rather 80 mole percent benzene so by boiling the mixture we have created a vapor which is more concentrated in benzene than the original liquid now we need to come up with an apparatus which will allow us to take advantage of the fact that this vapor is of a different composition depicted in this image is a simple distillation apparatus or a simple still the components of the simple steel are as follows a boiling flask which is placed on a heat source next is a three-way condenser or it's still head whose purpose is to divert vapor from the headspace of the boiling flask into a cooler environment where it can be recondense and collected the cooling is provided by a device known as a West condenser which is a long narrow tube with a water jacket around the outside water is plumbed in the bottom and out the top of the West condenser in order to provide cold surface area on which vapor can rican dense next we had a vacuum adapter at the end of the West condenser the vacuum adapter serves two purposes first diverting the flow of our condensed liquid into our receiving flask and second having a hose barb open to the atmosphere which means that we're not heating a closed system finally the material flows through the vacuum adapter into a receiving flask which is placed over an ice bath or kept cool in some other fashion so that the condensed liquid remains in the liquid phase if we place our liquid mixture back into the boiling flask and we heat this mixture will notice that the vapor will still begin to form at a ratio of 80% benzene to 20% toluene however in this case because we have the steelhead attached instead of simply escaping the vapor is now diverted into the West condenser where it can later be collected and you'll notice if you watch carefully that only about one in five molecules which escapes this boiling liquid is actually toluene or as one in two molecules in the embroiling liquid is toluene so to take a look at an overall simple still as it operates we'll look at the entire system now again we built our simple still by attaching a boiling flask to a steelhead which diverts the flow of gas into a West condenser and that liquid then drains through the vacuum adapter ultimately landing in the receiving flask where it is collected if we begin with the mixture of 50 mole percent benzene our calculations based upon route Dalton's and ideal gas laws leads us to the prediction that what will accumulate in the receiving flask is in fact 80 mole percent benzene and over time we will collect a usable amount of our enriched benzene sample the liquid vapor composition plot is typically used to try to predict how efficient a simple distillation will be when separating two compounds from one another in order to construct a liquid vapor composition plot a plot is generated on which temperature is plotted as a function of mole percent of one constituent of the binary mixture in our case we'll use benzene we can start by tracing a line at the temperature at which we know our mixture was boiling at this particular temperature a mixture of 50 mole percent benzene and toluene is expected to boil recall from our calculations we determined that that 50 mole percent benzene mixture will actually be 80 mole percent when it reaches the vapor phase so we're going to plot these two points along our temperature line first the 50 percent liquid composition and then the 80 percent vapor composition if we were to perform similar calculations for a range of temperatures in a range of compositions what we would find is that there is a curve associated with the behavior of these systems and we can then connect the dots to produce what is known as a liquid vapor composition plot now that we have this information we can instead of using the routs law calculation simply go to the plot and select the composition with which we know we'll be starting and then determine the composition of the distillate when a simple distillation is performed in our next installment we'll discuss what to do when we want to have that 100 percent pure sample rather than something that is in our example eighty percent pure