Kinetic theory of gases

Kinetic theory of Gases provides the much-needed interlink between the macroscopic and the microscopic. It depicts the behavior of gases under different physical conditions.

1. Kinetic Theory of gases Contents: Assumptions for a gas to be ideal Ideal and Real Gases Kinetic Theory of Gases Ideal Gas Law Applications of Ideal gas Law Maxwell-Boltzmann Distribution for I deal Gases Analysis of M axwell-Boltzmann Distribution Curve Real Gases and Van der Wall’s correction Some Problems on Kinetic Theory of Gases Key points

2. Assumptions For a Gas to be Ideal 1. The gas is made up of large number of identical molecules. 2. The size of the molecules is much less as compared to the size of the container they are contained in. 3. Each molecule is free to move in any direction and they can attain any velocity. 4. The molecules behave as perfectly elastic rigid bodies and are subject to Newton’s laws of motion. 5. There are no intermolecular forces acting between the molecules other than the contact forces that act during collision of two molecules.

3. Ideal and Real Gases Ideal Gases Real Gases 1. Ideal gases obey all gas laws under all conditions of temperature and pressure. 2. The volume occupied by molecules is negligible as compared to the total volume occupied by the gas. 3. The force of attraction between the molecules is negligible. 4. Obeys Ideal Gas equation 1. Real gases obey gas laws only at low pressure and high temperature 2. The volume occupied by molecules is taken into account and is not negligible. 3. The force of attraction cannot be ignored at all temperatures and pressure. 4. Obeys Van der Wall’s equations

4. Kinetic Theory of Gases The Kinetic Theory of Gases describe the gas as an ensemble or collection of large number of sub-microscopic particles, all of which are in constant rapid motion that has randomness arising from their many collisions with each other and with the walls of the container. Kinetic theory connects the large to the small. It describes the macroscopic properties of a system like temperature, pressure, viscosity, electrical conductivity and volume in terms of their molecular composition and motion.

5. Ideal Gas Law The Ideal Gas law relates the various macroscopic properties of a system namely, pressure (P), volume (V), amount of matter in the system (n), and temperature of the system (T). P = Pressure Unit: Pascal or a tm 1 atm = 101,325 Pascal 1 Pascal = 1N/   V = Volume Unit: Litres or At STP: V = 22.4 litre/mole In SI Units: V= 0.0224   R = Universal Gas Constant Value: At STP: 0.08205 L-atm/ mol -K In SI units: 8.314 J/ mol -K n = No. of moles of gas Units: mol 1 mol = 6.023 x   T = Temperature Units: Kelvin or 1 Kelvin = 273.15  

6. Applications of Ideal Gas Law The Ideal gas equation contains four variable terms (namely: P, V, n, and T) and a constant(R). These variables can be arranged in different ways to find the value of any one variable in terms of other three. 1. Boyle’s law : This law gives the relationship between Pressure and Volume when the temperature remains constant. According to this law, at constant temperature, pressure inside a system is inversely proportional to the volume of the system. 2. Charle’s law : According to this law, for a system with fixed mass and constant pressure, the volume occupied by the gas is directly proportional to the temperature of the system. 3. Gay-Lussac’s Law : According tot this law for a given mass and constant volume of an ideal gas, The pressure exerted on the sides of the container is directly proportional to the temperature of the system.

7. Maxwell-Boltzmann distribution for Ideal gases The Maxwell-Boltzmann distribution gives us the distribution curve for speed of molecules in a gas at a fixed temperature. This distribution function can be used to find the most probable speed, root mean square speed and average speed of the molecules. It is noteworthy to mention that this distribution curve does not give us the speed of individual molecules, rather it shows us what fraction of molecules are having a particular speed. Maxwell-Boltzmann distribution equation

8. Analysis of Maxwell-Boltzmann Distribution Curve Maxwell-Boltzmann distribution curve gives us three important parameters: 1. Average Speed : It is the average speed possessed by most number of molecules. Although, the average speed accounts for most relatively large number of molecules, still a lot of molecules that have speeds greater than average speed. 2. Root Mean Square speed : As the name suggests, it is the square root of the mean of square of all the velocities. It is the rms speed that gives the most accurate description of the average speed possessed by molecules. 3. Most Probable Speed : It is the speed that is most likely to be possessed by large fraction of molecules. This speed lies just beneath the peak of the distribution curve.

9. Analysis of Maxwell-Boltzmann Distribution Curve Cont.…

10. Real gases and Van der Waal’s correction Corrections: The intermolecular forces between molecules is not negligible and must be taken into account. This leads to correction in pressure term 2. The volume occupied by each molecule has to be taken in to account. This leads to a correction in volume term. Rest equation remains the same as Ideal gas equation. m akes changes in the ideal gas equation by taking into account the intermolecular forces present between the molecules. The first corrective term, The second corrective term , -nb accounts for the total volume occupied by of molecules. V alue of both the parameters a and b cannot be determined theoretically and has to be found out using experimental methods.