A gas container filled with N2 at STP has a mass of 37289 g

A gas container filled with N_2 at STP has a mass of 37.289 g. The same container filled with CO_2 at STP has a mass of 37.440 g. With an unknown gas at STP, the container\'s mass is 37.062 g. What is the unknown gas and what is its molecular weight?

Solution

Given,

Mass CO2 = 37.440 g - 37.062 g

= 0.378 g
Mass N2 = 37.289 - 37.062 g

= 0.227 g
We know the molar mass of CO2 is 44.0 g/mol

The number of moles of CO2 = 0.378 g x 1 mol / 44.0 g

= 0.00859 mol

Since both gases have the same volume at the same temp and pressure, Avogadro\'s hypothesis guarantees that both masses will have the same number of molecules. Also the same number of moles.

Therefore,

0.227 g is 0.00859 mol, and the molar mass is 0.227 g / 0.00859 mol = 26.4 g/mol

Then,

0.378 g / 0.227 g = (44.0 g/mol) / (x)

x = 26.4 g/mol