Question

The vapor density of a gas is 22.4. The density of the gas at STP is:
(a)- 2 g/L
(b)- 1 g/L
(c)- 3 g/L
(d)- 1.5 g/L

Answer 1

This question can be solved by applying the following formula: first, by calculating the molar mass of the gas which is equal to twice the value of the vapor density, and second by calculating the density by taking the ratio of mass to the volume.

Complete step-by-step answer: We are given the value of vapor density which is equal to 22.4. So,
Vapor Density = 22.4
We know that at STP, i.e., standard temperature and pressure, the volume of the gas is always 22.4 liters/mole. So,
At STP, volume = 22.4 L/mol
This question can be solved by applying the following formula: first, by calculating the molar mass of the gas which is equal to twice the value of the vapor density, and second by calculating the density by taking the ratio of mass to the volume.
So, according to the first formula, we can write:
Molar mass = 2 x Vapor density
Now, putting the values, we get:
Molar mass = 2 x 22.4 = 44.8 g/mol.
So, the molar mass of the gas is 44.8 g/mol.
Now, using the second formula, we can write:
$Density=\dfrac{Mass}{Volume}$
So, putting the value, we can write:
$Density=\dfrac{44.8}{22.4}=2g/L$
So, the density of the gas is 2 g/L.

Therefore, the correct answer is an option (a).

Note: STP means standard temperature and pressure in which there is a specific value of temperature and pressure which is equal to ${{0}^{\circ }}C$ or 273.15 K of temperature and 1 bar of pressure.