12 Questions
What is the change in momentum in one collision of a gas molecule inside the cubical vessel?
2mCx
What is the total rate of change of momentum of a gas molecule moving along the x, y, and z axes inside the cubical vessel?
2m/l (Cx^2 + Cy^2 + Cz^2)
What is the formula for Root Mean Square velocity (Crms) of gas molecules?
{(C1^2 + C2^2 + ... + Cn^2)/N}^(1/2)
What is the equation derived for pressure (P) in terms of gas properties and Crms?
P = 1/3 (mN Crms^2/V)
What is the relationship between Kinetic Energy and Temperature according to the kinetic gas equation?
K.E = 3/2 nRT
How is Boyle's Law derived from the kinetic gas equation?
PV = CONSTANT
Explain the postulate of the Kinetic Theory of Gases related to the size of gas molecules.
The gas molecules are extremely small in size and are separated by large distances. The actual volume of the gas molecules is negligible compared to the total volume occupied by the gas.
How does the Kinetic Theory of Gases explain the pressure exerted by a gas?
The pressure is due to the bombardment of gas molecules on the walls of the vessel.
What is the nature of collisions between gas molecules according to the Kinetic Theory of Gases?
The collisions are perfectly elastic with no loss of energy.
Explain the concept of the average kinetic energy of gas molecules in relation to the absolute temperature.
The average kinetic energy is directly proportional to the absolute temperature of the gas.
How do gas molecules move according to the Kinetic Theory of Gases?
Gas molecules move freely in all directions in straight lines, changing speed and direction upon collisions.
What is the Kinetic Gas Equation and how is it derived?
The Kinetic Gas Equation is PV = 1/3 (m N Crms2), derived on the basis of the Kinetic Molecular Theory of Gases. Here, m = mass of one gas molecule, N = Avogadro’s number, and Crms = root mean square velocity.
Study Notes
Postulates of Kinetic Theory of Gases
- Gases consist of a large number of minute particles called molecules.
- Gas molecules are extremely small and separated by large distances, making their actual volume negligible compared to the total volume occupied by the gas.
- Pressure is exerted by the gas due to the bombardment of molecules on the walls of the vessel.
- Gas molecules collide with each other and the walls of the vessel, with perfectly elastic collisions and no loss of energy.
- The distance between gas molecules is large, resulting in no effective force of attraction or repulsion between them.
- Gas molecules move freely in all directions in straight lines, with changing speed and direction upon collision.
- The average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas.
- There is no effect of gravity on gas molecules.
Kinetic Gas Equation
- The equation is: PV = 1/3 (mN Crms2), where m is the mass of one gas molecule, N is Avogadro's number, Crms is the root mean square velocity, P is the pressure, and V is the volume.
- The equation relates pressure, volume, mass, and root mean square velocity.
Derivation of Kinetic Gas Equation
- Consider a cubical vessel with one mole of gas moving in all directions.
- The rate of change in momentum of a gas molecule is 2mCx/l, where m is the mass of the molecule and Cx is its velocity along the x-axis.
- The total rate of change of momentum is the sum of the rates of change along the x, y, and z axes.
- Total rate of change of momentum of all molecules is (2mN/l) x Crms2.
- Pressure (P) is the force per unit area, given by F/A = (2mN/l) x Crms2/6l2.
- Rearranging the equation yields PV = 1/3 (mN Crms2).
Relationship between Kinetic Energy and Temperature
- According to the kinetic gas equation, PV = 2/3 K.E.
- Rearranging the equation yields K.E = 3/2 nRT, where n is the number of moles and R is the gas constant.
- For a given mass of gas, K.E is directly proportional to T.
Derivation of Gas Laws
Boyle's Law
- According to the kinetic gas equation, PV = 2/3 K'E.
- Since K.E is directly proportional to T, PV = constant for a given temperature.
Charles' Law
- According to the kinetic gas equation, PV = 2/3 K'E.
- Since K.E is directly proportional to T, V/T is constant for a given mass of gas.
Test your knowledge on the fundamental postulates of the Kinetic Theory of Gases, including concepts like gas molecules, their size and behavior, and the pressure exerted by gases.
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