Because it's fully dispersed, it is really hard to talk about atmospheric CO2 in PPMv (since the CO2 and the atmosphere occupy the same volume. It pretty much has to be in PPMm.

The calculation requires an assumption about the volume of air the CO2 mixes with

No - the mass of the air it mixes with, not the volume. And within a very few years it can be assumed to be fully mixed.

So, if the atmosphere has a pressure of 101.15 kPa at the earth's surface, in a gravitational field of 9.81 N/kg, then there is a mass of 10.3 T of air over every square meter of land, which turns into 5.26 e18 kg. If the atmosphere was 'thick' relative to the diameter of the earth, then the calculation would be much more sophisticated. As the vast majority of the atmosphere is within 100km of the surface, and the radius o the planet is about 6400 km, it is relatively 'thin', so this complexity can be ignored.

So, 1000T of CO2 adds 1.9e-7 ppm to what is there right now.

Dear Saeideh Baghanian

"As of January 2007, the earth’s atmospheric CO2 concentration is about 0.0383% by volume (383 ppmv) or 0.0582% by weight. This represents about 2.996×1012 tonnes, and is estimated to be 105 ppm (37.77%) above the pre-industrial average." Wikipedia

Therefore 1000 tonnes will equal 1000 x 383/ 2.996 x 1012 = 127837 x 10-12 = 1.28 x 10-7 ppm, i.e. not very much.

NB. A short (US) ton weighs 2000 lbs, a long (Imperial) ton weighs 2240 lbs, and a (metric) tonne weighs 1000 kg = 2204.6 lbs. I leave it as an exercise for you work out the ppms per ton :-)