Answer :
Answer : The diatomic gas is nitrogen gas, N₂.
Explanation :
First we have to calculate the moles of gas.
Using ideal gas equation:
[tex]PV=nRT[/tex]
where,
P = Pressure of gas = 1.00 atm
V = Volume of gas = 4.4 L
n = number of moles of gas = ?
R = Gas constant = [tex]0.0821L.atm/mol.K[/tex]
T = Temperature of gas = [tex]22.0^oC=273+22.0=295.0K[/tex]
Putting values in above equation, we get:
[tex]1.00atm\times 4.4L=n\times (0.0821L.atm/mol.K)\times 295.0K[/tex]
[tex]n=0.1817mol[/tex]
Now we have to calculate the molar mass of gas.
[tex]\text{Molar mass of gas}=\frac{\text{Given mass of gas}}{\text{Moles of gas}}[/tex]
[tex]\text{Molar mass of gas}=\frac{5.1g}{0.1817mol}=28.07g/mol[/tex]
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 = [tex]\frac{28.07}{2}=14.04g/mol[/tex]
From this we conclude that the nitrogen atom has mass of 14.04 g/mol.
Thus, the diatomic gas is nitrogen gas, N₂.