Question

How does the density of a gas depend on the molar mass of the gas?

Answer 1

Answer:

The density of the ideal gas is directly proportional to its molar mass.

Explanation:

Density is a scalar quantity that is denoted by the symbol ρ (rho). It is defined as the ratio of the mass (m) of the given sample and the total volume (V) of the sample.

$\rho = \frac{m}{V}$                          ......equation (1)

According to the ideal gas law for ideal gas:

$PV = nRT$                                       ......equation (2)

Here, V is the volume of gas, P is the pressure of gas, T is the absolute temperature, R is Gas constant and n is the number of moles of gas

As we know,

The number of moles: $n = \frac{m}{M}$

where m is the given mass of gas and M is the molar mass of the gas

So equation (2) can be written as:

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

⇒ $PM= \frac{m}{V} RT$

⇒ $\frac{PM}{RT}= \frac{m}{V}$             ......equation (3)

Now from equation (1) and (3), we get

$\frac{PM}{RT}= \frac{m}{V} = \rho$  

⇒ Density of an ideal gas: $\rho = \frac{PM}{RT}$  

⇒ Density of an ideal gas: ρ ∝ molar mass of gas: M

Therefore, the density of the ideal gas is directly proportional to its molar mass.