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A solution containing pentane and hexane produces a vapor that is 36.3% by weight of pentane.

Molar masses: Pentane=72.15 g/mol, Hexane=86.18 g/mol
Vapor pressures: Pentane: 425 torr, Hexane: 150 torr

The percent pentane by weight in the original solution is:
A. 16.4%  B. 19.0%  C. 23.5%  D. 40.0%

I thought that it would 36.3%, because Henry's Law states that the mass of gas dissolved in the solution is proportional to the vapor pressure of the gas. Can someone clarify please?

[UG]

Sounds more like an application of Raoult's Law than Henry's Law.

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Sounds more like an application of Raoult's Law than Henry's Law.

So then, I could do P=x*425+(1-x)*150, where x=mole fraction of pentane, but where would I get the P, or total pressure from?

[Borek]

You don't need total pressure - in the end it will cancel out.

Use 36.3% w/w to calculate partial pressure (in therms of fraction of total pressure) of pentane.

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How? I tried starting out by letting there be 100 g of vapor, so there are 36.3 g of pentane and 63.7 g of hexane. This means that there are 36.3/72.15=.503 mol pentane and 63.7/86.18=.739 mol hexane. The mole fraction of pentane is therefore (.503)/(.503+.739)=0.405, and the mole fraction of hexane is then 1-.405=.595 .

Would it be valid to then let the total pressure to be 1, and if it is valid, would the partial vapor pressure be .405 torr for pentane and .595 for hexane?

If that is even right in the first place, how do I go from the partial pressure to its percentage in the solution?

[Borek]

0.405 is correct.

Now, you already expressed total pressure in terms of given vapor pressures of pure substances. Can you express partial pressure of pentane in terms of total pressure and (yet unknown) solution composition?

How does the molar fraction of a gas depend on its partial pressure?

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Well, if 0.405 is correct, then shouldn't partial pressure of pentane be 0.405*P, if P is total pressure? And since they give us no additional information, we can assume that the mole fraction in the solution is also 0.405? I think we would be able to get percentage by weight then if we had density, right?

How does the molar fraction of a gas depend on its partial pressure?

Is this just P=x*425+(1-x)*150, where x=mole fraction of pentane? If this is right, then can we plug in 0.405 for x, so that P=261.375 torr?

[Borek]

Well, if 0.405 is correct, then shouldn't partial pressure of pentane be 0.405*P, if P is total pressure?

Yes.

And since they give us no additional information, we can assume that the mole fraction in the solution is also 0.405?

No - that would be the case only if vapor pressures of both substances were identical, they are not.

How does the molar fraction of a gas depend on its partial pressure?

Is this just P=x*425+(1-x)*150, where x=mole fraction of pentane?

This would be total pressure. Note that I wasn't clear and I think in effect you confused molar fraction in the solution with molar fraction in the gas. I asked about gas phase - if molar fraction of the pentane in the gas phase is 0.405, and total pressure is P, what is partial pressure of the pentane?

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So I set the two partial pressures equal to each other for both pentane and hexane:

.405 P = x*425
.595 P = (1-x)*150
where x is the mole fraction of pentane in the solution.
I solved to get x=.194, and then I let there be m moles of solution, so there are .194 m moles of pentane and .806 m moles of hexane. I then multipled .194 m by the molar mass of pentane 72.15 g/mol, and divided this over .194m*72.15+.806m*86.18 to get 16.7%, which is close, but not exactly to the answer, A. Should I assume that the .3% difference is from rounding errors, or did I do something wrong?

[Borek]

That's what I got too. If it is wrong, I have no idea how to solve the question.