Kinetic Theory of Gases Flashcards for NEET — 20 cards

First 8 of 20 Kinetic Theory of Gases flashcards

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1. Card 1 of 20

   Write the Ideal Gas Equation in terms of both the number of moles (n) and the total number of molecules (N).

   Hint: R is the Universal Gas Constant. k_B is the Boltzmann Constant.

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   Answer

   1. In terms of moles: PV = nRT 2. In terms of molecules: PV = N $k_B$ T

2. Card 2 of 20

   What is Avogadro's number ($N_A$) and how does it relate the Universal Gas Constant (R) to the Boltzmann Constant ($k_B$)?

   Hint: k_B is essentially the gas constant per molecule.

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   Answer

   $N_A$ = 6.022 × 10²³ mol⁻¹ (Number of molecules in one mole). Relation: R = $N_A$ × $k_B$

3. Card 3 of 20

   State the three most critical assumptions of the Kinetic Theory of Gases regarding volume, forces, and collisions.

   Hint: These assumptions explain why internal energy is entirely kinetic.

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   Answer

   1. Volume of individual molecules is negligible compared to the total volume of the gas. 2. There are NO intermolecular forces of attraction (except during collisions). 3. All collisions (between molecules, and with the walls) are perfectly elastic.

4. Card 4 of 20

   Relate the average translational kinetic energy of a single gas molecule (Eₐᵥ$_g$) to its absolute temperature (T).

   Hint: This is the Kinetic Interpretation of Temperature. Temperature is a direct measure of average molecular kinetic energy.

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   Answer

   Eₐᵥ$_g$ = (3/2) $k_B$ T

5. Card 5 of 20

   Write the formula for the Root Mean Square (RMS) speed of a gas.

   Hint: RMS speed is directly proportional to √T and inversely proportional to √M.

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   Answer

   vᵣₘₛ = √(3RT / M) or vᵣₘₛ = √(3$k_B$ T / m) Where M is Molar Mass and m is the mass of a single molecule.

6. Card 6 of 20

   State the Law of Equipartition of Energy.

   Hint: Energy per mole per degree of freedom is (1/2)RT.

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   Answer

   In thermal equilibrium, the total energy of a dynamic system is equally distributed among its various degrees of freedom. The energy associated with each degree of freedom is (1/2) $k_B$ T per molecule.

7. Card 7 of 20

   What are the Degrees of Freedom (f) for a Monoatomic gas (like He, Ne)?

   Hint: They cannot rotate or vibrate effectively to store energy.

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   Answer

   f = 3 (They only possess 3 translational degrees of freedom along x, y, and z axes).

8. Card 8 of 20

   What are the Degrees of Freedom (f) for a rigid Diatomic gas (like O₂, N₂) at normal temperatures?

   Hint: At very high temperatures, non-rigid diatomic gases add 2 vibrational degrees of freedom, making f = 7.

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   Answer

   f = 5 (3 Translational + 2 Rotational). Rotation along its own bond axis has negligible moment of inertia.