Based on the kinetic-molecular theory, which of the following is/are true?
I.At a given temperature, all gases have the same average kinetic energy.
II.At a given temperature, different gases have the same average velocities.
III.The average kinetic energy is proportional to the absolute temperature.

• A. I only
• B. II only
• C. I & III only
• D. I, II & III

Answer: (C)

Verified step by step guidance

1. Understand the kinetic-molecular theory: This theory explains the behavior of gases, stating that gas particles are in constant random motion and that their kinetic energy depends on temperature.
2. Analyze statement I: 'At a given temperature, all gases have the same average kinetic energy.' According to the kinetic-molecular theory, the average kinetic energy of gas particles is directly proportional to the absolute temperature (in Kelvin). Therefore, at a given temperature, all gases indeed have the same average kinetic energy.
3. Analyze statement II: 'At a given temperature, different gases have the same average velocities.' The average velocity of gas particles depends on both the temperature and the mass of the particles. Since different gases have different molar masses, their average velocities will differ at the same temperature.
4. Analyze statement III: 'The average kinetic energy is proportional to the absolute temperature.' This is a fundamental aspect of the kinetic-molecular theory. The average kinetic energy of gas particles is given by the equation: <math xmlns='http://www.w3.org/1998/Math/MathML'><mi>E</mi><msub><mi>k</mi><mi>avg</mi></msub><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mi>k</mi><mi>T</mi></math>, where <math xmlns='http://www.w3.org/1998/Math/MathML'><mi>k</mi></math> is the Boltzmann constant and <math xmlns='http://www.w3.org/1998/Math/MathML'><mi>T</mi></math> is the absolute temperature.
5. Conclude which statements are true: Based on the analysis, statements I and III are true according to the kinetic-molecular theory, while statement II is false. Therefore, the correct answer is 'I & III only.'