To identify a diatomic gas (X2X2), a researcher carried out the following experiment: She weighed an empty 4.0-LL bulb, then filled it with the gas at 2.00 atmatm and 30.0 ∘C ∘C and weighed it again. The difference in mass was 9.1 gg . Identify the gas.

N₂

Explanation:

Using ideal gas law, you can find moles of the gas:

PV = nRT

PV / RT = n

Where P is pressure (2.00atm); V is volume (4.0L), n are moles of gas; R is gas constant (0.082atmL/molK); and T is absolute temperature (30.0°C +273.15 = 303.15K)

Replacing:

2.00atm×4.0L / 0.082atmL/molK×303.15K = n

0.322 moles of gas = n

The difference in mass is equal to mass of the gas. Knowing both moles and mass of the gas, molecular mass of the gas is:

9.1g / 0.322mol = 28.3g/mol

As the gass is a diatomic gas, each atom weights 28.3/ 2 = 14.1g/mol and this is the mass of nitrogen atom. Thus, the diatomic gas is N₂