What form of the ideal gas law would you use to calculate the temperature of a gas?

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Answer 1 · 2014-07-27T19:47:15

You can use any form of the Ideal Gas Law, but usually one form is more convenient, depending on the information given.

There are three forms of the Ideal Gas Law.

Form 1

$P V = n R T$ $PV = nRT$

If the question gives you the number of moles $n$ $n$ , this is the most convenient one to use.

Form 2

$P V = \frac{m}{M} R T$ $PV = m/MRT$ , where $m$ $m$ is the mass of the gas and $M$ $M$ is its molar mass.

If the question gives you the mass $m$ $m$ , this is the most convenient one to use.

Form 3

$P = ρ/MRT$ , where $ρ$ is the density of the gas.

If the question gives you the density $ρ$ , this is the most convenient one to use.

EXAMPLE

What is the temperature of a sample of ethane, C₂H₆, that has a density of 1.264 g/L at a pressure of 1 atm?

Solution

Since we know the density, it is more convenient to use Form 3.

$P = ρ/MRT$

The molar mass of C₂H₆ is 30.07 g/mol

$T = (PM)/(ρR) = (1"atm" × 30.07"g·mol⁻¹")/(1.264"g·L⁻¹" × 0.082 06"L·atm·K⁻¹mol⁻¹")$ = 289.9 K =
(289.9 – 273.15) °C = 16.8 °C