Question

I asked this question in the biology stack-exchange but thought it might be more appropriate here.

I am running a batch experiment using penicillin bottles where I have bacteria growing for 21 days in a highly alkaline media (pH 10). I am measuring the CO2 and O2 content in the headspace over time, but I am specially interested in the CO2 production. Usually I can simply use the CO2 content measured with a gas-chromatographer (GC) but because of the pH of my media, the CO2 will be dissolved into my media. This I have seen in the sharp drop of pH over time as well.

I want then, to calculate the amount of CO2 that has dissolved into my media. I know I require Dalton's Law of partial pressures and Henry's constant/Law. The thing is that, I am a bit confused because as I measured the pressure inside my closed bottles, the pressure in these bottles became negative. So my calculations are returning a negative value for my concentration of gas in the solution. Furthermore, I do not know if the formulas I used (Dalton and Henry), take into consideration the pH of my aqueous media.

Answer 1

The student's question about calculating the amount of dissolved CO2 in an alkaline medium can be approached using Henry's Law and the Henderson-Hasselbalch equation to understand the balance between gaseous CO2 and bicarbonate ions in the solution. However, negative pressure in the headspace and the high pH environment complicates these calculations.

Step-by-step explanation:

The question pertains to the calculation of CO2 dissolved in an alkaline media during a bacterial growth experiment. It is indeed true that Henry's Law is crucial for determining the solubility of gases; the law states that at a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.

However, the complexities of alkaline solutions and the formation of bicarbonate and carbonate ions should also be taken into account, as the total concentration of dissolved CO2 also includes the species formed subsequent to the dissolution of CO2.

There are additional considerations for the case of negative pressure in the headspace which may arise due to the consumption of oxygen by aerobic bacteria creating a vacuum, or the dissolution of gases into the media decreasing the pressure.

This situation complicates the use of Henry's Law, and it's important to ensure that all measurements and calibrations are accurate before proceeding with calculations.

To fully understand the buffer system and the shifts in equilibria between CO2, bicarbonate, and carbonate within your experiment, the Henderson-Hasselbalch equation may be useful. For solutions of bicarbonate in equilibrium with CO2, the pH can give an indication of the relative concentrations of the acid and base forms according to the equation:

pH = pKa + log ([HCO3-]/[H2CO3])

This would need to be used in conjunction with the equilibrium constants for carbonic acid to give a fuller picture relevant to your media's pH. Keep in mind that the actual calculation is more complex due to the multiple equilibria involved and the high pH of your solution, which affects the distribution of carbonate species.