16 THE PROPERTIES OF SOLUTIONS. [CH. I. 



are freely ionised ; whilst " weak " acids, like acetic acid, 

 are only feebly ionised. 



By electrical measurements of the conductivity of the 

 solution it has been shewn that o.i N.HC1 is ionised to the 

 extent of 84 per cent, at i8C. If it were completely 

 ionised there would be o- i gm. of hydrion per litre. As it is 

 only partially ionised, 



(H) is o-i x = 0-084 = 8-4 x io- 2 at 18 C. 

 100 



Similarly, o.iN. acetic acid is only dissociated to the 

 extent of 1*36 per cent. So in this case 



(H) = o-i x ?- = 0-00136 = 1-36 x io~ 3 . 

 100 



This method of expressing the hydrogen ion concentra- 

 tion is not convenient. It is preferable to adopt the nota- 

 tion of Sorensen, who introduced the symbol PH to denote 

 the " hydrogen-ion-exponent." PH is the logarithm to the 

 base io of (H), the negative sign being omitted. In other 

 words 



PH = -log io (H). 



A few examples should make its meaning clear. 

 o-iN.HCl has (H) = 8-4 x io~ 2 . Now Iog 10 8-4 = 0-92. 

 So 8-4 x io- 2 = io' 92 - 2 = IO- 1 ' 08 . So P H = 1-08. 

 o-iN. acetic acid has 



(H) = 1-36 x io- 3 = io- 133 - 3 = io- 2 - 867 . 

 So PH = 2-867. 



It will be observed that PH decreases as the acidity in- 

 creases. Also that if (H) is doubled, P H is not halved, but 

 only decreased by 0-301, since Iog 10 2 = 0-301. 



It is important to note that the P H of a solution cannot 

 be determined by the ordinary method of titration. Let 

 us consider the case of o-i N.HC1 and o-i N. acetic acid. 

 If these be titrated with o-i N.NaOH until they each give 

 a pink with phenol phthalein, io cc. of each acid will 

 require exactly ic oc. of the alkali, and will therefore 



