FUNDAMENTAL EQUATIONS OF IDEAL GASES 387 



31. A More General Application of the Gibhs-Dalton Rule. 

 A more general reaction equation than (114) [309] may be 

 readily obtained by applying the Gibbs-Dalton rule in the 

 form p = 2pi using the equation (VII) to compute the pi's. 

 The equations for energy (53), entropy (54), and \p (55), have 

 already been given, and from these the equation for 2 vim may 

 be formed and the equilibrium equation found, i.e., 



(129) [309] 



2 ^1^1 = 0' 



2j vi log kp = 2^vi log poXi - 2 y "-'bIhx 



where Sj'i log pnXi is given by equation (114) [309]. The 

 second term of the right hand member of (129) [309] may be 

 written, using (Vila) and omitting ai, 0:2, • • . 



-is ''^^^^^ = i [S ''^^^ Rt-1^ '^''^^^ ^^30) 



Substituting in (129) [309] there is obtained 



2j vi log pxi — 2j^i log poXi 



"^1^1X1 Ai Si'i.riiSi 



Rt 



V- (131) 



Thus it is seen that at constant temperature the left hand mem- 

 ber, or the quantity log K^/Kq should vary with the pressure. 

 For the reaction N2O4 -^ 2NO2 we may write 



log KJK, = - 



■(2^1 + ^2) (2Ai + A,) 



Rt 



(Rty 



] 



Xip 



+ 



'§2 



Rt 





(132) 



where /3i, (32, Ai, A2, are the constants of the equation of state 

 for the gases NO2 (mol fraction Xi) and N2O4 (mol fraction x^). 

 At constant temperature and low pressure, Xi the mol fraction 

 of the simple species is small, and log Kp/Ko depends more 

 largely on the second term of the right hand member, which is 

 independent of Xi but proportional to pressure. The coefficient 



