[Dave2013]

The density of a saturated hydrocarbon containing 80% wt carbon was measured against pressure at 20 degrees Celcius according to the following data:

density(g/L)   | 0.298 | 0.692 | 1.188 | 1.784 | 2.491 |
P(atm)          |   0.2  |    0.4  |   0.6  |   0.8  |  1.0   |

what is the exact molecular weight of the gaseous hydrocarbon?
anyways how do you approach these type of problems with given data? Thanks in advance!              

[Hunter2]

PV = nRT RT = const. 
pV = n*K,
pV = m/M*K,
V = m/Rho,
p*m/Rho =m/M*K
p/Rho = K/M

p, K and Rho  are given.

[Dave2013]

I think that would be the case if presented with only 1 value for density and 1 value for pressure. But how do I account for multiple values such as this one? How do I come up with only one answer? I already thought of averaging them out but then again its incorrect. any other ideas? oh and thanks by the way

[Hunter2]

What did you get for each M.

[Dave2013]

if I solve for each individual values of M then:
P=CRT
where C is concentration expressed in mole/L
for the first values of density and pressure
0.2=(0.298/M)x0.08206x(20+273.15)
where the molecular weight would be = 35.82 g/mol
similarly for the other 4 values i get 41.62 g/mol, 47.63 g/mol 53.644 g/mol and 59.92 g/mol respectively.
but it says here in the book that the right answer is 30.187 g/mol

[Hunter2]

You have to convert to SI-units. The pressure is given in atm. Please convert to Pascal.

[Dave2013]

the gas constant that I used was 0.08206 whose units are atmxL/molxK, so it is correct.
converting to SI units that you're saying is unnecessary since it will give the same results i.e
P=CRT
0.2(101325)=(0.298x1000/M)x8.3145x(20+273.15)
where M would be = 35.84 g/mol which is the same and the units for R is Pa m^3/mol x K
I think there's no problem regarding that. My problem is how do I deal with these multiple values to produce just one molecular weight?

[Dave2013]

by the way the answer was suppose to be 29.675 not 30.187 g/mol but I still dont know how to arrive at that answer! 

[Borek]

I have a feeling there is something wrong with the data. For a gas ratio of density and pressure should be constant, but here it isn't. It still could be OK, as density is changing when there is reaction taking place, but you were told its a saturated hydrocarbon, so I don't see how it can react with itself. Especially taking into account fact that molar mass more or less fits ethane.

[Dave2013]

Borek, never thought of it that way but I think that's right. better ask my professors about their opinion on this problem. Nevertheless if you happen to get the answer or another idea behind this problem please do inform me. 

[Borek]

Actually it is a little bit more complicated, as the ratio is constant for ideal gas only, but I would not expect the differences to be so large near STP.

What is context of the problem - I mean, what were you taught lately and on what level? Just the ideal gas equation, or perhaps some more advanced version like Van der Waals equation?

[Dave2013]

well, it came from a reviewer but it's in the physical chemistry section. So that's about it. I was just trying to answer some of the questions and stumbled on this problem..

[randy]

Hi...new here just thought i might give a little help

Data on a gas are most correct when one extrapolates to zero pressure...to allow for perfect (ideal) gas conditions and assumptions.  Taking the pressures you have as x-axis values, and the calculated molecular weights as y-axis values....graph this and get a trendline which will give you the y-intercept of 29.675

hope this might help

[billnotgatez]

Some interesting thoughts

Ethane Molar mass 30.07 g/mol
Ethene Molar mass 28.05 g/mol
Ethyne Molar mass 26.04 g/mol

Carbon Standard atomic weight 12.011
For 2 carbons 24.022
Divided by .8 is 30.0275 for the 80%
Divide by 30.07 is 0.798
Divided by text book value below 30.187 g/mol is 0.796
Divided by randy value 29.675 is 0.8095