Concept Explanation: Relative Density and Molar Mass

Relative density (also called vapor density) of a gas with respect to another gas (here oxygen) is defined as the ratio of their densities under the same conditions of temperature and pressure. Since density is mass per unit volume, and under same T and P, equal volumes of gases contain the same number of moles (Avogadro's Law), the relative density is also equal to the ratio of their molar masses.

Step-by-Step Solution:

Step 1: Understand the formula for relative density.

Relative density of gas A with respect to gas B is given by:

$\mathrm{Relative\; Density}=\frac{{\rho }_A}{{\rho }_B}=\frac{M_A}{M_B}$

Where ${\rho }_A$ and ${\rho }_B$ are densities, and $M_A$ and $M_B$ are molar masses of gases A and B respectively.

Step 2: Identify the given values.

Relative density of gas (A) with respect to oxygen (B) = 1.5

Molar mass of oxygen gas (O₂), $M_B=32g/\mathrm{mol}$

Step 3: Substitute into the formula.

$1.5=\frac{M_A}{32}$

Step 4: Solve for the unknown molar mass $M_A$.

$M_A=1.5\times 32$

$M_A=48g/\mathrm{mol}$

Final Answer: The molar mass of the gas is $48g/\mathrm{mol}$.

Related Topics:

• Avogadro's Law
• Ideal Gas Law
• Molar Mass and Molecular Weight
• Density of Gases

Important Formulae and Theory:

1. Relative Density (Vapor Density):

$\text{Relative Density}=\frac{{\rho }_{\text{gas}}}{{\rho }_{\text{reference}}}=\frac{M_{\text{gas}}}{M_{\text{reference}}}$

2. Molar Mass from Relative Density:

$M_{\text{gas}}=\text{(Relative Density)}\times M_{\text{reference}}$

3. Avogadro's Law: Under the same temperature and pressure, equal volumes of all gases contain the same number of molecules. This implies that the density of a gas is directly proportional to its molar mass.