Question

The volume of 0.1 mole of gas at NTP is
$
  A)0.22\,litre \\
  B)2.24\,litre \\
  C)1\,litre \\
  D)22.4\,litre \\
 $

Answer 1

Hint: We can define molar volume as the volume occupied by one mole of any substance at standard temperature and pressure. We can calculate molar volume by dividing the molar mass by mass density. We can define molar gas volume as one mole of gas at a particular temperature and pressure contains the fixed volume.

Complete step by step answer:
We know the molar volume is directly proportional to molar mass and varies inversely with density. We can write the formula of molar volume as,
Molar volume=$\dfrac{{Molar\,mass}}{{Density}}$
The standard temperature is ${0^ \circ }C$ or 273K.
The standard pressure is 1atm or 760mmHg.
Practically, one mole of any gas occupies 22.4 Liters of volume at standard temperature and pressure. We can write molar volume in terms of expression as,
1mole of gas at STP=22.4 Liters of gas
We have to calculate the volume for 0.1 mole of gas at NTP. We can calculate the volume for 0.1 mole of gas using the expression,
1mole of gas at STP=22.4 Liters of gas
0.1mole of gas at STP=$0.1 \times 22.4$
0.1mole of gas at STP=$2.24\,Litres$
The volume occupied by 0.1 mole of gas at NTP is $2.24\,Litres$.
$\therefore $Option (B) is correct.

Note:
Equal volume of all gases at the standard temperature and pressure comprises the same number of particles. Molar volume for crystalline solids could be measured with the help X-ray crystallography. For ideal gases, the ideal gas equation gives the molar volume.
Let us calculate the molar volume for the given example.
Example 1: Calculate the molar volume for a sample of the molar mass of nitrogen if the density of the gas is $1.270\,g/L.$
In this case, we can calculate the molar volume of the sample using the molar mass and density.
We know the molar mass of nitrogen is $28.01\,g/mol$.
The given density is $1.270\,g/L.$
We can calculate the molar volume by dividing the molar mass to the density. We can write the formula to calculate the molar volume as,
Molar volume=$\dfrac{{Molar\,mass}}{{Density}}$
Molar volume=$\dfrac{{28.01\,g/mol}}{{1.270\,g/L}}$
Molar volume=$22.05\,L$
The molar volume of gas sample is $22.05\,L$.