The vapor above a mixture of pentane and hexane at room...

The vapor above a mixture of pentane and hexane at room
temperature contains 35.5% pentane by mass. What is the mass
percent composition of the solution? Pure pentane and hexane
have vapor pressures of 425 torr and 151 torr, respectively, at
room temperature.

Transcript

00:01 Okay, so raul's law says that the vapor pressure above a solution is just a mole fraction of its constituents times the vapor pressure of each of those constituents when they are cured.

00:17 We're going to use c5 for penton.

00:21 C6 is going to be hex.

00:24 All right, so this is the same as dalton's law because each of these things put together is just the partial pressure of those compounds.

00:34 Okay.

00:34 And the other thing to remember about gases is that pv nrt, so pressure is nrt over v.

00:46 Since for both of our constituents, rt over v is going to be the same.

00:50 Pressure is going to be directly proportional to number of moles.

00:54 All right.

00:55 The first thing we can do is figure out roughly what the mole percent is of the vapor.

01:04 So we're going to say the number of moles of c5 is going to be the mass percent divided by the mole mass.

01:22 So what we've actually done here, what we've actually done here is just assumed that we have one gram of vapor.

01:35 So what's the number of moles in each of each thing in one gram of vapor? and for hexanes, it's just going to be one over, or sorry, one minus.

01:53 All right, so in a certain one gram of vapor, we have this many moles of each constituent.

02:03 Now, consider this.

02:05 Number moles of c5 over a number of moles of c6 is going to be the same.

02:12 Let's just start with this.

02:13 P equals n.

02:16 Right, so imagine we have p1 is n1 over r2 or v.

02:21 Take that divide by a second ideal gas equation for the other constituent.

02:28 Now, if we divide these two equations, r2 over v cance is out and we have n1 over n2 is pressure 1 over pressure 2.

02:37 Okay so now we're getting something.

02:39 Now let's look back here.

02:41 Pressure 1 and pressure 2 are just going to be these multiplications here.

02:49 So what we can say is number moles of c5 over number moles of c6 is going to be pressure of c5 over the pressure of c6, which is going to be multiple.

03:03 Fraction of c5 times pure phase air pressure of c5, molfax fraction c6 over pure phase.

03:15 Now we have two unknowns.

03:17 We know both of these actually...

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