What volume did the hydrogen occupy?

Question

The total mass of the hydrogen gas in the Hindenburg zeppelin was 18,000 kg. What volume did the hydrogen occupy? (Assume that the temperature of the hydrogen was 0°C and that it was at a pressure of 1 atm.)

Answer 1

Hello, Emma,

Let's start by calculating the number of moles of hydrogen gas is contained in 18,000 kg. H₂ has a molar weight of 2 g/mole, so divide that into the total mass, after you first convert it to g to keep the units consistent:

18,000,000g/2(g/mole)

Grams cancel and moles moves to the top to give us 9,000,000 moles of H₂. One mole of any gas occupies 22.4 liters at STP. So multiply 22.4 liters/mole times the number of moles to get liters. I get 2.02 x 10⁸ liters. (That's the volume in a cube with 139 feet per side!).

Then use the gas laws to determine what will change if we are not at STP. [Note: we are at STP so the following explanation is not needed for this problem, but will prove helpful for when there are different conditions, such as a higher temperature]. Since we are at STP, we have 2.02 x 10⁸ liters of H₂.

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If, however, the problem had stated final temperature and pressure other than 0^oC and 1 atm, follow this procedure:

Using subscripts 1 for initial and 2 for final, the simplified equation for this is

P1V1/T1 = P2V2/T2 Temperatures must be in Kelvin.

The number of moles cancels since it doesn't change.

Make a chart of what you'll use for all these values and rearrange the equation to find to find the final volume, V2.

V2 = P1V1T2/(P2T2)

and enter the values to calculate the result.

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Bob