To identify a diatomic gas (X2), a researcher carried out the following experiment: She weighed an empty 3.6-L bulb, then filled it with the gas at 2.00 atm and 24.0 ∘C and weighed it again. The difference in mass was 8.3 g . Identify the gas.

The gas was N₂

Explanation:

V = 3.6L

P = 2.0 atm

T = 24.0°C = 297K

R = 0.0821 L.atm/K.mol

m = 8.3g

M = molar mass = ?

Using ideal gas equation;

PV = nRT

n = no. Of moles = mass / molar mass

n = m/M

PV = m/M * RT

M = mRT / PV

M = (8.3*0.0821*297) / (2.0*3.6)

M = 28.10

Since X is a diatomic molecule

M = 28.10 / 2 = 14.05 g/mol

M = Nitrogen

X = N₂