Question

The density of a gas if found to be proportional to the molar mass of the gas (according to the Ideal Gas Law). Of the following gases: Ar, CO2, CO, O2, Cl2, which one has a density of 1.89 g/L if the temperature is 280.15 K and the pressure is 750.1 torr?

Answer 1

Solution: CO₂

Explanation:

According to ideal gas law,

From the above equation,

D is proportional to Molar mass of the ideal gas i.e

where the proportionality constant is

As per the given problem,

P = 750.1 torr

Converting it into atm, using the conversion,

1 torr = (1/760) atm

Therefore,

750.1 torr = (750.1/760) atm = 0.98697 atm

and R = Gas constant whose value is 0.08206 atm.L/mol.K

T = 280.15 K

For Ar gas:

( Rounded off to three significant figures )

For CO₂ :

   ( Rounded off to three significant figures )

For CO gas:

( Rounded off to three significant figures )

For O₂ gas:

  ( Rounded off to three significant figures )

For Cl₂ gas:

  

( Rounded off to three significant figures )

From the above calculations of densities, it is clear that when pressure is equal to 750.1 torr and temperature is 280.15 K,  CO₂ has a density of 1.89 g/L . (Ans.)