A solution contains a mixture of pentane and hexane at room temperature. The solution has a vapor pressure of 258 torr. Pure pentane and hexane have vapor pressures of 425 torr and 151 torr, respectively, at room temperature. What is the mole fraction composition of the mixture? (Assume ideal behavior.)

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Hello everyone today we are being given the following problem and asked to solve for it. It says the vapor pressure of acetone and acetone I trial is 20 at 20 degrees Celsius as one a detour and 72 2 respectively. Been asked to calculate the mole fraction of acetone in the vapor above above the solution if an ideal solution of the two compounds has the vapor pressure of 98 tour at 20 degrees Celsius. And so the first thing I wanna do is we want to calculate our total pressure of the system that we have. So we have the pressure of our acetone plus our pressure of our tuxedo night trial. And so rearranging this equation we get our pressure of acetone is equal to X, which is our mole fraction times our partial pressure of acetone present. We then use a secondary equation from this original derived equation. We see that the pressure of our casino night trial. So our pressure of acetone I trial is equal to the mole fraction of aceto night trial as before times the partial pressure of that aceto night trial. So we have two different equations that we can use this for. And so to start off to find our mole fraction for a cedo night trial we can say that we have one minus the mole fraction of our acetone. And so combining these two equations from our original equation up here we get that the total pressure is equal to our mole fraction of acetone times the partial pressure of acetone plus one minus our mole fraction of acetone. Times our partial pressure of aceto night trial. We know that our total pressure is 98 tour. As given to us any questions stem You have 98 tour. We don't have our mole fraction of acetone, but we do have the pressure of acetone as given in the question is tour. We then fall on the equation and we can conclude that we then have plus one minus our mole fraction of acetone, which we don't have. And then we're gonna multiply that by our vapor pressure of acetone. I trial, which is 72 tour Continuing along this equation, we have 98. Tour is equal to our mole fraction of acetone As before equal to 1 80 tour. We can get rid of that plus one minus acetone by saying that we have plus tour minus our mole fraction of acetone times 72. We can subtract both sides by 72 to get 26 on this side, on the left hand side will eventually end up with X acetone or a mole fraction of acetone times 180. Tour. The next thing we want to do is we want to divide both sides by this number. And when we do that we end up with our mole fraction of acetone Being 0.144. And so now we have to take this and incorporate that into our initial equation for our pressure of acetone over here, we're going to draw on the right over here. So we're going to say our pressure of acetone is going to be equal to the mole fraction of acetone times our vapor pressure of acetone. And we plug these numbers in. We get our Value from the original question. We have 0.144 times 1 80 tour. And when we do that, we're going to get an answer of 26. However, we're being asked to find it in vapor form. So in the vapor form we have to take our mole fraction of acetone. We have to equal that to the pressure of acetone over our total pressure. And so in doing that, We get our total pressure or pressure of acetone being 26/98, which is our total pressure, giving us a final answer of 0.265. I hope this helped until next time.

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Key Concepts

Raoult's Law

Mole Fraction

Ideal Gas Behavior