A METHOD FOR THE CALCULATION OF SOME QUANTITATIVE PROBLEMSL Some of the problems frequently arising in quantitative analysis require the calculation of the volume of the reagent or the weight of the product expected. Many of our textbooks insist on the value to the student of making these calculations before the analysis is begun. A general method for this purpose is outlined below. I t depends upon first finding the number of equivalents ("n") represented in the pure sample taken as standard or in the product obtained. This is derived from the molecular weight (given in parentheses in the illustrations) hut is either the molecular weight or some fraction of the latter, depending on the nature of the reaction involued. This quantity, n, will he not only the number of equivalents of the standard taken but also of the reagent used and of the resulting product, if this is weighed; it is also the number of cubic centimeters of 1 I am indebted to Professor M. G . MeUon, of Purdue, for his interesting article on I, NO. 6 ) "Calculating the Results of a Volumetric Analysis" (THISJOURNAL, and for the suggestion of publishing the present method, covering somewhat different ground than his.
VOL.2. No. 5
CALCU~ATION OP SOMEQUANTITATIVE PROBLEMS
345
any normal solution-of the sample, of the reagent or of any soluble product. The method is therefore quite inclusive for the particular problem. With this explanation, consider the following illustrative exercises: (1) From a pure sample of sodium chloride calculate the number of cubic centimeters of a silver nitrate solution (0.2N) required to precipitate the chlorine. (2) From a sample of standard Mohr's salt calculate the volume of concentrated ammonium hydroxide necessary to precipitate the iron, after oxidation; and (3) The cubic centimeters of concentrated nitric acid needed to oxidize the above iron. For these problems we have the following rapid solutions:
-
(1) NaCI(58 4 6 ) 270.6 (2) Mohr's Salt (392.1) 1000 (3) Mohr's Salt (392.1) 1000
"
No, of equivaleols N S/r Normality
S Mgs. $ample taken
58.46 130.7
392.1
'
4.63
02
7.65
15.1
2.54
47.4
-
z
Cc. reagent required
n/N AgNOs (0.2) 23.15 NHfiOH (15.1) 0.5
HNOs (15 8 ) 0 .05
NOTE1. The equivalent (e) of sodium chloride in (I), and of Mohr's salt in oxidation in (3), is the same as the molecular weight; but that of Mohr's salt, after oaidation and in precipitation as ferric hydroxide in (2), is one-third of the molecular weight. NOTE 2. The normality of the reagenLq to hydrogen is given in parenthesis. The normality used in the case of silver nitrate and ammonium hydroxide, marked N, is the same; but the normality of nitric acid, being here used as an oxidizing agent, is three times as great.
Another kind of problem is closely allied to the above, i. e., to find the normality of a solution to be used as a standard, from the weight of a product. The solution is illustrated as follows: P Mgs. 01 product obtained
-
n
P/e
cc. Reagent wed
z
Normality or reasent = d c e .
Other illustrations might be drawn from the standardization of sulfuric acid on the basis of the weight of barium sulfate produced, etc. Sometimes it is desired to know the weight of a precipitate expected from a sampie of pure salt. The method here is a slight modification of that given in the first three problems:
S Mgs. nample
(5) Mohr's Salt
(6) Mohr's Salt (392.1)
s
130.7 98.03
-"
No. of equivalent.
z
d
Mg.. pmdurt - n X d
7.65
26.6
FQO* (159.7)
10.21
116.7
BaSOd233.4) 1192
S/#
NOTE 1. From the previous discussion, the fraction of the molecular weight, proper to give the correct equivalent, c or c', will he readily understood. The primary determination, as shown by the six illustrations, is the establishment of the number of equivalents, "n". With this in hand, the student seems to have little difficulty in solving all the direct problems of the nature indicated.
