Final answer:
The question examines concepts related to the Maxwell-Boltzmann distribution and the d. ideal gas law, focusing on calculating various molecular speeds for gases at given temperatures.
Step-by-step explanation:
The question relates to the principles of gas behaviors and how they can be described mathematically. In particular, it focuses on the Maxwell-Boltzmann distribution and how it can be used to determine various speeds of gas molecules at different temperatures. The average speed of gas molecules is important for understanding gas behaviors under different conditions, which relates to the kinetic theory of gases. The average, most probable, and root mean square (rms) speeds are different indicators of molecular motion, with each having unique calculations based on the temperature and molecular mass of the gas in question. These principles are essential for solving problems regarding gas molecule speeds and are used within the context of the ideal gas law, which combines Boyle's, Charles's, and Avogadro's laws.
The correct answer is d) Ideal gas law. The ideal gas law states that the average speed of particles in a gas is directly proportional to the square root of the temperature and inversely proportional to the square root of the molar mass of the gas.
For example, if we compare two gases with the same temperature, the gas with a lower molar mass will have a higher average speed. Similarly, if we compare two gases with the same molar mass, the gas with a higher temperature will have a higher average speed.