Molecular Speed of Gases

Skills to develop

Explain the distribution of molecular speed of a gas.

Molecular Speed of Gases

The quantitative relationship of temperature effect on chemical reaction rates are discussed in form of activation energy, depicted as E_a in the diagram. For reactions having large E_a values, high temperatures are required to have a measurable reaction rate. The reason behind this is due to the small number of molecules having sufficient energy to overcome E_a, the energy barrier of forming an activated reaction intermediate.

At a certain temperature, not all gas molecules are moving with the same speed, some fast and some slow. The kinetic energies of molecules are not all equal. The fast moving ones have high kinetic energy, and they may have enough energy to overcome the reaction energy barrier E_a.

A plot of number of gas molecules at certain speed versus speed gives a distribution curve. Careful studies of gases show that the distribution is not a bell or NORMAL distribution, but a Maxwell- Boltzmann distribution.

A sketch of a Maxwell distribution is given here. The peaks are not symmetrical. There are more molecules at higher speed than at lower speeds. When the temperature increases, the peak shifts to the right. A more carefully plotted diagram is shown below, and a computer simulated plots will be more illustrative, however the simulation program was only available in the DOS version of CAcT earlier.

You will learn the theory and the statistics at a higher year. For the moment, you may notice how the distribution curve shift as temperature increases.

Confidence Building Questions

Which curve has a bell shape?
a. Normal distribution
b. Maxwell-Boltzmann distribution
c. Chi-square distribution

Skill -
Name the various distributions.
Which of the following gases have the lowest most-probable speed: H₂, He, Ne, N₂, O₂, F₂, Ar, or Xe?

Skill -
Explain how molecular masses affect the average speed.
The gas with the heaviest molecular mass has the lowest average speed. UF₆ is a gas used for enrichment of the isotope U-235.
For N₂ at 300 K, which of the following speeds is the highest?
a. Most probable speed
b. Average speed
c. Root-mean-square speed

Discussion -
The Root-mean-square speed is the square root of (3 R T / M), where R = gas constant, T = temperature, M = molecular mass.
For N₂ at 300 K, which of the following speeds is the lowest?
a. Most probable speed
b. Average speed
c. Root-mean-square speed

Discussion -
The formulas for the three speeds mentioned here can be derived by mathematical techniques. The most probable speed is the square root of (2 R T / M), where R = gas constant, T = temperature, M = molecular mass.
For the gas N₂, which temperature gives the highest most probable speed:
500 C, 600 K, or 700 F?

Discussion -
It is easy to calculate the most probable speed if you know the formula to use. Note that 500 C is higher than 700 F. Do you know what does the temperature scales measure?