Most probable speed

Definition

The most probable speed is the speed at which the largest number of gas molecules are moving in a given sample. It is derived from the Maxwell-Boltzmann distribution of molecular speeds.

5 Must Know Facts For Your Next Test

1. The most probable speed can be calculated using the formula $v_p = \sqrt{\frac{2k_BT}{m}}$, where $v_p$ is the most probable speed, $k_B$ is Boltzmann's constant, $T$ is the temperature in Kelvins, and $m$ is the mass of a molecule.
2. At a given temperature, lighter molecules have higher most probable speeds compared to heavier molecules.
3. The most probable speed increases with increasing temperature.
4. Most probable speed represents the peak of the Maxwell-Boltzmann distribution curve for molecular speeds in a gas.
5. In an ideal gas, the most probable speed differs from both the average speed and root mean square (rms) speed.

Review Questions

• What formula is used to calculate the most probable speed of gas molecules?
• How does temperature affect the most probable speed in a gas sample?
• Why does the most probable speed differ from average and rms speeds?

Related terms

Maxwell-Boltzmann Distribution: A statistical distribution of speeds for particles in an ideal gas that describes how particle speeds are spread out at different temperatures.

Root Mean Square Speed: $v_{rms} = \sqrt{\frac{3k_BT}{m}}$, it represents an average value of molecular speeds squared and then square-rooted.

Average Speed: $\langle v \rangle = \sqrt{\frac{8k_BT}{\pi m}}$, it denotes the arithmetic mean of all molecular speeds in a gas sample.