80 METHODS FOR DETERMINING MOLECULAR SIZE AND SHAPE 



2. Diffusion 



It is well known that thermal motion effects a homogeneous distribu- 

 tion of molecules in solution if enough time elapses for the equilibrium 

 state to be reached. The Brownian motion is the visible result of thermal 

 motion, being due to numerous impacts by molecules on a visible par- 

 ticle; the actual motion observed is the resultant of the collisions occur- 

 ring practically simultaneously. It should be plausible that a molecule's 

 motion will be inversely related to its size. Since thermal equilibrium 

 means equal average molecular energies, the bigger molecules will have 

 smaller velocities. Thus, if we could follow the individual molecules well 

 enough to measure their average velocities, we could compute their mass 

 from the average thermal energy, using the formula 



average thermal energy = \ mass X (velocity) 2 

 or 



#therm = 2 ^^ ■ 



In practice, however, this approach is unworkable, because the mole- 

 cules of interest arc not large enough to be seen in the light microscope. 

 Indeed, if they could be seen, their masses could be estimated from their 

 volumes and some reasonable estimate or measurement of their densities. 

 Thus, when we wish to obtain information about masses of invisible 

 molecules, we have to resort to various stratagems. In the section on 

 centrifugation, it is shown how the information can be obtained by using 

 high speed rotors. Here we indicate how similar information can be ob- 

 tained from measurement of the thermal velocity. 



Since we cannot make visible the motion of a single molecule, we use 

 the device of measuring the motion of a large number of molecules. In 

 Fig. 37 we picture a tube on its side set up with the molecules of interest 

 in only one of the two compartments. When the compartments are slid 

 so that molecular interchange can occur, there is an average motion of 

 the molecules of interest, and it is this advancing boundary that gives us 

 a handle on the measurement. In the figure we see schematically what 

 happens when the two compartments are slid together. 



In the left-hand column of sketches, we represent the concentration of 

 solute molecules. In the right-hand column, we present the plot of con- 

 centration at various positions in the connected compartments. After a 

 while, the sharp concentration difference becomes blurred, as molecules 

 move towards the right. In the second column of sketches, we further in- 

 dicate the positions where the concentrations are '-\'\ of the original con- 

 centration and also Vi of the original concentration. As can be seen, as 

 time goes on these positions separate more and more from each other. By 

 measuring the actual concentration curve by optical absorption means 



