Which of the following statements is true regarding molecular weight and speed of molecules at the same temperature?

When considering the relationship between molecular weight and the speed of molecules at the same temperature, the principle of kinetic molecular theory plays a crucial role. According to this theory, the average kinetic energy of gas molecules is directly proportional to the temperature of the gas. This relationship can be mathematically expressed using the equation for kinetic energy:

[ \text{KE} = \frac{1}{2} mv^2 ]

where ( m ) is the mass (or molecular weight) of the molecule, and ( v ) is the speed of the molecule.

At a constant temperature, the average kinetic energy of the molecules remains constant. If we denote the kinetic energy as equal for different gases (since they are at the same temperature), then an increase in molecular weight (mass) is associated with a decrease in the speed of the molecules. This is because for a fixed kinetic energy, a larger mass must result in a lower velocity, according to the rearrangement of the formula:

[ v = \sqrt{\frac{2 \cdot \text{KE}}{m}} ]

As molecular weight increases, the denominator in this fraction increases, leading to a smaller value for ( v ), the speed of the molecule. Therefore, the