166 ACIDITY 



of the less concentrated to titrate a given quantity of the more concen- 

 trated. If solution A is titrated against solution B, the following rela- 

 tionship holds: 



volume of A X normality of A = volume of B X normality of B 



Thus if the normality of A is known, that of B may be calculated from 

 the titration data, since from the above equation it may be seen that 



volume of A X normality of A 



normality of B 



volume of B 



As an example of a typical standardization let us assume that 21.4 

 ml. of a solution of sodium hydroxide are required to neutralize 25 ml. 

 of tenth-normal (O.LV) oxalic acid. The normality of the sodium hy- 

 droxide solution will then be equal to 



25X0.1 ^,,^ 

 -^j;^ = 0.117 



We should say, therefore, that the sodium hydroxide solution is 0.117 

 normal, which means simply that it is 0.117 times as concentrated as a 

 normal solution. 



It is obvious that if solution A is one-tenth as concentrated as solution 

 B, a given volume of A is equivalent to one-tenth of that volume of 

 B. Likewise in the example just considered, 1000 ml. of the solution 

 that is 0.117 normal is equivalent to only 117 ml. of normal solution. 

 The volume of a solution used in a titration when multiplied by its 

 normality gives the equivalent volume of normal solution. In other 

 words, by means of this calculation one determines the volume that 

 the solution would occupy if it were exactly normal. 



Analysis of biological materials 



In order to determine the percentage of a given constituent in any 

 material, two things must be known, namely, the weight of sample taken 

 and the amount of standard solution needed to titrate it. The follow- 

 ing calculation of the citric acid content of lemon juice is typical: 



Weight of sample 5-0 g. 



Volume of alkali, normality 0.103, for titratioa 34.6 ml. 



Molecular weight of citric acid (HsCgHsOt) 192 



Hydrogen equivalent of citric acid 3 



Equivalent weight of citric acid 64 



Weight of citric acid per ml. of normal reagent 0.064 g. 



Volume of normal citric acid equivalent to alkali used for 



titration (34.6 X 0.103) 3.56 ml. 



Weight of citric acid in sample (3.56 X 0.064) 0.2278 g. 



(0.2278 X 100 \ 

 I 4.56 per cent 



