Questions: Select the relation that properly connects the density (p) of a gas with its molecular weight (MW) in the ideal gas law.

Solution Steps

The ideal gas law is given by the equation:

\[ PV = nRT \]

where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

Density (\( \rho \)) of a gas is defined as mass per unit volume. For a gas, the mass can be expressed in terms of moles and molecular weight (\( MW \)):

\[ \rho = \frac{m}{V} = \frac{n \cdot MW}{V} \]

From the ideal gas law, we can express \( n \) as:

\[ n = \frac{PV}{RT} \]

Substituting this into the density equation gives:

\[ \rho = \frac{PV \cdot MW}{RT \cdot V} = \frac{P \cdot MW}{RT} \]

We need to find the relation that correctly connects the density (\( \rho \)) of a gas with its molecular weight (\( MW \)) using the ideal gas law. From the derived equation, the correct relation is:

\[ \rho = \frac{P \cdot MW}{RT} \]

Final Answer