Question

How do you calculate the density of a gas with temperature change?

Answer 1

The Ideal Gas Law can be stated as `PV = nRT` where the symbols have their usual meanings. Write `n` as `M/M_0` where `M` is the mass of the gas and `M_0` is the molar mass.

`\iff PV = (M/M_0) RT`

`\iff P M_0 = (M/V) RT`

`\iff PM_0 = dRT`

`\iff d = (PM_0)/(RT) \propto P/T`

Use the above equation to calculate the density of a gas with temperature change.

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This has many implications that should be easy to understand.

• Density is directly proportional to pressure because high pressure results in compression of a gas, meaning that you have a chunk of gas in a less amount of space, meaning higher density.

• Density is inversely proportional to temperature because increasing temperature always causes the decompression of particles.