Final answer:
False, The molar volumes of solids and liquids vary and are typically much smaller than those of gases due to molecular packing differences.
Step-by-step explanation:
The statement that the volumes of one mole of different solid and liquid substances are the same is false. While the molar volume of a substance is the volume that one mole of the substance occupies, there's significant variation in the molar volume between different substances, especially when transitioning between states of matter like solid, liquid, and gas.
For solids and liquids, the molar volume can vary, but it will generally be much less than that of a gas. This is because molecules in a solid or a liquid are much closer together, while in a gas, they are spread far apart.
Avogadro's hypothesis is particularly important for gases, as it states that equal volumes of all gases at the same temperature and pressure contain the same number of gas particles. However, the same does not apply to solids and liquids due to the differences in density and molecular packing.
Therefore, while the molar volumes of solid and liquid phases of a substance may be similar because of the proximity of molecules, they are not necessarily the same as each other or as that of gases.