To identify a diatomic gas (X2), a researcher carried out the following experiment: She weighed

an empty 3.1-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 3.5 g. Identify the gas.

Aluminium

Explanation:

Given dа ta:

Volume = 3.1 L

Pressure = 1.0 atm

Temperature = 28.0 °C (28 + 273.15 = 301.15 K)

Mass = 3.5 g

Identify the gas.

Solution:

First of all we will find the number of moles.

PV = nRT

n = PV/RT

n = 1 atm * 3.1 L / 0.0821 L. atm. K⁻¹. mol⁻¹ * 301.15 K

n = 3.1 L. atm / 24.72 L. atm. mol⁻¹

n = 0.13 mol

Now we will find the molar mass.

molar mass = 3.5 g / 0.13 mol

molar mass = 26.9 g/mol

The gas is diatomic so, atomic mass will be half of 26.9 g/mol.

26.9 g/mol / 2 = 13.45 g/mol

The element which has atomic mass closer to the 13.45 is aluminium.