Question

To identify a diatomic gas (X2), a researcher carried out the following experiment: She weighed an empty 4.4-L bulb, then filled it with the gas at 1.00 atm and 22.0 ∘C and weighed it again. The difference in mass was 5.1 g . Identify the gas.

Answer 1

Answer : The diatomic gas is nitrogen gas, N₂.

Explanation :

First we have to calculate the moles of gas.

Using ideal gas equation:

$PV=nRT$

where,

P = Pressure of gas = 1.00 atm

V = Volume of gas = 4.4 L

n = number of moles of gas = ?

R = Gas constant = $0.0821L.atm/mol.K$

T = Temperature of gas = $22.0^oC=273+22.0=295.0K$

Putting values in above equation, we get:

$1.00atm\times 4.4L=n\times (0.0821L.atm/mol.K)\times 295.0K$

$n=0.1817mol$

Now we have to calculate the molar mass of gas.

$\text{Molar mass of gas}=\frac{\text{Given mass of gas}}{\text{Moles of gas}}$

$\text{Molar mass of gas}=\frac{5.1g}{0.1817mol}=28.07g/mol$

As we are given that the gas is diatomic X₂.

As, 2 atoms of gas X has mass = 28.07 g/mol

So, 1 atom of gas will have mass = $\frac{28.07}{2}=14.04g/mol$

From this we conclude that the nitrogen atom has mass of 14.04 g/mol.

Thus, the diatomic gas is nitrogen gas, N₂.