This is one of the reasons I hate doing air sampling. Too many units to cancel out to get to the final results.
ucanmoruk, you have a difficult task to begin learning the work, I hope you get it figured out.
To simplify, I would calculate the amount in the solvent you inject, which will be in mg/ml. Then if you extract the entire charcoal in the tube, you can ignore the weight of the charcoal and just convert to the mass in the air. Take the mg you have in the entire solution and divide that by the volume of air in meters cubed.
If you have a solution that is 10mg/ml and you have 10ml of that solution you have a total of 100mg. If the air volume was 0.1 cubic meters, then you have 100mg/0.1m^3 or 1000mg/m^3.
The charcoal is simply an intermediate container, similar to what would be if you placed the 10ml of solvent into a 1 L flask, you can ignore the volume of the flask if you know the volume of the solvent and you use all of the solvent in the next step. The charcoal is the intermediate flask for the volume of air you are sampling, therefore it can be ignored to simplify the equation. The equation works as if you concentrate the total volume of air into the total volume of solvent then you measure the solvent to determine how much of an analyte was in the air.