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# NEET Important Chapter - Kinetic Theory of Gases

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## Kinetic Theory of Gases - An Important Concept for NEET

Last updated date: 16th Jul 2024
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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.

 Name of the Concept Key Points of the Concept Behaviour of Gas Molecules Here in the Ideal system we assume molecules to be point masses having no mutual interaction between them.The no. of gas molecules per unit volume remains constant for all gases at particular temperature and pressure.Since the molecules are moving in random motion their average speed in the x,y and z axis is zero. Ideal Gas Equation Molecules are supposed to follow the ideal gas equation at low pressures or at high temperatures for the above mentioned behaviour. This equation is considered as the ideal gas equation PV=nRT Kinetic Theory of an Ideal Gas There are few assumptions for kinetic theory  :The molecules present in the gas move randomly in all directions.The size of the molecule is infinitesimally small.The collisions happening between two molecules or between a molecule and wall are perfectly elastic with a small value of collision time.There are no forces exerted between the  molecules or on the walls of containers except during collision. Kinetic Interpretation of temperature E=$\dfrac{3}{2}NK_{b}T$The relation clearly states that the average kinetic energy of a molecule is directly proportional to the temperature where Kb is the Boltzmann constant and N is total no of molecules.Whereas for pressure the relation is P=$\dfrac{1}{3}nmv^{2}$ Law of Equipartition of Energy According to this law in thermal equilibrium the energy associated with dof of each molecule is $\dfrac{1}{2}NK_{b}T$ where Kb is the Boltzmann constant and N is total no of molecules. Degree of Freedom The number of independent modes of exchanging energy or no.of  independent motion which the particle can undergo is called as Degree of freedom.For monoatomic molecules dof =3 (only translational modes) and $\gamma$ = 1.67(The ratio of Cp and Cv)For diatomic molecules dof = 5 (3 translational and 2 rotational) with $\gamma$ =1.40For triatomic molecules $\gamma$ =1.33 Distribution of Molecular Speeds For a given mass of gas the velocities of all molecules are not same even their macroscopic parameters are fixed hence Maxwell introduced various speeds likeMost probable speed-The speed which is attained by large no of molecules having value $v_{p} = 1.41\sqrt{\dfrac{kT}{m} }$Average speed- Average sum of all the speeds of molecules with value $v_{a} = 1.59\sqrt{\dfrac{kT}{m} }$Root mean squared - Value of this speed is $v_{rms} = 1.73\sqrt{\dfrac{kT}{M} }$

### List of Important Formulas

 Sl. No Name of the Concept Formula Average Kinetic Energy E=$\dfrac{3}{2}NK_{b}T$ Average pressure of gas P=$\dfrac{1}{3}nmv^{2}$ Law of Equipartition of Energy E= $\dfrac{1}{2}NK_{b}T$ Most probable speed $v_{p} = 1.41\sqrt{\dfrac{kT}{m} }$ Average speed $v_{a} = 1.59\sqrt{\dfrac{kT}{m} }$ Root mean squared $v_{rms} = 1.73\sqrt{\dfrac{kT}{M} }$ 7. Mean free path $\lambda= \dfrac{1}{\sqrt{2}n\pi d^{2}}$

### 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.

1. 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 $U = \dfrac{U}{2RT}$

1. 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.

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## FAQs on NEET Important Chapter - Kinetic Theory of Gases

FAQ

1. What is the weightage of the Kinetic Theory of gases in NEET?

Nearly 1-2 questions arise in the exam from this chapter covering about 10 marks which makes about 1 % of the total marks.

2. What are the key points that need to be practiced for solving questions from Kinetic Theory of gases?

Students should practice the numericals and learn the formulas mainly for  solving the questions from the Kinetic Theory of gases.

3. Are previous year questions enough for JEE Mains?

To score 600+ in NEET, NCERT (both 11th and 12th) and previous year NEET papers are sufficient. Solving previous 10-year NEET  examinations offers us a tremendous advantage because 2-3 questions with the identical alternatives are guaranteed to be repeated every year.

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