Question

Density of oxygen at NTP is 1.429 g/litre. Calculate the standard molar volume of the gas.
(A) 20 $litre.mo{l^{ - 1}}$
(B) 11.39 $litre.mo{l^{ - 1}}$
(C) 22.4 $litre.mo{l^{ - 1}}$
(D) 22 $litre.mo{l^{ - 1}}$

Answer 1

Hint: Density can be defined as mass per unit volume and standard molar volume refers to the volume of 1 mole of compound at NTP conditions.

Complete answer:
-Density is basically defined as mass per unit volume. It is mathematically written as:
  $density = \frac{{mass}}{{volume}}$

From the above given expression we can say that density decreases with increase in volume and increases with decrease in volume. Density is more specifically known as specific weight. Also density is an intensive property which means that it does not change with change in amount of substance. Its unit is: g/litre.

-Standard molar volume of a gas is defined as the volume occupied by one mole of the gas at standard pressure and standard temperature.

-NTP conditions means that the standard temperature is 293.5 K and standard pressure is 1 atm.
-According to the question the density of oxygen at NTP is = 1.429 g/litre
-We know that the molar mass of ${O_2}$ is = 16 × 2 = 32 g/mole

-Now using the values of density and mass we will find out the volume.
     Using the formula:
     $density = \frac{{mass}}{{volume}}$
     $1.429 = \frac{{32}}{V}$
     $V = \frac{{32}}{{1.429}}$
     = 22.39 = 22.4 litre
Hence, the standard molar volume of ${O_2}$ gas is 22.4 litre/mole.

So, the correct answer is “Option C”.

Note:
Density of ${O_2}$ is 1.429 g/litre only at NTP conditions and it is 1.43 g/litre at STP conditions. This difference is small but density does not remain the same at all conditions. The density of any substance varies with temperature and pressure conditions. The variation in density is small for solids and liquids but greater for gases.