Molecular Speed Distribution

The temperature of a substance is a measure of the average kinetic energy of the molecules in the substance. Kinetic energy is the energy that molecules have from translational motion (moving from point A to point B). It can be calculated using the following formula: Ek = ½mv2, where m is the mass of the molecule and v is the velocity (or speed) of the molecule. The faster a molecule moves, the more kinetic energy it has, and the higher the measured temperature. When water is at room temperature (20 °C or 68 °F), the average speed of the water molecules in the water is approximately 590 m/s (≈1300 mph).

But this is only the average (or mean) speed of the water molecules. Some of the water molecules are actually moving faster than 590 m/s, and some of the water molecules are moving slower. The Maxwell-Boltzmann distribution (see below) describes the distribution of the speeds of the water molecules when the water is in thermodynamic equilibrium (held steady at a constant temperature). As you can see, while most of the molecules are moving between 400 and 740 m/s, 25% of the molecules are moving slower than 400 m/s and 25% of the molecules are moving faster than 740 m/s (sometimes much slower and much faster).

What happens if we decrease the temperature of the water to 0 °C or 32 °F (the freezing point of water) or increase the temperature of the water to 100 °C or 212 °F (the boiling point of water)? At 0 °C, the average speed of the water molecules slows down to approximately 565 m/s (≈1250 mph). At 100 °C, the average speed of the water molecules speeds up to approximately 660 m/s (≈1500 mph).

Students often think that the water molecules are barely moving in a liquid state, but moving really fast in a gas state. However, as you can see, the water molecules are moving really fast in a gas state at 100 °C and only slightly slower in a liquid state at 0 °C. In fact, some of the water molecules in the liquid state are moving faster than the average water molecule in the gas state, and some of the water molecules in the gas state are moving slower than the average water molecule in the liquid state.