Exam-Style Kinetic Theory of Gases Problems with Solutions
FAQs on Kinetic Theory of Gases: Essential Practice Exercises
1. What is the kinetic theory of gases?
The kinetic theory of gases explains the behavior and properties of gases based on the idea that gas particles are in constant, random motion. It connects macroscopic gas laws to microscopic particle motion by describing how collisions, speed, and energy contribute to gas pressure, temperature, and volume. Important points include:
- Gas molecules are made up of tiny, fast-moving particles.
- Collisions between particles are perfectly elastic, meaning total kinetic energy is conserved.
- The pressure exerted by gas is due to continuous collisions of particles with container walls.
- Temperature is directly related to the average kinetic energy of the molecules.
2. State the main postulates of the kinetic theory of gases.
The kinetic theory of gases is based on several important assumptions or postulates:
- Gases consist of a large number of small particles called molecules.
- Molecules are in constant, random motion and move in straight lines until they collide.
- The volume of individual gas molecules is negligible compared to the total volume of the gas.
- There are no forces of attraction or repulsion between molecules except during collisions.
- Collisions between molecules and with the walls are perfectly elastic (no energy loss).
- The average kinetic energy of gas molecules is directly proportional to the absolute temperature.
5. What are the limitations of the kinetic theory of gases?
While the kinetic theory of gases explains many properties of gases, it has some important limitations:
- It assumes no intermolecular forces, which isn't true for real gases at high pressures or low temperatures.
- The theory treats gas molecules as point particles with negligible volume.
- It cannot explain behavior of real gases near condensation or at high densities.
- Does not account for interactions between non-ideal gas molecules.
- Fails to predict certain thermodynamic phenomena like deviations from ideal behavior.
7. How does the kinetic theory explain pressure exerted by gases?
The kinetic theory states that gas pressure results from millions of microscopic collisions of gas molecules against the container walls. The net force from these collisions, distributed over the area of the walls, leads to the observed pressure. Important aspects:
- Each collision transfers momentum to the wall.
- More frequent and energetic collisions (higher kinetic energy) mean higher pressure.
- Pressure increases with temperature, as molecules move faster and hit the walls more often.
8. What is Boyle’s Law and how is it explained by kinetic theory?
Boyle’s Law states that at constant temperature, the pressure of a given mass of gas is inversely proportional to its volume. Kinetic theory explains this by showing that:
- If volume decreases but temperature stays the same, molecules hit the walls more frequently due to reduced space.
- This leads to higher pressure since more collisions occur per unit area.
9. What are ideal and real gases according to the kinetic theory?
Ideal gases perfectly follow all gas laws and the assumptions of kinetic theory, while real gases deviate under certain conditions. Key points:
- Ideal gas: No intermolecular forces, negligible volume of molecules, perfectly elastic collisions.
- Real gas: Have intermolecular attractions and repulsions, occupy finite volume, deviations seen at high pressure/low temperature.
10. Calculate the root mean square velocity of oxygen molecules at 300 K. (Molecular mass of O2 = 32 g/mol)
The root mean square velocity of gas molecules can be found using the equation: vrms = sqrt(3RT/M), where:
- R = 8.314 J mol-1 K-1
- T = 300 K
- M = molecular mass in kg/mol = 0.032 kg/mol
- vrms = sqrt[(3 × 8.314 × 300)/0.032] ≈ 484 m/s
