Question

Calculate the mass of neon gas in a neon sign with a volume of 50.0 L at 10.0°C and 3.1 kPa

Answer 1

According to the ideal gas law, the number of the moles $n$ of a gas relates to its volume $V$, absolute temperature $T$ and pressure $p$ as:

$pV = nRT$ ,

where $R$ is the ideal gas constant , equal to 8.314 J mol^-1 K^-1.

The mass can be calculated from the number of the moles, using the molar mass of neon $M=20.18$ g/mol:

$m = n·M$ .

Therefore, the mass of neon gas is:

$m = \frac{pV}{RT}·M$

$m = \frac{3.1·10^3(\text{Pa})·50·10^{-3}(\text{m}^3)}{8.314(\text{J/(mol K)})·(10.0+273.15)\text{K}}·20.18\text{ g/mol}$

$m = 1.33$ g.

Note: don't forget to convert the temperature in °C to the temperature in K, adding 273.15 to the value in °C.

Answer: the mass of the neon gas is 1.33 g.