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PROTOPLASM 



means that pH 4 is, in actual concentration of hydrogen ions, one 

 thousand times as great as pH 7. Furthermore, in comparing 

 pH values and in making averages, actual hydrogen-ion con- 

 centration values must be used and not the logarithms of these 

 values, i.e., not pH values. The same should really be done 

 when plotting curves, if a true picture is to be given, but the 

 values become cumbersome. Striking and significant differences 

 are sometimes obtained when a curve is plotted on the basis of 

 pH values and then plotted for the same experiment on the 

 basis of actual hydrogen-ion concentrations. The error in using 

 the average of several pH values instead of the pH value of the 

 average of the hydrogen-ion concentrations is illustrated in the 

 following example. The average of pH 5 and 6 is pH 5.5, but 

 the pH of the average of the two hydrogen-ion concentrations 

 for which pH 5 and 6 stand is pH 5.3. Obviously, the latter is 

 the correct value to use. 



As there is a corresponding hydroxyl ion concentration for 

 every hydrogen-ion concentration, alkalinity as well as acidity 

 may be expressed in terms of pH. Hydroxyl ion concentration 

 could be expressed in terms of pOH as well, but pH serves the 

 same purpose. The following table gives a series of pH values 

 and the corresponding actual H+ and 0H~ concentrations in 

 molecules per liter, which, as each H+ ion weighs 1, become, in 



