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how much sulphate of potass is present, and how much sulphate of soda?

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The 20 grammes of the mixture consist accordingly of 12.9 Na O, SO,, and 7.1 K O, SO,.

b. Indirect separation of chlorine from bromine, (§ 133, 1, B.) Let us suppose the mixture of bromide of silver and chloride of silver to have weighed 20 grammes, and the decrease of weight consequent upon the transmission of the chlorine to have amounted to 1 gramme. How much chlorine does the mixture contain, and how much bromine ?

Here it need simply be borne in mind that the decrease of weight is the difference between the weight of the bromide of silver originally present and that of the chloride of silver which has replaced it, to understand the following formula without difficulty. The difference between the respective equivalents of bromide of silver and chloride of silver is to the equivalent of bromide of silver as the ascertained decrease of weight is to a, i. e. to the bromide of silver originally present in the mixture; or, expressed in numbers:

556.43 2348.64 :: 1: x

x= 4.221

The twenty grammes of the analysed mixture contained accordingly 4.221 grammes of bromide of silver, and consequently 20-4.221-15.779 grammes of chloride of silver.

It results from this calculation, that we need simply multiply the ascertained decrease of weight with

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in order to find the amount of bromide of silver originally present in the analysed mixture. And if we once know this, we know of course likewise the amount of the chloride of silver, and from these data

we deduce subsequently, according to 2. the respective amount of bromine and chlorine present in the analysed mixture, and, according to 1. the respective percentage weight of these elements.

APPENDIX To I.

AVERAGE VALUES, DFFICIENCY, AND SURPLUS IN ANALYSES.

$162.

If, in the analysis of a substance, we estimate one constituent from the deficiency, or, in other words, if we estimate the amount of one constituent by subtracting from the original weight of the analysed substance the omitted weight of the remaining constituents, it is quite evident that in our subsequent calculation upon percentage weights, we must of necessity invariably obtain 100 as sum total. Every deficiency or surplus occurring in the determination of the respective individual constituents will fall exclusively upon the one constituent which is estimated from the difference between the original weight of the analysed compound and the united weight of the constituents which have been directly determined; it is evident, accordingly, that quantitative estimations of this kind afford a sufficient degree of accuracy only in cases where the other constituents have been determined with great precision. The accuracy of the results will be greater, of course, the less the number of the constituents that have been determined in the direct way.

If, on the other hand, every constituent of the analysed compound has been determined individually, it is obvious that, were the results absolutely accurate, the united weight of the several constituents must be exactly equal to the original weight of the analysed substance. Since, however, as we have seen at § 70, certain inaccuracies attach to every analysis, without exception, the sum total of the results in the calculation upon percentage weights will sometimes exceed, and at others fall short of one hundred.

In all cases of this description, the operator should express the results actually found.

Thus, for instance, PELOUZE found, in his analysis of chromated chloride of potassium,

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Thus BERZELIUS found in his analysis of potasso-peroxide of uranium :

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It is altogether inadmissible to distribute any chance deficiency or surplus, proportionally upon the whole of the constituents, since such deficiency or surplus is not equally attributable to the several estimations of the individual constituents, and, moreover, because this way of arranging the calculation of the results deprives other chemists of all power of judging of the accuracy of the analysis. No one need be ashamed to confess having obtained somewhat too little or somewhat too much in his analysis, provided, of course, the deficiency or surplus be confined within certain limits, which are different in different analyses, and which the experienced chemist knows invariably how to fix properly.

In cases where an analysis has been made twice or several times, it is usual to take the average value as the most correct result. It is obvious that this average result deserves the greatest confidence the less it differs from the results of the individual

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analysis, (which should always be given either fully, or at least, as regards the maximum and minimum.)

Since the accuracy of an analysis is not dependent upon the quantity of substance subjected to the analytical process, (provided always this quantity be not altogether too small,) the average of the results of several analyses is to be taken quite independently of the quantities respectively used in the several analyses, which means, in other words, that the operator must not add together the quantities respectively used, on the one, and the respective weights of the determined constituent on the other hand, and deduce from these data the percentage amount; but the latter is to be calculated for every individual analysis and the average is to be subsequently deduced from the results.

Suppose a substance AB. to contain fifty per cent. of A.; and suppose two analyses of this substance to have yielded the following results:

1)2 grammes of AB. yielded 0.99 grammes of A.

2) 50

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From analysis

No. 1, it results that AB. contains 49.50 per cent. of A.

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It would be quite erroneous to say

2+50=52 of AB yielded 0.99+24.00=24.99 of A.

which would give for 100 of AB. .. 48.06 of A;

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for it will be readily perceived that this way of calculating destroys nearly altogether the influence of the better analysis of the two, (1) upon the average, on account of the proportionally small amount of substance subjected to the analytical process.

II. DEDUCTION OF EMPIRICAL FORMULE.

$ 163.

If the percentage composition of a substance is known, a so styled empirical formula may be deduced from this under any

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circumstances, which means, in other words, the relative proportion of the several constituents may be expressed in equivalents-in a formula which, upon re-calculation upon percentage weights, gives figures corresponding perfectly or nearly with those deduced from the analysis of the substance in question. For all those substances of which we cannot determine the atomic weights, such, for instance, as mannite, wood fibre, mixed substances, &c., we are compelled to confine ourselves to the expression of empirical formulæ.

The method of deducing empirical formula is very simple and will be readily understood from the following reflections:

How would we proceed to find the relative number of equivalents in carbonic acid?

We would say:

The equivalent of the oxygen is to the proportional amount of oxygen in the atomic weight of carbonic acid, as 1 is to x, i. e. to the number of atoms of oxygen contained in carbonic acid; accordingly

100 200 :: 1: x
x=2

In the same manner we would find the number of atoms of carbon present in carbonic acid, by the following proportion :

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Now let us suppose, we did not know the atomic weight of carbonic acid, but simply the percentage composition of this acid, viz.,

27.27 of carbon

72.73 of oxygen

100.00 of carbonic acid;

yet the relative proportion of the equivalents must appear, even though we select any other given number, e. g. 100, as the atomic

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