304 PROTOPLASM 



expressed by the values 1 and 10 '^ which represent the actual 

 weight in grams of the hydrogen io7is in a normal acid and a 

 normal alkaline solution. As the weight of H+ ions in pure 

 water is 10"'^ gram per liter, while in a normal solution of alkali 

 it is but 10"^*, some of the free hydrogen ions in water must 

 be lost (taken up) when an alkali is added. The product 

 [H+] X [OH"J = 10~^* remains constant in all aqueous solutions. 

 Neither the selected maximum of the hydrogen-ion scale (1 gram 

 of hydrogen per liter as represented by a normal solution of 

 acid) nor the minimum (lO"^"* gram of hydrogen per liter as 

 represented by a normal solution of alkali) is a true maximum 

 or minimum, for twice or thrice normal acid and alkali possess a 

 greater proportion of acid or alkaline ions. Normal hydrochloric 

 acid contains 1 gram of hydrogen ions per liter; twice normal 

 contains 2 grams; and thrice normal, 3 grams. Such concentra- 

 tions are practically never met with in nature and rarely in 

 physiological work. Consequently, normal acid and normal 

 alkali give a convenient and practical range of acidity and 

 alkalinit}^, from 1 gram to 10~^^ gram by weight of hydrogen 

 per liter. The value of 10"'^ gram per liter of hydrogen ions 

 for pure neutral water is the midway point and becomes an 

 indication of neutrality (at 20°C.). 



To express or plot as a curve the entire range in hydrogen-ion 

 concentration from 1 to 10~^* gram, with 1 inch equivalent to the 

 change from 0.0000001 to 0.000001 (10"^ to 10-«), would require a 

 sheet of paper 2,000,000 inches, or nearly 32 miles, long. Seldom 

 is it necessary to plot so great a range, but often the range is 

 extensive. It is evident that an abbreviated form in which to 

 express hydrogen-ion concentration is needed. If we select any 

 convenient mixture of, say, acetic acid and sodium acetate with 

 a hydrogen-ion concentration of 0.000018 gram per liter, this 

 value can be stated in any of the following ways: 



1.8 X 10-5 = lOO-^s X 10-5 = 10-"-^^ 



The simplest of these figures is the last or, with the 10 understood, 

 just the negative logarithm, —4.75. The negative logarithm, 

 therefore, is sufficient to express a hydrogen-ion value. The 

 actual hydrogen-ion concentration, in grams per liter, of normal 



