I need help on a gas law problem?

Question

Nitrogen and hydrogen gas react to form ammonia gas as follows:
N2(g) + 3H2(g) -> 2NH3(g)

At a certain temperature and pressure, 1.2 L of N2 reacts with 3.6 L of H2. If all the N2 and H2 are consumed, what volume of NH3, at the same temperature and pressure, will be produced?

At first I thought you could just add the volumes, but the densities of the gases would be different so it wouldn't work. Then I thought that you colud use the idea that a mole of gas occuptied 22.4 L at STP, but you don't know if the gases are at STP. What do you do? Thanks.

Answer 1

The answer is that a molecule of gas takes up the same volume no matter what atoms are involved if the temperature and pressure are the same. In your problem 4 molecule(1 N2 and 3 H2) become 2 molecules(2NH3)
since the original gases filled 4.8 liters and there are half as many molecules there would be 2.4 liters of gas at the same temperature and pressure as the original gasses before the chemical reaction.

Answer 2

1.2LN2 x 2LNH3/1LN2 = (1.2)(2)/(1) = 2.4LNH3

Avogadro's principle: Equal volumes of gases at the same T and P have equal numbers of molecules. So the balanced equation works in liters as well as in moles.