How do you solve for volume to volume conversions and empirical formula?

Question

2. Ammonia is often formed by reacting nitrogen and hydrogen gases. How many liters of ammonia gas can be formed from 24.5 L of hydrogen gas at STP?

                            N2(g)  +  3 H2(g)  --->  2 NH3(g)

Answer 1

Hello, Jaida,

There is a wonderfully useful, although suspicious, conversion factor for all gasses at STP. Remember it. It makes a good ice breaker at parties is often employed in gas problems. One mole of any gas occupies 22.4 liters. It took me a long time to accept that this could possibly be true, but when you think about how small molecules actually are, most of that 22.4 liters is just empty space, in spite of the fact one mole means 6.02 x 10²³ molecules/atoms. The heavier ones carry a lot of momentum for a specific temperature, and the lighter ones simply race around with lots of kinetic energy. So they exert the same pressure for the same temperature and volume.

It's a conversion factor: 22.4 liters/mole [It is tempting to write 22.4 moles/liter, since many other units in chemistry start with moles per something, so be careful. liters/mole].

24.5 liters of H₂ at STP is (24.5Liters)/(22.4 Liters/mole) = 1.09 moles of H₂ [Note: If you are given liters of a gas at other than STP, use the gas laws to convert to liters at STP and you can then use this conversion to find moles].

The molar ratio of NH₃ to H₂ is 2/3 (from their coefficients in the balanced equation). That means it takes three moles hydrogen to make 2 moles of ammonia. So we use the ratio (2/3) when calculating how much ammonia we'll get from the 1.09 moles H₂.

(1.09 moles H₂)*(2/3)= 0.729 moles NH₃

Note that this assumes we have enough nitrogen to consume all of the hydrogen.

Assuming that conditions are still at STP, we can use the 22.4 moles/liter conversion again.

(0.729 moles NH₃)*(22.4 liters/mole NH₃) = 16.3 liters NH₃

I hope this helps,

Bob