ON ELECTROLYSIS IN ITS PHYSICAL AND CHEMICAL BEAEINGS. 367 



' For strong acids and bases a8j(3y is a number of several millions, while .r is 

 necessarily always less than 1 and n : hence to satisfy the equation it is neces- 

 sary that (1 — .(■) (n—x) shall be very small (unless^ is enormous) ; that is to say, 

 X must be almost equal to 1 (if n is greater than 1), or to »t (if n is less than 1). 



(24) If one mixes a strong acid ivith a strong base, they unite for the most 

 part to a salt, in such a wag that there is formed a quantity of salt 

 always a little less than that of the hydrate of which one has added 

 the smallest equivalent portion. 



[This is rather an anticlimax.] 



The clearest way to see this is to work some numerical examples. We have 

 therefore made calculations onmixtiu'es of a strong base (caustic soda) with a strong 

 acid (nitric acid) on the one hand, and of a weak base (ammonia) with a feeble 

 acid (boracic acid, supposed monobasic) on the other. The figures employed are 

 taken from apre^dous section,' with the supposition that the molecular conductivitv 

 of ammonic borate is equal to that of ammonic carbonate (an hypothesis which 

 ought to be approximately correct). We have thus calculated that if one mixes 

 1 equivalent of acid with n equivalents of base in 100 equivalents of water, the 

 amount of salt formed (.i) is given in the table below for several values of n. 



1 Nitric Acid and n Caustic Soda. 



1 Boracic Acid and n Ammonia. 



[The molecular conductivities used in this calculation are probably — 



For HNO, 

 For NaHO 

 For NaNOj 

 For H,0 . 



a= 3x10-5 

 S = 1^5 X 10-5 

 |3 = 6 X 10-« 

 y= 10 



\t 



For boracic acid . a = 4^4 x 10-* 

 For ammonia . 8 = 8^4 x 10-** 

 For ammonic borate /3 = 4 x 10-" 

 For water . . y = 10"'^ 



so that — - in the first case equals 10 , and in the second case equals 100, or 



py 

 thereabouts.] 



What we have just said applies specially to the formation of salts of strong acid 

 and base when the quantity of water is very considerable. From the above example 

 (the formation of NaNOj), as well as from proposition 24, we proceed to de- 

 duce the following observation, true for salts of strong acid and bases : — 



(25) The quantity of salt formed when one adds a strong base to a strong add 

 is sensibly proportional to the quantity of base added, until the acid is 

 saturated, after which the formation of salt sensibly ceases. 



An entirely different aspect is presented by the figures calculated for the for- 

 mation of a salt from feeble constituents, such as borate of ammonium. In this 

 case a8//3y is not excessively great, so that for considerable quantities of water {p) 

 it is not necessary for either l-.r or n-r to nearly vanish. That is to say, 

 although the acid is in excess, the free portion of base is nevertheless sensible, and 

 vice versa. In this case we may apply equation (4), regarding aU quantities con- 

 tained in it except .i- and n as constant, and q (the original amount of salt) as zero. 

 We thus find that — 



dn , . ./I 1 1\ 



= 1 + («-.?■)- + + — ) 



' \1 — .r p + X X / 



dx 



' [§ 5, i.e., from Kohlrausch's tables of molecular conductivity, as then published.] 



