FUNDAMENTAL EQUATIONS OF IDEAL GASES 379 

 In terms of v and t as independent variables [276] gives 



1 mi 8 m2 m3 , , , , 



- ai log — + - a2 log - - as log - (108) ]302] 



= A+Blogt- c/t, 



in which the values of ^, 5 and C are given by [303], [304], [305]. 

 The mass law is contained in the left-hand member of (108) 

 [302]. For, on multiplying and dividing each term by the 

 respective molecular weights, there results 



(1 , wi 8 , 1712 1 , wisN ,^^^^ 



rrr log — + rrr log — - — log — )• (109) 

 9ilf 1 ^ V QMz * y Ms V / ^ ' 



Multiplying and dividing the bracketed member by ilf 3 = 18, 

 and taking Mx = 2, M2 = 32, gives 



-|_log-+-log--log-j (110) 



but — ' etc., become — :' — :' ~~:' Using Dalton's law of par- 

 V Qit a2t azt 



tial pressures in its usual form pi = pxi, we jQnd 



The term in the partial pressures is the usual mass law expres- 

 sion, or Kp as the quantity is commonly designated, while the 

 remaining term in the a's is a constant. The case where /3i -|- 

 /32 — 1 is zero corresponds to the case where the sum of the 

 exponents of the partial pressures vanishes. An example exists 

 in the case of the union of H2 and I2 to form 2HI, where the 

 total pressure does not enter the reaction equation. 



27. Restatement of the Above in Different Notation. Em- 

 ploying mols as the unit of mass, and recognizing from the 

 foregoing that the variations of mass 5wi, bnii, . . . need only be 

 considered as ratios equal in value to the coefficients in the 

 chemical reaction, we write [300] as 



Smii'i ^ 0, (112) [300] 



