cool in a desiccator, weigh it. Transfer 2-3 grams of sample to the crucible, obtaining the exact weight; put the crucible and its contents in the oven at 110°-115° and dry for four hours or overnight; allow to cool in desiccator and weigh. Repeat the drying, cooling and weighing until constant weight is obtained (§ 49). The loss in weight is taken as representing the amount of moisture. 179. Indirect Determinations.12 - Indirect determinations are based upon the principle that if we have a mixture of two salts having the same acid or basic radicle it is possible to calculate the weight of each salt from the weights of the mixture and of the common radicle. Thus if we start with a known weight of a mixture of potassium and sodium chlorides and determine the weight of chlorine, then we can calculate the respective weights of the potassium chloride and the sodium chloride. The example that we have chosen, namely, the case where we have a mixture of potassium and sodium chlorides, has been purposely selected because it represents not only the best case which can be handled by the method of indirect determinations but also the most frequent case which is met with in practice.

Let it be given then that the weight of the mixed potassium and sodium chlorides taken for analysis was 0.5324 gram, and that the weight of the chlorine obtained from this sample was 0.2838 gram; we are to find the respective weights of the two chlorides.

12 For extended information on the subject of Indirect Determinations, consult the following: Mellor, loc. cit., § 13, p. 229.

J. Fages y Argili, Die indirekten Methoden der analytischen Chemie. Stuttgart, 1911.

W. M. Dehn, "Analysis of Mixtures of Halogen Acids," J. A. C. S. 31, 1273 (1910).

A variation of the foregoing scheme is to use one unknown quantity, but this scheme, while simplifying the algebra of the problem, complicates the arithmetic, as can easily be verified by working through the following solution:

A third scheme, which in the author's experience is far superior to either of the two preceding schemes, is this. Instead of letting x and y represent the grams of KCl and NaCl in the mixture, let them represent the number of moles of KCl and NaCl. This method leads to equations similar in form to those just considered but often easier to solve because the coefficients are not fractional, thus,

Let

x=

y

moles KCl in mixture

66

moles Cl in mixture

And 74.56 x = grams KCl

of Indirect Determinations cannot be applied to all pairs of salts, as a study of the following considerations will show.

13 The subject matter of this paragraph is adapted largely from Mellor, loc. cit., § 13, p. 229.

Let the two salts have the formula MA and NA, and let their combined weight in a mixture solely of the two be w, while the weight of the common constituent A is u.

Since the weight of the mixture itself is w, we have as the percentage of M in the mixture

wA u (A + N)

X

พ

and a similar expression for the percentage of N.

We see at a glance that the first factor of the right-hand member is constant for a particular pair of salts, and that the greater the value of this factor, the greater the influence of errors in the determination of u and w on the final result. With a mixture of potassium and sodium chlorides, the factor is nearly 7; with magnesium and calcium sulphates, 9; and with nickel and cobalt sulphates, 555. Thus so far as the calculations themselves are concerned, it is easy to see that the indirect method is applicable to a mixture of magnesium and calcium sulphates with almost as much reliability as it is to a mixture of potassium and sodium chlorides, while in the case of nickel and cobalt sulphates, the method is valueless because the errors in the determination are multiplied so enormously.

Hence, other things being equal, the calculated values of M and N will be the more accurate,

(1) The smaller the numerical values of the equivalent weights of the constituents M and N

(2) The greater the difference between the equivalent weights of the constituents M and N

(3) The greater the equivalent weight of the single constituent A.

In general, it is to be remarked that indirect methods of analysis are to be avoided.

181. Examples.

1. In standardizing an approx. 0.1 molar silver nitrate solution for use in Mohr's method, the following results were obtained by a student: c.c. silver nitrate solution required

g. NaCl used

What was the molarity of the silver nitrate solution?

Ans. 0.1063 M

2. How many g. of silver nitrate per liter will give a solution equivalent to 1 mg. of chlorine per c.c.?

Ans. 4.79 g.

3. What molarity of silver nitrate solution will be required in order that 1 c.c. of the solution shall represent 1% of potassium chloride in a sample when 0.500 g. of sample is taken for analysis? Ans. 0.06706 M

4. How many c.c. of 0.2 M HCl must be taken in order to yield a precipitate of 0.500 g. AgCl? Ans. 17.44 c.c.

5. From 0.5324 g. of a mixture of potassium chloride and sodium chloride, 1.1472 g. of silver chloride were obtained. What were the weights of potassium and of sodium in the mixture? Ans. 0.1567 g. K 0.0920 g. Na

6. A mixture of NaCl and KCl was treated with sulphuric acid, evaporated to dryness and ignited at red heat. The weight of the residue was 0.8066 g. This was dissolved in water and treated with an excess of BaCl2 after slightly acidulating the solution with hydrochloric acid. The precipitate was filtered off on a Gooch crucible, dried, and found to weigh 1.1670 g. What were the weights of NaCl and KCl in the original mixture?

7. From 0.5170 g. of a mixture of Na2CO3 and NaHCO3, 0.2420 g. of CO2 were obtained. What were the weights of each carbonate?

CHAPTER XI

FURTHER APPLICATIONS OF SOLUBILITY PRODUCT PRINCIPLE

PRIOR REMOVAL OF SILICON IN ANALYSIS. DETERMINATION OF SULPHUR AND PHOSPHORUS. VARIOUS ANALYSES INVOLVING SILICON, SULPHUR AND PHOS

PHORUS. FURTHER USE OF FACTOR VALUES

182. In proceeding to show further applications of the solubility product principle to the determination of some of the more common elements, it will be advantageous to select not only simple laboratory exercises for each element but to supplement such simple exercises by additional determinations that will involve the difficulty of one or more prior separations as an essential preliminary to the determination of the element or constituent desired.

Now it will be found in a great number of various determinations that the very first separation that must be effected before further work can be done on the desired constituent is the separation of silicon, so that the logical thing to do at this juncture is to familiarize ourselves somewhat in detail with this problem.

183. Prior Removal of Silicon. The frequency of the separation arises from two facts: first, that silicon (as silicic acid) is dragged down to a surprising degree by practically every insoluble precipitate; secondly, silicon is almost invariably associated with those elements which have to be determined by means of their insoluble precipitates, particularly such frequently occurring elements as phosphorus, aluminum, calcium, and magnesium that engage so large a part of an analyst's time because of their occurrence in the important classes of substances represented by iron and steel products, ferrous alloys, rocks, clays, soils, slags and cements.

The separation of silicon, in whatever form it may be found in the sample submitted, is based upon the procedure of getting it in the form of free silicic acid, then evaporating the silicic