Question

A gas cylinder filled with nitrogen at standard temperature and pressure has a mass of 37.289 g. The same container filled with carbon dioxide at STP has a mass of 37.440 g. When filled with an unknown gas at STP, the container mass is 37.062 g. Calculate the molecular weight of the unknown gas, and then state its probable identity.

Answer 1

Answer:

Molar mass = 3.9236 g/mol ≅ 4 g/mol

This corresponds to Helium gas.

Explanation:

Let the moles of nitrogen gas = x moles

Moles of carbon dioxide = x moles ( As both are filled at same temperature and pressure conditions )

Given:

$Mass_{Container}+Mass_{Nitrogen\ gas}=37.289\ g$

Molar mass of nitrogen gas, $N_2$ = 28.014 g/mol

The formula for the calculation of moles is shown below:

$moles = \frac{Mass\ taken}{Molar\ mass}$

Thus,

$x\ moles= \frac{Mass}{28.014\ g/mol}$

Mass of nitrogen gas = 28.014x g

So,

Let, $Mass_{Container}=y$

$y+28.014x=37.289$

Similarly,

$Mass_{Container}+Mass_{Carbon\ dioxide\ gas}=37.440\ g$

Molar mass of nitrogen gas, $CO_2$ = 44.01 g/mol

The formula for the calculation of moles is shown below:

$moles = \frac{Mass\ taken}{Molar\ mass}$

Thus,

$x\ moles= \frac{Mass{44.01\ g/mol}$

Mass of nitrogen gas = 44.01x g

So,

$y+44.01x=37.440$

Solving the two equations, we get :

$Mass_{Container}=y=37.025\ g$

x = 0.00943 moles

Thus, Given:

$Mass_{Container}+Mass_{Unknown\ gas}=37.062\ g$

$37.025\ g+Mass_{Unknown\ gas}=37.062\ g$

Mass of the gas = 0.037 moles

Moles = 0.00943 moles

The formula for the calculation of moles is shown below:

$moles = \frac{Mass\ taken}{Molar\ mass}$

Thus,

$0.00943\ moles= \frac{0.037\ g}Molar mass}$

Molar mass = 3.9236 g/mol ≅ 4 g/mol

This corresponds to Helium gas.