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.
Skill -
Name the various distributions.
Skill -
Explain how molecular masses affect the average speed.
The gas with the heaviest molecular mass has the lowest average speed.
UF_{6} is a gas used for enrichment of the isotope U-235.
Discussion -
The Root-mean-square speed is the square root of (3 R T / M),
where R = gas constant, T = temperature, M = molecular
mass.
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.
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?