I can't think of any reason why you couldn't. Basically, a cartridge consists of the actual bullet (usually of lead) tucked into a casing that contains gunpowder and a primer. When the hammer hits the primer, it ignites the powder. The solid powder almost instantaneously turns into gas, which takes up a lot more volume or space than the solid. This sudden increase in pressure forces the bullet out of the cartridge at high speed. The same thing should happen in space. Of course the bullet will have no air resistance in the vacuum of space, so I guess it would just keep going until it hit something or something hits it. I wondered at first if the lack of oxygen would keep the powder from igniting, but the ignition happens inside the sealed cartridge, so I doubt it. I doubt that we'll be seeing any firearms on space flights however. It's just too dangerous and there aren't likely to be any problems that the astronauts can solve by shooting at them.

The whole idea of pressure and volume is an important one. It explains a lot of things, from how our lungs work to why we have wind and other types of weather. It also explains how rockets get into space to begin with.

Yes. Bullets don't need air to fire. When the gunpowder in the cartridge ignites and explodes, it creates a lot of hot gas which expels the bullet out of the gun.

There is a possible complication, though, when firing a gun in space. If you are in a microgravity environment, conservation of momentum becomes a very noticeable effect. Imagine that you and a friend are on roller blades or ice skates and one of your pushes on the other one. What happens? You both move away from each other because there is not much friction and total momentum (mass X velocity) is basically conserved. Since you and your friend had no momentum to start with, your mass X speed after the push must equal that of your friend who is going in the opposite direction. So what do you think would happen if you were floating in space and fired a gun?

This is a great question and it has quite the debate among my friends and I. While I am sorry to say I can not offer a concrete answer, I will give you the answer we think is probably correct. It is most likely impossible to fire a gun in space, assuming you are talking about a standard firearm. By this I mean a gun that fires a bullet containing gun powder. The reason you could not fire this gun is because there is very little oxygen in space and oxygen would be necessary to cause a spark to cause the powder inside the bullet to ignite and the gun to fire.

If you were talking about a pressurized gun, like a pellet gun with a CO₂ cartridge, it may be possible to fire. Here the problem would be that we are dealing with zero-gravity and we are not sure what implications it has when talking about projectiles.

Thanks for the great question.