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

Answer:

The chemical formula of the gas is $N_2$.

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 = $\frac{m}{M}$

Using ideal gas equation:

$PV=nRT$

$PV=\frac{m}{M}RT$

$M=\frac{mRT}{PV}=\frac{9.5 grams \times 0.0821 atm L/mol K\times 300 K}{1.80 atm\times 4.6 L}=28.26 g/mol\approx 28 g/mol$

Atomic mass of the element X = $\frac{28 g/mol}{2}=14 g/mol$

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