NEET Important Chapter - Kinetic Theory of Gases

The chapter kinetic theory of gases starts with the basic revision of all the concepts we studied in our lower grades to build the connection between the advanced parts of the kinetic theory of gases. In the kinetic theory of gases we have discussed the molecular nature of matter, behaviour of gases, kinetic theory of an ideal gas,  law of equipartition of energy, specific heat capacity, mean free path etc. 

The chapter Kinetic theory of gases deals with macroscopic to microscopic properties of gas which includes quantities like temperature, pressure,speed and kinetic energy.

Moving further we got introduced to a few more important concepts like the law of equipartition of energy,degrees of freedom and Maxwell’s distribution of molecular speeds.

Now, let us move on to the important concepts and formulae related to NEET and NEET mains exams along with a few solved examples.

Important Topics of Kinetic Theory of Gases

• Behaviour of Gas Molecules

• Ideal Gas Equation

• Kinetic Theory of an Ideal Gas

• Kinetic Interpretation of temperature

• Degree of Freedom

• Law of Equipartition of Energy

Important Concepts of Kinetic Theory of Gases.

List of Important Formulas

Solved Examples of Kinetic Theory of Gases

1. Calculate the rms speed of nitrogen at STP(pressure =1atm and temperature = $0^{\circ}$ C. The density of nitrogen in these conditions is 1.25kg/m3.

Sol:

Given,

At STP the pressure is $1 \times 10^{5}$ N/m2 

hence the rms speed is $v_{rms} = 1.73\sqrt{\dfrac{p}{⍴} }$

where p is the pressure of gas and ⍴ is the density 

So $v_{rms}$ = $1.73\sqrt{\dfrac{10^{5}}{1.25}}}$ = 490m/s

     Key point: Here only the formula of $v_{rms}$ should be remembered by the student.

2. Calculate the number of molecules in each cubic metre of a gas at 1atm and $27^{\circ}$ C.

Sol: 

From the ideal gas equation PV=nRT

Where P is the pressure of gas

R= gas constant

V = volume of gas 

T= temperature of gas and n = no. of molecules

Hence n = $\dfrac{PV}{RT}$ 

=$\dfrac{10^{5}}{300\times 1.38\times 10^{-23 }}$

Hence n = $2.4\times 10^{5}$

Key point: Here only the formula of ideal gas equation should be remembered by the student

Previous Year Questions 

1. A gas mixture consists of 2 moles of $O_{2}$ and 4 moles of Ar at temperature T. Neglecting all the vibrational modes, the total internal energy of the system is:- (NEET 2017)

Sol: 

Here oxygen being a diatomic molecule will have no vibrational mode

So U(oxygen) = $2\times\dfrac{5}{2}RT$= 5RT 

Similarly argon being monoatomic gas having only translational mode has 4 moles

So U(Ar) = $4\times\dfrac{3}{2}RT$ = 6RT 

Hence total internal energy of system = U(oxygen)+ U(Ar) = 11RT

Trick: Here only the concept of degrees of freedom  should be remembered by the student with the formula $U = \dfrac{U}{2RT}$

2. A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas?  (NEET 2016)

Sol: 

From ideal gas equation 

PV= nRT

And n = $\dfrac{PV}{RT}$

Also we know that k = $\dfrac{R}{N_{a}}$

$\dfrac{nN_{a}}{V}$ = $\dfrac{P}{kT}$

Multiplying both sides with m and after calculations we have 

Density = $\dfrac{mP}{kT}$

Trick: Here only the formula of the ideal gas equation should be remembered by the student.

Practice Questions

1. The translational kinetic energy of molecules of one mole of monatomic gas is U=$\dfrac{3NKT}{2}$. The value of atomic specific heat of gas under constant pressure will be: (Ans:- $\dfrac{5}{2}R$)

2. A gas is at zero degree celsius. Upto what temp the gas has to be heated so that the root mean square velocity of its molecules be doubled? (Ans:- 819 degree celsius)

Conclusion

In this article we have provided important information regarding the chapter kinetic theory of gases such as important concepts, formulae, etc.. Students should work on more solved examples and kinetic theory of ideal gas examples for securing good grades in the NEET exams.