To identify a diatomic gas (X2), a researcher carried out the following experiment: She weighed an empty 5.1-L bulb, then filled it with the gas at 1.00 atm and 20.0 ∘C and weighed it again. The difference in mass was 5.9 g. Identify the gas.

Answer: Nitrogen gas

Explanation:

Using ideal Gas's law

PV = nRT

where

Pressure of gas, P = 1atm

Volume of gas, V = 5.1L

no of moles of gas, n=

Ideal gas constant, R = 0.0821

Temperature of gas, T = 20°C = 20+273 = 293K

also, n = (mass/molar mass)

mass of the gas m = 5.9g

Molar mass of the gas = ?

So, PV = (mRT/M)

We're looking for molar mass M, then

M = mRT/PV

M = (5.9 * 0.0821 * 293) / (1 * 5.1)

M = 141.93/5.1

M = 27.8g/mol ~ 28g/mol

Since the gas is diatomic, then we say,

Atomic mass of gas = 1/2 * molar mass

Atomic mass = 1/2 * 28

Atomic mass = 14

Therefore, the gas is nitrogen.