56 IONISATION 



[OH~] =the fraction of the total water which is disso- 

 ciated into hydroxyl ions 



and [H 2 O] =the fraction of the total water which is left 



undissociated. 



Stated in words, the product of the concentration of hydrogen 

 ions and hydroxyl ions is always equal to a constant quantity K w , 

 The value of K w , the ionisation constant of water, depends only 

 on the temperature. 



1 



At or ~K = n^ 



w 10,000,000,000,000,000' ' k ' 

 At 23 C. K w = 100;000;000;000;000 ( 2 ) 



OQ 



At 40 C. r 



ioo,ooO,000,000,000 .................. 



At 100 C. K w =- 4S ..(4) 



100,000,000,000,000 



To save writing those cumbrous fractions, the index notation 

 is used. Thus fraction 



(1) is = 0-01 xlO- 14 =C W at C. 



(2) is - 1 xlO~ 14 =C W at 23 C. 



(3) is = 28 XlO- 14 =C W at 40 C. 



(4) is = 48 X10~ 14 =C W at 100 C. 



Now, as the quantity of water dissociated is so very small 

 compared with the total quantity of water, it is clearly legitimate 

 to put [H 2 O] 1 in the mass action equation, which now becomes : 



It is obvious that H + and OH" are produced in equal amounts, 

 and therefore [H+] =[OH~] W^. 



Between 22 and 23 C. water has a dissociation constant with 

 which it is convenient to work, and measurements of hydrogen 

 ion concentrations are usually made at this temperature or 

 referred to this temperature ; 



i.e. at 23 C., K w =10~ 14 ; 

 .'. [H+]x[OH-]=10- 14 . 

 [H+] is therefore equal to JlQ- 1 * =10~ 7 , 

 and [OH-] VlO^-lO- 7 . 



It is usual to write H* for H+ and OH' for OH~. 



