What does the root-mean-square (r.m.s) speed equation c=√(3RT/M) depend on?

The root-mean-square (r.m.s.) speed equation ( c = \sqrt{\frac{3RT}{M}} ) illustrates how the speed of gas molecules depends on temperature and molar mass.

In this equation, ( R ) is the ideal gas constant, ( T ) is the absolute temperature in Kelvin, and ( M ) is the molar mass of the gas in kilograms per mole. The equation shows a direct relationship between the r.m.s speed and temperature, meaning as the temperature increases, the kinetic energy of the gas molecules increases, leading to a higher r.m.s speed.

Conversely, molar mass has an inverse relationship with the r.m.s speed. A higher molar mass results in a slower speed because the same amount of thermal energy (which is dependent on temperature) is distributed across a larger mass of gas molecules. Therefore, the r.m.s speed is higher for lighter gases at the same temperature and lower for heavier gases.

Thus, the correct interpretation involves recognizing that the r.m.s speed is fundamentally determined by both the absolute temperature of the gas and its molar mass, making this choice the correct one.