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Yes. It is absolutely possible to fire a gun in space, 

Unlike the old days, modern ammunition is not dependent on the the atmospheric oxygen to create the chemical reaction that results in the discharge of a round from a gun. The oxidizing agents are present both in the primer and the propellant of the ammunition. 

This would mean that the gun can also be fired underwater but it won't be very effective. On the other hand, firing a bullet while in space is also a totally different ball game than firing it normally on the surface of the earth. Here are the differences:

1. You won't hear the gunshot because of the vacuum of the space

2. The recoil of the gun would push you and will permanently change the trajectory of your motion in space, On earth the recoil is countered by the frictional forces between your foot and the ground.

3. The smoke leaving the gun barrel would expand like a sphere from the muzzle (unlike the earth, where the smoke leaves the muzzle as a trail)

In movies or games such as Call of Duty: Ghosts The outer space mission is depicted as shooting in space, whether it is a shotgun or a gun fired in space and what is the effect?

Returning to the original question, the answer is yes, it can happen, a conventional firearm in most circumstances will work well even in a room without oxygen.

This is because inside the gunpowder shells have their own oxidation material which is needed in the combustion process without an external source.

But there is a difference between shooting on earth and space. That is sound, there is no sound of eruption because in a vacuum does not allow sound waves to be delivered. Second, if on earth shooting will make the bullet target forward, but if in space what happens is when the bullet shot to the front of the shooter will be shot in the opposite direction, bounced or even turned backwards in the infinite space. Third, if on earth , the bullet will accelerate until it stops because of the target or if it misses then the bullet will continue to accelerate until its energy weakens and the earth's gravity pulls it to the ground. While in space, bullets will be more accurate when heading to the target because there are no air and wind barriers (the speed of the bullet is the same on earth and in space), but if missed the target there will be a unique phenomenon that occurs,

Yes it is possible to fire a gun in space as the cartridges today have their own chemical reaction that doesn't require oxygen to fire them. We all know space doesn't have oxygen so that wouldn't be an issue.

You won't hear the gunshot because of the vacuum so you would have no idea if it had even been fired really.