170 PHENOMENA, ATOMS, AND MOLECULES 



surrounded by a gas, where the vapor must diffuse outward through the 

 gas, the partial pressure of the vapor at the surface of the sohd will be less 

 than that of the saturated vapor. In other words, there will be a "concentra- 

 tion-drop" at the surface, just as there is a "temperature drop" in the 

 analogous case of heat conduction, and a "slip" in gases where viscosity 

 effects are involved. Analogy suggests that this concentration drop will be 

 inversely proportional to the pressure. 



In the previous calculations of the dissociation of hydrogen it was 

 assumed that the concentration of the hydrogen atoms close to the wire, 

 was that corresponding to equilibrium at the temperature of the wire. As 

 the experiments underlying these calculations were made at atmospheric 

 pressure, this assumption involved no serious error, but at the low pressures 

 which we are now to consider, such an assumption would render the 

 results worthless. 



In analyzing the effect of the surface concentration drop in our present 

 experiments, we may follow methods entirely analogous to those which we 

 adopted in estimating the temperature drop. 



Let us consider the mechanism of the phenomena occurring on and 

 aromid a tungsten wire surrounded by hydrogen, and heated to such a 

 high temperature that the hydrogen is partly dissociated. The hydrogen 

 molecules striking the surface come from an average distance of approxi- 

 mately l (the mean free path). A certain proportion of these molecules 

 leave the surface without change (reflected) and another portion is ab- 

 sorbed by the wire and may thus be dissociated. Similarly, hydrogen atoms 

 striking the filament may be absorbed or reflected. The hydrogen which is 

 absorbed probably reaches chemical equilibrium within the wire and the 

 atoms and molecules in certain proportions diffuse out and away from the 

 wire. We assume that the hydrogen not absorbed undergoes no chemical 

 change. 



Let lUo represent the rate at which hydrogen molecules strike the 

 surface of the filament (in grams per sq. cm. per second) and lui be the 

 corresponding rate for the hydrogen atoms. Let ai?ni be the rate at which 

 the hydrogen atoms are absorbed by the wire and aoino be the rate at which 

 the molecules are absorbed. Now in a stationary condition the total amount 

 of hydrogen escaping from within the wire must be equal to the rate at 

 which it is absorbed. We may look upon the surface of the wire as the 

 boundary of a space containing hydrogen in equilibrium. The rate at which 

 the hydrogen atoms in the metal reach the surface (from within) we shall 

 call III, and the corresponding rate for the molecules n-y. Similarly, we 

 shall let j^iiii be the rate at which atoms escape from the metal and /52n2 the 

 rate at which molecules escape. Then in a stationary state we have 



^i«i -h /?2W2 = aivii -f a2?M2. (15) 



