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, 

 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 C H , as has been done above, SSrenson 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 1.3xlQ- 3 . Since 

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



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 C H , or P H , 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 H- 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 P O H, 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 = 

 113864 



*Strictly speaking, PH is the logarithm to the base 10 of the concentration of H ions in grams 

 per liter, the negative sign being understood. 



flf we wish to express the value of PH in ordinary notation, we must find the antilogarithm 

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

 the antilogarithm of 0.55 being 3.55, the CH is 3.55 x 1Q- 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, PH-* 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 fiters 

 constitutes a neutral solution (PH = 7). 



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

 given, it is most convenient to use the former. 



