CO2 compression?

Question

Hi, Could anyone tell me which would be the resulting pressure (on atm) if containing 75000g of C02 at a temperature of 150 degrees on a 30000cm3 volume? Thank you. Paco.

Answer 1

CO2 Mol.mass = 44g/mol.

75,000g / 44g/mol. = 1,705moles.

1,705mol. x 22.4L/mol at STP.

= 38,192L. At STP (1atm and 273K).

Combined Gas Law. P1xV1xT2 = P2xV2xT1.

1atm x 38,192L x 423K = P2 x 30L x 273.

P2 = (38,192 x 423) / (30 x 273).

=  16,155,216 / 8,190 = 1,973atm.

Note: The critical temperature for CO2 is 31°C. That means that NO AMOUNT of pressure applied to CO2 gas at or above 31°C will cause the gas to liquefy or solidify at or below that temperature.

Answer 2

I agree with pappu in using PV=NRT, if you assume the ideal gas law.

75 kg in 30L sounds ... unfamiliar at best.

Answer 3

Is that even possible? 75kg in 30L? the density would be considerably higher than solid CO2 at atmospheric pressure, and most solids are not very compressible.

You might double check the position of your decimal points

[EDIT] well, okay, it won't be solid, but it is counter intuitive to think that a supercritical fluid could be significantly denser than a solid (I'm not saying it absolutely can't be, just that it is counter intuitive) and 2.5g/cm^3 is significantly higher that 1.6g/cm^3

In any case a supercritical fluid is not an ideal gas, so i seriously doubt the gas laws apply.

I still think the the person who asked the question should double check their decimal points.

[2nd EDIT] I don't know why I believed Norrie,  I just looked at the Wikipedia article on Critical temperature, and I see; "Above the critical temperature a liquid cannot be formed by an increase in pressure, but with enough pressure a solid may be formed" Of course people will complain about Wikipedia, so I looked it up in some printed books; "Separation to a gas and a solid phase may occur at sufficiently high pressure" (43)  Lee, John Francis, <i>Thermodynamics</i>, Massachusetts, Addison-Wesley, 1963

I knew the density of solid CO2 would be of some relevance.

While I haven't found any information on the compressibility of solid CO2, I seriously doubt it can be compressed to 2.5g/cm^3 anywhere on earth, at least not 30 liters of it, maybe a microscopic quantity in a diamond anvil pressure cell.

After I wrote the last paragraph, I did find this: https://www.llnl.gov/str/Yoo.html

While it doesn't mention density, it does have some interesting information on solid CO2 at high pressures (in a diamond anvil pressure cell, GMTA)

This is an example of a "sanity  check" if the results don't make sense, there is probably an error somewhere, sure you can run the numbers through the combined gas equations, and get a value for the pressure, but if the end result doesn't make sense, then one has to question the process. Plus it is well know that the ideal gas laws are only an approximation for real gases. (and they certainly don't apply to solids)

Answer 4

The other answers are nicely done, but not quite complete.

You don't say what scale the 150° is in, which is needed for any calcs. This means the problem could be in two different ranges.

For a lower level class, they want you to use theoretical approaches, and the  combined gas law is the way to go. Even here, they should warn you that anything significantly over about 200 bar typically correlates poorly. Gases at high pressures just don't match low pressure models like the combined gas law. Most likely this was the intent of the problem, so likely you have the wrong numbers.

Higher level courses typically use experimental data to determine actual material performance. If it is a higher level course, there should have been a reference for CO2 properties. To get the correct answer at higher pressures, use  the density-pressure phase diagram, see link:

http://en.wikipedia.org/wiki/Supercritic...

Correct method is to look at the chart, sketch in a curve for the temp you have, run over from the density, and pick the pressure off the sketched curve.

Now, density is 75000g/30000cm3, or 2.5.

Looking at the diagram, densest CO2 in this temp/pressure range (assuming 150°C) is less than 1. No can do chief!  The chart covers normal pressures used in engineered systems. Higher pressures many be used in tiny very exotic one-off science projects with few or no practical applications.

Now, assuming you meant 150°K, CO2 is a solid of 1.6 density at 215°K, so it would have to be in this colder type of regime to possibly be this dense. You would need the corresponding data at this temperature to determine performance. Tinker is correct that at ridiculous pressures, materials act differently. However, solids rarely compress more than about 5%, so not likely to make the specified density at any pressure that keeps the atoms stable.

So, no matter which of the two temps you mean,  probably, either you have the wrong numbers, trick question, or error by  professor.

By the way, supercritical is no big deal. It just means there is no separate gas and liquid phases. It has densities similar to those of the liquids in much of the regime.

Answer 5

PV=nRT

n=75000/44=1704.55

R=0.0831

P= in atm

V=30000/1000=30ltr

T=150C +273= 423 K

For more accuracy

(P-a*n^2/V^2)(V-nb)=RT