**branches of physics**and various types of topics in physics taught in

**class 11**. One such topic is the

**Kinetic Theory of Gases Class 11**. The kinetic theory of gases demonstrates the 3 visible features of a gas in terms of the microscopic nature of atoms and molecules forming the gas. Normally, the physical aspects of solids and fluids can be determined based on their area, form, mass, volume, etc. In the point of gases, they have no distinct shape, size, and mass and volume are not directly calculable. Here, in this article, we discuss all details about the

**Chapter 13 kinetic theory of gases**class 11.

### Detailed Table of Chapter 13 Notes – Kinetic Theory of Gases Class 9 Notes PDF

1. |
Board |
CBSE |

2. |
Textbook |
NCERT |

3. |
Class |
Class 11 |

4. |
Subject |
Notes |

5. |
Chapter |
Chapter 13 |

6. |
Chapter Name |
kinetic theory of gases |

7. |
Category |
CBSE Revision Notes |

## Kinetic Theory of Gases Class 11 notes PDF -Short Notes

**What is Kinetic Theory?-**

- The kinetic theory of gases describes how gases behave by assuming that the gas is made up of quickly moving atoms or molecules.
- The kinetic theory of gases explains the random movement of molecules in a gas.
- We’ll also look at why kinetic theory is considered a successful theory.
- The following things are explained by the Kinetic theory:

**Molecular Nature of Matter**

- Many scientists have proposed the atomic hypothesis. According to this theory, atoms make up everything in the universe.
- Atoms are tiny particles that move around in a constant order, attracting one another when they are close enough. When they are forced to be very close to each other, however, they repel each other.
- When gases combine chemically to form another gas, their volumes are in small integer ratios, according to Gay Lussac’s law.

**Why was Dalton’s Theory a Success?**

- Molecules are made up of atoms, which are built up of molecules.
- An electron microscope can examine atomic structure.

**Solids, Liquids, Gases in Terms of Molecular Structure**

Basis of Difference |
Solids |
Liquids |
Gases |

The Inter Atomic Distance or the distance between the molecules. | The molecules in solids are very tightly packed and the inter-atomic distance is minimum. | The liquid molecules are less tightly packed and the inter-atomic distance between the liquid molecules is more than the solids. | The gas molecules are loosely packed. The gas molecules move freely in space and the inter-atomic distance is minimum in gas particles. |

The average distance a molecule can travel without colliding is known as the Mean Free Path. | Solids have no mean free path. | Less mean free path than gases. | Mean free path is present in gas molecules. |

**Behavior of Gases**

- Gases at low pressures and temperatures much higher than those at which they liquefy (or solidify) approximate a relationship between pressure, temperature, and volume.

PV=KTPV=KT

………..(1)

This is the universal relationship that all gases satisfy.

where P, V, and T denote pressure, volume, and temperature, and K denotes the constant for a given volume of gas. It fluctuates depending on the amount of gas present.

K=NkBK=NkB , where N is the number of molecules, KBKB is the Boltzmann constant whose value never changes.

- From equation (1),

PV=NkBTPV=NkBT

- Therefore, PVNT=kBPVNT=kB , will be the same for all gases.
- Two gases having pressure, temperature, and volume as (P1, T1, V1) and (P2, T2, V2) are considered.
- Therefore, P1V1N1T1=P2V2N2T2P1V1N1T1=P2V2N2T2
- The conclusion for the above relation is that it is satisfied by all gases at high temperatures and low pressures.

**Justification of Avogadro’s Hypothesis from the Equation of Gas**

- According to Avogadro’s hypothesis, all gases have the same number of molecules in equal volumes at the same temperature and pressure.
- Consider the equation PVNTPVNT = constant: if P, V, and T are the same for two gases, then N (number of molecules) will be the same as well.
- At constant P and T, Avogadro’s hypothesis states that the number of molecules per unit volume is the same for all gases.
- NA stands for Avogadro number. Where NA is equal to 6.02×10236.02×1023. It has universal significance.

**Perfect Gas Equation**

- A perfect gas equation is given by the following formula: PV=μRTPV=μRT , where P is pressure, V is the volume, T is the absolute temperature, μμ is the number of moles and R is the universal gas constant.

R=kBNAR=kBNA , where kBkB is the Boltzmann constant and NANA is the Avogadro’s number.

- This equation describes how gas behaves in a specific condition.
- If a gas fulfils this equation, it is referred to as a perfect gas or an ideal gas.

**Different Forms of Perfect Gas Equation**

- PV=μRTPV=μRT, where μμ is a number of moles; μ=NNAμ=NNA , N is the number of molecules and NA is the Avogadro number.

Now, PV=NNARTPV=NNART

After simplification, PV=NkBTPV=NkBT

P=NVkBTP=NVkBT , where n=NVn=NV

So, P=nkBTP=nkBT, where n is the number of density

- Also, μ=MM∘μ=MM∘ , where M is the mass of the sample and Mo is the molar mass of the sample.

So, PV=MM∘RTPV=MM∘RT

P=MVRTM∘P=MVRTM∘

P=ρRTM∘P=ρRTM∘ , where ρρ is the mass density of the gas. ρ=MVρ=MV

**Ideal Gas**

- At all pressures and temperatures, a gas that exactly fulfills the perfect gas equation.
- The concept of an ideal gas is purely theoretical.
- There is no such thing as an ideal gas. The term “real gas” refers to a gas that is ideal.
- For low pressures and high temperatures, real gases approach ideal gas behavior.

**Real Gases Deviation from Ideal Gas**

- For low pressures and high temperatures, real gases approach ideal gas behavior.
- According to the ideal gas equation: PV=μRTPV=μRT, PVRTPVRT = constant. So, for an ideal gas, the graph should be a straight line (parallel to the x-axis). This means it has the same value regardless of temperature or pressure.
- However, at high temperatures and low pressures, the graph of real gases approaches ideal gas behavior.

In the above graph it is shown that at low pressures and high temperatures, real gases approach the ideal gas behavior.

**Deduction of Boyle’s Law and Charles Law from Perfect Gas Equation**

**Boyle’s Law:**Boyle’s law is being derived from the perfect gas equation, PV=μRTPV=μRT. The T is the temperature and μμ is the number of moles and both of these values are considered constant.

Therefore, PV = constant. So, at a constant temperature, the pressure of a given mass of gas varies inversely with volume, according to Boyle’s law.

**Charles’s Law:**Here the pressure (P) is considered as constant. According to the ideal gas equation, PV=μRTPV=μRT

VT=μRPVT=μRP = constant

Therefore, VTVT = Constant

Hence, according to Charles’s law, at constant pressure, the volume of a gas is directly proportional to its absolute temperature.

** ****Deducing Dalton’s Law of Partial Pressures**

- The overall pressure of a mixture of ideal gases is equal to the sum of partial pressures, according to Dalton’s partial pressure equation.
- If a vessel contains many ideal gases mixed together, the total pressure of the vessel equals the sum of partial pressures.
- Consider the following: – Consider a vessel containing a mixture of three gases, A, B, and C. As a result, the partial pressure of A equals the pressure applied just by A, assuming B and C are absent. Similarly, when A and C are absent, the partial pressure of B is equal to the pressure applied just by B. Similarly, the total pressure of the mixture is equal to the sum of the partial pressures of A, B, and C, according to Dalton’s law.

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