Important questions based on NCERT syllabus for Chapter 13 - Kinetic Theory:
Question-1: The volume occupied by one mole of any (ideal) gas at STP is called molar volume (STP : 0 °C, 1 atmospheric pressure). Prove that molar volume is 22.4 litres.
We know that the ideal gas equation: PV = nRT
Where, R is the universal gas constant = 8.314 J mol-1 K-1
n = Number of moles = 1
T = Standard temperature = 273 K
P = Standard pressure = 1 atm = 1.013 × 105 Nm-2
Thus, V = (nRT)/p
= (1 x 8.314 x 273)/( 1.013 × 10^5)
= 0.0224 m3
= 22.4 liters
Thus, it is proved that molar volume of a gas at standard temperature and pressure is 22.4 liters.
Question-2: In a 50 m3 room, at a pressure of 1 atm and temperature 270C, what is the number of air molecules (oxygen, nitrogen, water vapour and other constituents) present?
Volume of the room, V = 50.0 m^3
Temperature of the room, T = 27°C = 300 K
Pressure in the room, P = 1 atm = 1 × 1.013 × 105 Pa
According to gas equation:
PV = kBNT
Where, kB is Boltzmann constant = 1.38 × 10^-23 m2 kg s-2 K-1
N is the number of air molecules in the room
Now, N = PV/ kBT
= (1.013 x 105 x 50) / (1.38 × 10^-23 x 300 ) = 1.22 x 10^27
Therefore there is 1.22 × 10^27 molecules in the room.
Question-3: Give the assumptions of Kinetic Theory of Gases
Solution: 1.Every gas consists of extremely small particles known as molecules. The molecules of a given gas are all identical but are different from those of another gas.
2.The molecules of a gas are identical spherical, rigid and perfectly elastic point masses.
3.Their molecular size is negligible in comparison to intermolecular distance (10-9m).
4.The speed of gas molecules lies between zero and infinity (very high speed).
5.The distance covered by the molecules between two successive collisions is known as free path and mean of all free path is known as mean free path.
6.The number of collision per unit volume in a gas remains constant.
7.No attractive or repulsive force acts between gas molecules.
8.Gravitational to extremely attraction among the molecules is ineffective due small masses and very high speed of molecules