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Distribution of Molecular Speeds
Ludwig Eduard Boltzmann (influenced by the work of James Clerk Maxwell) developed the kinetic theory of matter to predict the distribution of speeds of molecules in a gas to be expected at a given temperature.  
This work suggested that if we plot a graph of the number of molecules, N, which have speeds in narrow ranges, from v to v+Δv, against speed, v, then we should find the following distribution.  
 
The results are based on the assumption that the molecules move independently of each other except for collisions between molecules which have a duration much less than the time between collisions.  
vo corresponds to the "peak" of the curve, called the most probable speed.  
If we take a narrow range of speeds centered on vo we should find that this range has the greatest number of molecules.  
vm is the mean (or average) speed of the molecules (a little greater than vo as the curve is not symmetrical).  
   
 
As the temperature of the gas increases, both the range of speeds and the mean (average) speed increases.  
Therefore, for the same quantity of gas, at a higher temperature, the distribution is as shown by the red curve.  
These predictions have been verified by experiment, thus giving support to the kinetic theory.  
   
Some approximate average speeds (actually "root mean square" speeds) for molecules of different gases at different temperatures are given in the table below.  
The speeds are in ms-1.  
Gas 273K 373K
H2 1.81103

2.10103

He 1.30103

1.52103

N2 4.90102

5.73102

 
   
Notice that, for a given temperature, the lower mass molecules have much higher average speed  
   
Notice also that these figures illustrate the fact that absolute temperature of the gas is proportional to the average kinetic energy (which, remember, is proportional to speed squared) of its molecules, as shown below:  
 
Compare this figure with the ratios of the speeds squared for each type of gas  
Hydrogen
Helium
Nitrogen
 
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