Density of CO2 Vapor

[DM2]

I'm trying to write a formula in an Excel spreadsheet to calculate the loss of CO2 through an opening. One part of the equation requires the "Density of CO2 Vapor" in "Lb/ft3".

For the most part I could use a standard value at 70°F, but as it happens, I'm dealing with an area where the temperature could be higher, like closer to 120°F or more.

I believe that at standard temperature and pressure the value would be 0.123607/ft3 (1.98kb/m3). (if this is incorrect don't hesitate to let me know).

If the temperature, in Fahrenheit, is known, how would I determine the density at that temperature?

Thanks for the help.
Dan Marr.

 

[mbeychok]

DM2:

Keep in mind that the density of a gas depends upon its pressure as well as its temperature.

Using the combined gas laws:

Density, lb/ft³ = (1/Z)(M/10.73)(P/T)

where:

M = Molecular weight = 44 for carbon dioxide (CO₂)
P = absolute pressure, psia
T = degrees Rankine = 459.7 + [°]F
10.73 = the gas law constant R
Z = the gas compressibility factor at P and T

In most cases, Z=1 for all practical purposes.

Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[DM2]

I'm sorry for being so late in responding to your input.

For the formula you supplied, will "P" be 14.5?

 

[sdlee2008]

DM2,

not too sure on American units, but just make sure that you're using Pabs and not Pgauge.

Pabs = Pgauge +Patm (psia) and you're good to go.

 

[mbeychok]

DM2:

The density of a gas depends upon the temperature, pressure and molecular weight of the gas.

If the gas is at atmospheric pressure, then P would be 14.697 psia (pounds per square inch absolute) if it is at sea level. If the gas is at some other pressure, then that would be P. For example, if the gas is at 10 psig (pounds per square inch guage), then P would be 14.696 + 10 =24.696 psia again at sea level.

I stress the "sea level" bit, because atmospheric pressure decreases with altitude. In other words, atmospheric pressure will be less than 14.696 psia if you live atop a mountain.

If you live in a metric country, atmospheric pressure is 101,325 Pascals absolute at sea level, which is the same as 1.01325 bar absolute.



Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[DM2]

Milton,
Thanks for the info. I've got the numbers plugged into a spreadsheet, but am not sure it they're right. If you're willing to look at it, I'll try and post it.

Thanks,
Dan Marr

 

[Renoyd]

I think mbeychok has got it. Just a reminder that the gas compressibility factor (Z) does change WRT the operating pressure just like the density. Normally when the pressure increases, Z will reduce.

 

[dcasto]

Wait till you see the compressibility factor of CO2, ouch, you are not going to like it. Try this:

van der Waals Equation
van der Waals equation is:
(p + (n2a/V2))(V - nb) = nRT


Table: Van der Waals Coefficients of Selected Gases
Gas a b
atm dm6/mol dm3/mol
ideal 0.0 0.0
He 0.034 0.0237
Ar 1.345 0.0322
O2 1.360 0.0318
N2 1.390 0.0391
CO2 3.592 0.0427
CH4 2.253 0.0428
H2 0.244 0.0266

Example. The volume of one mole of oxygen molecules is 31.8 cm3 according to the van der Waals coefficient values tabulated. If the molecular diameter is taken as 0.370 nm, an approximate molar volume would be NAd3, or 30.5 cm3.The volume actually occupied by one mole of oxygen gas at 25oC, according to the ideal gas law, is 24465 cm3. The molecules of the gas actually occupy only 0.13% of the total volume occupied by the gas at 25oC.

 

[mbeychok]

dcasto:

Did you not mean this?

(p + (n²a/V²))(V - nb) = nRT

Milton Beychok
(Visit me at www.air-dispersion.com)
.

 

[dcasto]

yeah, you can rearrange to (p + a/V^2) * ( V-b) = RT where V is now Molecular Volume volume per mole.

 

[dcasto]

oh, this is from my Chem E thermo book Balzhiser, Samuels, Eliassen

 

[Malimedo]

Span, R., Wagner, W: „A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100K at pressures up to 800MPa“. J. Phys. Chem. Ref. Data 25, (1996.) p.1509–1596.

This article above could be helpful.

I'm wondering if someone has the simple p-Z diagram for a range of isotherms from 0°C to 500°C, maybe calculated by S&W EOS?

 

[Michael2006]

If I need physical properties of a common pure gas over just a limited range of P, T conditions I've found the NIST Chemistry WebBook (

http://webbook.nist.gov/chemistry/)

is often quite handy. Under "Fluid Properties" it lets you generate a table of data that you can copy into Excel. For getting the density I'd calculate the compressibility factor over the P,T range of interest from the densities given in the WebBook table. With a bit of luck Z won't change too much and you can use mbeychok's equation for your exact P,T conditions with the right Z.