Molecular Speeds Diffusion and Effusion

The principal tenet of kinetic theory is that molecules are in constant random motion. Now we will look at the speeds of molecules and at some conclusions of kinetic theory regarding molecular speeds. 

The root-mean-square (rms) molecular speed, u, is a type of average molecular speed, equal to the speed of a molecule having the average molecular kinetic energy. It is given by the following formnla  

The distributions of speeds of H2 molecules are shown for 0°C and 500°C. Note that the speed corresponding to the maximum in the curve (the most probable speed) increases with temperature. 

In applying this equation, care must be taken to use consistent units. If SI units are used for i (= 8.31 kg m /(s K mol)), T (K), and (kg/mol), as in the following example, the rms speed will be in meters per second. Note that in these units, H2, whose molecular weight is 2.02 amu, has a molar mass of 2.02 X 

Values of the rms speed calculated from this formula indicate that molecular speeds are astonishingly high. For example, the rms speed of H2 molecules at 20°C is 1.90 X lO m/s (over 4000 mi/hr). 

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