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Topic: Gas molar fraction problem  (Read 2040 times)

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Offline Guitrz

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Gas molar fraction problem
« on: April 09, 2018, 07:46:19 PM »
Hello. First post on the forum.  ;D

I'm an undergrad in Chemistry here in Brazil (1st year), and I've been challenged by my veterans (talk about peer pressure) to solve a chemistry problem:

"There's a gaseous mixture of Ethane and Butane filled inside a 200cm³ flask, at 750mmHg, 20ºC. If the mass of the gas in the flask is 0,384g, what is the molar fraction of the Butane in the flask?"

I've been trying to solve this for about 2 hours now. Since they are gases, the same volume has the same amount of moles as long as temperature and pressure are kept constant, but I can't find how many moles that is, because I don't have the molar fraction of the gases (which is the solution to the problem itself).

I would be thankful if someone could shed me some light here, but please don't give it away at once, for I wanna try and solve it myself, as otherwise I would have no bragging rights when I DO get it, right?  ;D

Using p = PM/RT (Ideal Gas Density), I got the densities for both gases under the specified conditions, though they seem to be useless, since they are overshooting the overall mixture's mass by a lot, probably due to the big difference between ethane/butane and an ideal gas.
Dbutane = 0.0235 kg/L = 0.0235 g/mL
Dethane = 0.0121 kg/L = 0.0121 g/mL

Offline mjc123

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Re: Gas molar fraction problem
« Reply #1 on: April 10, 2018, 05:01:14 AM »
Your densities are seriously wrong. I know that air at STP is about 1.2 g/L, so ethane under the specified conditions should be something similar, which I confirmed by calculation. Are you mixing up units, and are you using the appropriate value of R for the units you're working in?
Supposing you calculate the densities correctly, can you work out an expression for the density of the mixture in terms of x, where x is the mole fraction of butane?

Offline Enthalpy

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Re: Gas molar fraction problem
« Reply #2 on: April 10, 2018, 06:00:31 AM »
Oi!

I wouldn't compute densities but rather numbers of moles. From PV=nRT you have the sum of the moles of ethane and butane in the flask. Compute the mass of an ethane and a butane mole, the mean mass of a mole in the flask, deduce the proportion.

Offline Guitrz

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Re: Gas molar fraction problem
« Reply #3 on: April 10, 2018, 07:32:43 AM »
Are you mixing up units, and are you using the appropriate value of R for the units you're working in?

I calculated that using an online density calculator, expecting it to be faster. M in g/mol, P in atm, R as 8,31 Joules, T in Kelvin. I checked again and you're right, the website is indicating the wrong unit for the R. Not sure how that passed unnoticed to everyone.



From PV=nRT you have the sum of the moles of ethane and butane in the flask.
Wonderful, this is just the formula I needed! Thanks!

Offline Enthalpy

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Re: Gas molar fraction problem
« Reply #4 on: April 12, 2018, 02:37:46 PM »
[...] the website is indicating the wrong unit for the R. Not sure how that passed unnoticed to everyone.

Because the author wasn't so reliable and didn't care that much, and the users didn't notice or didn't bother to tell the author, and even if he got a feedback, the author didn't care to improve.

Remember the bug about random keys in the Apache https secure server? A comment /* */ removed a pseudo-random source, only 65536 possible keys remained, which ruined the security of nearly all https servers worldwide. The "bug" (probably a sabotage by the Nsa) was patent in the published source code. It stayed there for years, because "anyone can check the open source" means "the other people should have done it".

Apparently, you have seen you first blatant error on the Web. I invite you to think at it and decide whether you can trust random websites to make your future science. Just as an example, almost every physical property of compounds on the Web is a software estimate: it's grossly wrong.

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