# Carbon dioxide concentration from pressure changes

Is there a way of determining the concentration of CO2 if we know the pressure in the container before the addition of CO2 and the pressure in the container after the addition of CO2 if we have no way of measuring the amount of CO2 delivered to the container (like with a CO2 controller with a CO2 monitor)? For instance, if we have a sealed container with air in it at 298 K, whose pressure is measured at 1 atm, and we introduce carbon dioxide gas causing the pressure to increase to 1.2 atm... can we use the ideal gas equation and assume that the 0.2 atm increase is due to addition of CO2 and is the partial pressure of CO2 and just use 0.2 atm/(0.0821 × 298) = 0.008 m/L (approx. 352 ppm) as the concentration of the CO2 in the chamber? Or, is there more to it?

• The m/L is correct, but how did you get that 352 ppm? – Chet Miller Jun 19 '19 at 11:01
• I was working on the molecular mass of carbon dioxide being about 44g/mol and 1M = 44g/L and so 44000 ppm, so 44000 x 0.008 = 352... is that correct? – Simon Jun 19 '19 at 12:43
• That would be the grams per liter. The mole fraction of CO2 is 1/6, and the mole fraction of air is 5/6. So, on a molecule basis, the ppm CO2 is 167000. What is it on a mass basis? – Chet Miller Jun 19 '19 at 13:15
• I found this: "To convert from ppm by mass to ppm by volume, divide by the density of the particles." so I am assuming I will need to determine the density of the carbon dioxide and will also need to know the volume of the container. – Simon Jun 19 '19 at 21:37
• Not really. I know that it may not make sense, but in common terminology, ppm volume means 1 million times the mole fraction. So you won't need to know the volume of the container. – Chet Miller Jun 20 '19 at 1:44

If you know the partial pressures of the gases, then you can calculate the mass fractions. In the present case, assume you have 1 mole of gas. Then the number of moles of CO2 is 0.167 moles and the number of moles of air is 0.833. The mass of CO2 is (44)(0.167)=7.33 grams and the mass of air is (29)(0.833)=24.2 grams. So the mass fraction of CO2 is $$\frac{7.33}{(7.33+24.2)}=0.233$$ So the ppm CO2 by volume = 167000 and the ppm CO2 by mass = 233000.