[cmaunder]

Hi all,

So hopefully a very easy question to answer.  I have experimental results from biological cultures in 500mL bottles (simplified there was 250ml water and 250ml headspace in a bottle) and I was trying to figure out how much CO2 would be present (have dissolved) in the water at equilibrium with the headspace.  The argument I've been writing in my thesis follows below, but I'd really appreciate if someone could tell me if I've made a big mistake somewhere.  The final concentration I calculated is tiny compared to the amounts of inorganic carbon needed by bacteria in most instances.  These are basic equations, I've checked the math several times, but I'm wondering if they're too basic for the purpose and thus I've missed something. Thanks so much for the help.

My argument:

The composition of the gasses in the headspace would likely have closely matched that of the globally averaged atmospheric composition during the years in which this study took place, meaning CO2 would have been present at a concentration of 380-390 ppm by volume (Tans, 2009).  Therefore, each time the headspace was freshly replenished with outside air, the volume of CO2 within the headspace would have been approximately 0.095mL to 0.098mL.  Of course, CO2 in the headspace would only dissolve to form CO2(aq) until equilibrium was reached.  According to the Ideal Gas Law, for CO2 in the headspace:

         pV = nRT                [1]

Where p represents the partial pressure of CO2, V the volume of the headspace in litres, n the number of moles of CO2 in the headspace, R is the ideal gas constant and T the temperature in degrees Kelvin.  Since 1 mol of any ideal gas at standard temperature and pressure is 22.4L, 0.095mL of CO2 is equal to 4*10-6 mols.  Inserting known values into equation [1], we find that p for CO2 in the headspace was 0.04 kPa.  Now subsequently inserting the estimated partial pressure of CO2 in the following equation from Henry’s Law:

       p = kHc      [2]

where kH is the Henry’s Law constant, gives us an estimate of c, the concentration of CO2 in the P. frederiksbergensis liquid media at equilibrium.  In this case c was found to be 1.4*10-5 mol/L.  With a known media volume of 200mL and knowing that one mole of CO2 equals 44g, this can be converted to 118.8 μg / 200mL or 0.594 ppm. 

[Borek]

You should take pH and acid dissociation into account, right now it is incorrect.

[cmaunder]

I think I may not have been clear enough in my original post. 

I know CO2 will dissociate into other carbonate species (primarily HCO3- at my pH of 7.4), but my interest isn't in how much CO2(aq) or H2CO3 is dissolved, it's how much dissolved inorganic carbon there is in the "water" (ie the sum of all carbonate species).  As there is no other inorganic carbon source contributing to the DIC, would the total amount of CO2 that dissolved from the headspace into the water (like I calculated) not represent the total amount of DIC?

Basically my concern with the calculation is that the concentration is SO low.  I was expecting something higher.  Bacteria find concentrations of 20-50ppm limiting to growth and what I calculated was WAY lower.

Thanks again for any help you can give.