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# CO2 dissolution in water/Henry's law

## CO2 dissolution in water/Henry's law

(OP)
Hi Mates,

As a chemical engineer who is not good in chemistry I have a question related to Henry's law. In a closed vessel which contains water at 70% vessel volume, CO2 gas is added to reach a pressure of 90 psig to produce carbonic acid used elsewhere in the process. After carbonic acid is drained from the vessel down to 50% of vessel volume, the pressure inside the vessel drops to 40 psig. Now to prepare the next batch of carbonic acid, fresh water is added to the vessel to bring the level back up to 70% and same process repeats itself.

Now my questions is as you are adding water to a vessel which already contains 50% water and 40 psig CO2, as the water level rises the CO2 gas in the headspace is compressed so the pressure should go up but at the same time that the pressure is going up, as per Henry's law more CO2 molecules will dissolve in water so the pressure should go down. Does this mean as your are adding water to the vessel, the pressure inside it remains unchanged and after you reach the 70% target water level you need to add more CO2 to bring the pressure back up to 90 psig? How can I calculate the amount of CO2 gas needed to prepare each batch of carbonic acid for this process?

### RE: CO2 dissolution in water/Henry's law

Henry's Law (C = k*p), where C is liquid phase concentration of the gas, k is the Henry's law constant, and p is the gas partial pressure above the liquid assumes the following:

1. the gas/liquid system has reached equilibrium
2. the gas does not chemically react with the liquid
3. the concentration of gas in the liquid is low
4. the gas pressure is low

I'm assuming your system operates within these assumptions since you are stipulating the use of Henry's law. You can calculate the amount of gas needed directly from Henry's law if you have the appropriate constant because you set what the concentration within the liquid should be and using the constant you can solve for the partial pressure of CO2 above the liquid. Knowing the CO2 pressure and system temperature, you could use the appropriate equation of state to calculate the volume or mass of gas.

Within the limits of Henry's law, the amount of gas being dissolved should be low enough that the pressure in the tank won't change.

I am inclined to think 90 psig is within the low pressure limits of Henry's law applications and the ideal gas law, so calculations shouldn't be very difficult.

### RE: CO2 dissolution in water/Henry's law

HI,
Henry's Law constant for CO2 in water is 1.67×10^8 Pa at 298 K

From that you can calculate the concentration ( composition) of CO2 in the liquid phase @ [b]equilibrium at different pressure (absolute) considering no change in temperature , should be easy to calculate the quantity of CO2 required , just define the volume of your vessel .

For a 1000 l reactor I got: 105.371 moles CO2 /batch

Pierre

### RE: CO2 dissolution in water/Henry's law

What about the acid reaction: CO2 (sol)+H2O <=> HCO3- + H+

Morten

--- Best regards, Morten Andersen

### RE: CO2 dissolution in water/Henry's law

The system of CO2/water is complex and the vapour liquid equilibrium is nowhere nearly as simple as just applying Henry's law.

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