The weapons are explained in the first Mass Effect book, Revelation. They don't fire particles of air, they rely on ammo. To quote from the book about assault rifles: 'The ammo clip on each weapon held over four thousand rounds; miniature pellets smaller than grains of sand. When fired at sufficient velocity, the nearly microscopic projectiles were capable of inflicting massive damage.'
In ME2 (don't worry, not really a spoiler), a soldier near where you arrive on the Citadel talks about a dreadnaught firing (numbers/facts may be wrong, this is from memory) a 20kg iron bolt at 1.3% of the speed of light, with the resultant impact being on a similar order of magnitude to a nuclear bomb.