3 replies to this topic

[mdusf]

Please help! I need to know how to calculate the below theoretical problem? What would be the derived formula.

There is a body of water open to atmosphere. At what depth would you need to inject 100mol of CO2 to keep it in solution. Assume standard temperature and standard atmospheric pressure.

Thank you,

[djack77494]

The CO2 will be maintained in solution when its partial pressure = total pressure * mole fraction of CO2 in liquid phase. Total pressure = the depth of water converted to pressure. For example, starting at atmospheric pressure and going to a depth of 100 feet, the pressure will be 100 / 2.31 = 43.3 psig. At your "standard temperature" (60F?) CO2 will have a certain partial pressure that can be looked up using standard references or the internet. However, you have still not provided us with a real problem. You want to keep 100mol of CO2 in solution, but you don't provide a quantity of water. I can keep probably hundreds of thousands of moles of CO2 in solution at a depth of 1 mm if I use the oceans to do so. We must know what volume of water you are talking about.
Doug

[mdusf]

Thank you so much for replying! The volume of water is a 100L.

[djack77494]

The volume of water is a 100L.

OK. So you have 100L of water and in that water is dissolved 100 mol (gram moles?) of CO2. You can calculate the vapor pressure of CO2 as a function of temperature using:

VP = C1 + (C2/T) + C3*ln(T) + C4*T^C5

at >216.6K. This is from Perry's Chemical Engineering Handbook, Table 2-6. Values of C1 to C5 can be found there, as well as unit definitions. At some unknown depth, the vapor pressure of the CO2 * its weight fraction + the vapor pressure of water * its weight fraction will equal the hydrostatic pressure of your solution. You may need to refer to good data sources such as NIST to get any data you are missing. I believe your approximate CO2 concentration if we think in simple terms will be:

1 gm-mol CO2 = 44 gm.
100 L of water = 1,000,000 gm.
Total = 1,000,044 gm mass & 1 liter volume
CO2 concentration = 44 gm CO2/1,000,044 gm solution= 0.00043998 weight fraction


(I've have neglected as non-idealities for this system, which could introduce some errors. Use caution, since CO2-H2O system will not be ideal.)