HYDROGEN-ION CONCENTRATION 27 



(0.1 N HC1) that is, a hydrochloric acid solution containing one tenth 

 of the molecular weight of hydrochloric acid in grams dissolved in a 

 liter of water. At this dilution HC1 is 91 per cent dissociated; therefore 

 the H-ion concentration (or C H as it is written for short) is 0.091 N t 

 or, in mathematical notation, 9.1 x 10 2 . 



Method of Expressing C H . To avoid the necessity of having to use 

 several figures to express CH, as has been done above, Sorenson has intro- 

 duced a scheme by which only one figure is required. This figure, des- 

 ignated by P H , is found by subtracting from the power of ten (i. e., 

 the figure standing behind 10) the common logarithm of the figure ex- 

 pressing the normality of the acid. In a decinormal HC1 solution, 

 therefore, we must subtract from the power 2, the common log. of 9.1, 

 which is .96 (ascertained from logarithm tables), leaving 1.04. . Take 

 another example: decinormal acetic acid is dissociated only to the ex- 

 tent of 1.3 per cent ; C H is therefore 0.0013 normal, or 1.3 x 10' 3 . Since 

 the logarithm of 1.3 is .11, P H equals 3-.11, or -2.89.* 



The only objection to the use of the exponent P H as an expression of 

 the H-ion concentration is that it increases in magnitude as the acidity 

 becomes less; this is because the negative sign of the power is disre- 

 garded. As stated above, it is usual to express the strength of alkalies 

 as well as acids in terms of CH, or PH, because it is easier to measure the 

 concentration of H ions than of OH ions. A 0.1 NaOH solution is 84 

 per cent dissociated; therefore the "OH" ion is 0.084 N (i. e., 0.084 gram 

 equivalents OH per liter), and since the product of the II and OH' 

 concentrations must always equal 10- 14 - 14 (at 20 C.), it is clear that as 

 the H ion increases in concentration, the OH ion must reciprocally de- 

 crease. Expressed according to the above scheme, the 0.084 N NaOH 

 solution gives P H 13.06; thus, 0.084 = 8.4 x 10' 2 ; the log. of 8.4 is .924, 

 and this subtracted from the power -2 = 1.08 as POH, or 14.14 - 1.08 = 

 13.06 as P H .** 



Similarly, P H of 0.1 N NH 4 HO solution is 11.286. Its dissociation is 

 1.4 per cent; therefore the solution contains only 0.0014 gram equivalents 

 HO i. e., 1.4 x 10- 3 P OH = 3 - 0.146 = 2.854 . . P H 14.14 - 2.854 = 

 11.286.f 



*If we wish to express the value of Pit in ordinary notation, we must find the antilogarithm 

 of the difference between the value of PH and the next higher whole numher; e. g., if PH = 7.45, 

 the antilogarithm of 0.55 being 3.55, the CH is 3.55 x 10' 8 , or 0.000,000,0355 N, or 3.55 gm. mol. 

 H ion in 100,000,000 liters. 



**It must be remembered that the power of a number indicates the number of times by which 

 that number must be multiplied by ten; thus, Pn- 6 does not mean that the H ion is six times less 

 than PH, but 1 x 10 x 10 x 10 x 10 x 10 x 10, or 1,000,000 times less. Similarly, Pn' 3 is 1000 times 

 as great as PH-, not twice as great. 



A solution containing almost exactly 1 gram molecule of dissociated hydrogen in 10,000,000 liters 

 constitutes a neutral solution (Pn 7). 



tThe expressions PH and CH may be used indiscriminately, but when the numerical value is 

 given, it is most convenient to use the former. 



