210 PHENOMENA, ATOMS, AND MOLECULES 



The coefficient 2 is due to the fact that two atoms of hydrogen are produced 

 from each molecule. We thus obtain the equation 



20; = vi9i — a^ejj.1. (4) 



In a similar way we may consider the role played by the molecular 

 hydrogen. Since we have assumed that molecular hydrogen does not exist 

 as such on the surface, each molecule condensing on the surface must 

 fill two adjacent elementary spaces as two separate atoms. The rate at 

 which molecular hydrogen is removed by condensation on the heated wire 

 is thus a26-\i2 gram molecules per sq. cm. per second. This process will 

 be reversible. That is, adjacent hydrogen atoms on the surface may com- 

 bine together to form molecular hydrogen which then escapes from the 

 surface. The rate at which this occurs will evidently be V2^i^, since the 

 chance of two hydrogen atoms occupying adjacent positions will be pro- 

 portional to ^1". The coefficient Vo is the rate of evaporation when the 

 surface is wholly covered by atomic hydrogen (^1 = i). 



The difiference between the two rates will be equal to (o, the rate at 

 which molecular hydrogen disappears. Thus we obtain 



w = 026^2 — Vie,\ (5) 



The fractions 6 and Oi must fulfill the condition ^^ 



B+Bi <= I. (6) 



These three equations, 4, 5 and 6, enable us to calculate the equilibrium 

 constant in the gas phase in terms of the quantities ai, a2, Vi and V2. 



There are several possible definitions of the equilibrium constant, as 

 follows : , , 



^p = piyp2 (7) 



K, = c,'/c2 (8) 



Kp = iuiVwj (9) 



Here pi and po are the partial pressure of atomic and molecular hy- 

 drogen in equilibrium with each other, while Ci and C2 are the correspond- 

 ing concentrations. The third equilibrium constant K^ as defined by (9) 

 will be found very convenient in dealing with heterogeneous reactions. 

 Since p = cRT the relation between Kp and Kc is 



Kp = RTK,. (10) 



« 



^^ Provided the surface is perfectly clean. The presence of a gas (othefwise inert) 



which is strongly adsorbed on the surface will cause the larger portion of the surface 



to be covered with inert molecules (or atoms). Thus the Equation 6 becomes + 6^ = 



-I — O2 where G2 represents the fraction of the surface covered by the inert substance. 



This theory of catalytic poisons will be developed in subsequent papers. 



