Question

To identify a diatomic gas (X2), a researcher carried out the following experiment: She weighed an empty 4.6-L bulb, then filled it with the gas at 1.80 atm and 27.0 ∘C and weighed it again. The difference in mass was 9.5 g . Identify the gas. Express your answer as a chemical formula. View Available Hint(s)

Answer 1

The chemical formula of the gas is
`N_2`.

Step-by-step explanation:

The difference between the container with gas and empty container is equal to the mass of the gas.

Let the gas be
`X_2`

Mass of the gas = m

Molar mass of diatomic gas = M

Pressure of the gas = P = 1.80 atm

Volume of the gas = V = 4.6 L

Temperature of the gas= T = 27.0 C = 27.0 + 273 K = 300 K

Moles of diatomic gas = n =
`(m)/(M)`

Using ideal gas equation:

`PV=nRT`

`PV=(m)/(M)RT`

`M=(mRT)/(PV)=(9.5 grams * 0.0821 atm L/mol K* 300 K)/(1.80 atm* 4.6 L)=28.26 g/mol\approx 28 g/mol`

Atomic mass of the element X =
`(28 g/mol)/(2)=14 g/mol`

The element is nitrogen and the diatomic gas is
`N_2`.