[HailToPitt]

Hi all,

I figured this would be the best place to throw this question out.  In the form I'm presenting, it's not exactly a ChE question, but once I get the fundamentals, it will evolve into one. Reading it, the problem statement might be overly ambiguous and unclear, but I'm not really sure.  If anything is unclear, please let me know.

Consider a large pressurized container with a relatively small amount of water in the bottom, and a relatively large gas space.  Assume the gas space is large enough that the pressure does not change significantly due to gas absorption, and the concentrations of each component in the gas do not change significantly. The gas is initially composed of water at saturation, and some amount of CO2, H2S, HCN, and NH3. Assume for simplicity that pH2O = 0.7*P

At a given T, assume gas and liquid phases come to equilibrium, what process would I need to go through to find the equilibrium concentration of each species in the water?

Currently, my track is this: 

Unknowns:
Gas Phase concentrations [4]
Liquid phase concentrations -
Waters [2]
HCN [2]
H2S [3]
NH3 [2]
CO2 [4]
Total [17]

I've written:
-Corrected Henry's Law equations for each gas [4 equations]
-Equilibrium equations for each species [1 for water, HCN, NH3, 2 for H2S, 3 for CO2, 8 equations]
-Charge balance [1 eq]
-Mass balance for each species [4 eq]
Total [17]

Writing all this out, I should be able to find a solution, but looking at it, it's nigh impossible to find an exact solution without knowing where to start.  So my questions are simple.

-Am I right in assuming each equilibrium statement acts rather independently, wherein the only similar term is the [H+] or [OH-]?
-Same question for Henry's Law and solubility.  For example, does dissolved HCN affect the solubility of H2S in any way besides that both contribute to [H+]?
-Once I have all these equations set up, is there a simple way to solve, or does it really come down to an iterative approach until you get complete convergence?


And again, if I did a terrible job explaining this, please let me know and I'll figure a better way to state the problem.

[Borek]

I doubt solubility of the gases is independent. For diluted solutions it can be treated as such, but the closer to saturation you get, the worse the situation is. I am not aware of any method of dealing with this problem (doesn't mean there are none).

But in general your approach is a right one. Write set of equations, solve. You should have the same number of equations as there are unknowns. The only viable approach is to use a numerical approach, you can use zero concentrations as the starting point.

I believe your equations miss Kw.

In this kind of problem mass balance can be easier to done using elements, not species. Also, you can't ignore water in the mass balance.

[mjc123]

It doesn't look like there's enough information to solve this. The phase rule tells you there are 5 degrees of freedom - temperature and the pressures of the 4 gases. But you say all gas phase and liquid phase concentrations are unknowns. You need some input data to define the state of the system.

[HailToPitt]

It doesn't look like there's enough information to solve this. The phase rule tells you there are 5 degrees of freedom - temperature and the pressures of the 4 gases. But you say all gas phase and liquid phase concentrations are unknowns. You need some input data to define the state of the system.

Sorry, this probably wasn't clear.  The partial pressures of each species are KNOWN, but I didn't put numerical values with them. I'll reread my OP and edit if necessary.

[billnotgatez]

forum rules suggest you not edit a post after people have responded to it
Please read forum rules
Just post more on the top of the thread as you go

[HailToPitt]

I doubt solubility of the gases is independent. For diluted solutions it can be treated as such, but the closer to saturation you get, the worse the situation is. I am not aware of any method of dealing with this problem (doesn't mean there are none).

But in general your approach is a right one. Write set of equations, solve. You should have the same number of equations as there are unknowns. The only viable approach is to use a numerical approach, you can use zero concentrations as the starting point.

I believe your equations miss Kw.

In this kind of problem mass balance can be easier to done using elements, not species. Also, you can't ignore water in the mass balance.

Kw was handled in the "equilibrium equations"

Much of the reason I took these liberties are because it more accurately describes the specific problem.  I'm going to have a drum continuously supplied by a saturated liquid / vapor stream wherein they are separated and go their separate ways.  The total incoming stream is relatively constant but I can control pressure / temperature, which would change the V/L equilibrium split. The purpose there is to figure out the proper state to run the vessel.

Of course, the problem with the situation is there are 4 gases that act as an acid / base, and I've never seen any examples which deal with acid / base equilibrium with 4 species. Even finding examples with 2 species is hard, and the paper solution is enormous amounts of plug-and-chug. Do you know of a tool that would be able to handle this situation non-iteratively?

[Borek]

Of course, the problem with the situation is there are 4 gases that act as an acid / base, and I've never seen any examples which deal with acid / base equilibrium with 4 species. Even finding examples with 2 species is hard, and the paper solution is enormous amounts of plug-and-chug. Do you know of a tool that would be able to handle this situation non-iteratively?

Numerical approach is the only way to go. These equations are not linear. If you try to solve them manually, at best you will get some high degree polynomial (something like 8^th degree for just the acid/base equilibrium*, not taking into account gas/liquid equilibria). This has to be solved numerically, so it is much easier to solve everything numerically from the very beginning.

*Compare http://www.chembuddy.com/?left=pH-calculation&right=pH-salt-solution - equation 11.16 is just a polynomial (get rid of denominators by multiplying both sides by them, rearrange). That was derived for just a salt (one multiprotic acid, one multiprotic base), but it should generalize nicely to a system combining more substances.