Question

To identify a diatomic gas (X2), a researcher carried out the following experiment: She weighed an empty 2.0-L bulb, then filled it with the gas at 1.00 atm and 28.0 ∘C and weighed it again. The difference in mass was 2.3 g . Identify the gas.

Answer 1

By using the ideal gas law:
                          PV=nRT

R = 0.0821 L atm/ (mol K)

P = 1 atm

V = 2 Liter

T = 28 oC = (273.15 + 28) K

   = 301.15 K

Calculate the number of moles of gas, n = PV/RT

Substituting all the above values

                              n = 1 *2/ 0.0821 * 301.15

                             n = 0.0808917

Molar mass of molecule = mass of molecule/ no. of moles of molecule

Mass of molecule = 2.3 gm

Therefore, Molar mass = 2.3gm/ 0.0808917 mol

                                       = 28.433077 g/mol

As the gas is diatomic, then the atomic mass = molar mass/ 2

                                                                        = 28.433077/2

                                                                        = 14.216539 g/mol

The element with an atomic mass closest to 14.2165 g/mol is Nitrogen (N₂) which has atomic mass 14.01 g/mol.