Causes of Errors.—In the work which has just been described, some causes of error may occur to which the attention of analysts should be called.
The first is the error which may arise from the consumption of the small quantity of uranium phosphate which is taken with a stirring rod when the liquid is tested with potassium ferrocyanid. It is very easy to be assured that the end of the reaction has really been reached. For this purpose it is only necessary to note the quantity of the solution already employed and to add to it afterwards four drops; shake, and make a new test with a drop of the potassium ferrocyanid placed near the spot which the last one occupied. If a decidedly reddish tint does not appear at the moment of removing the glass rod, it is to be concluded that the first appearance was an illusion, and the addition of uranium is to be continued. If, on the contrary, the coloration appear of a decided tint, the preceding number may be taken for exact. It is then always beneficial to close the titration by this test of four supplementary drops which will exaggerate the coloration and confirm the figure found.
The second cause of error, and one moreover which is the most frequently met with, consists in passing the end of the reaction by adding the uranium too rapidly. In place of giving then a coloration scarcely perceptible, the test with the drop of potassium ferrocyanid gives a very marked coloration. In this case the analysis can still be saved. For this purpose the analyst has, at his disposal, a tenth normal solution prepared with 100 cubic centimeters of the standard solution of phosphoric acid diluted to one liter with distilled water. Ten cubic centimeters of this tenth normal solution are added, and the titration continued. At the end, the amount of additional phosphoric acid used is subtracted from the total.
A third cause of error is found in the foam which is often found in the liquid, due to the shaking. This foam may retain a portion of the last drops of the solution of uranium which fall upon its surface and prevent its mixture with the rest of the liquid. If the glass stirring rod in being removed from the vessel pass through this froth charged with uranium, the characteristic coloration is obtained before real saturation is reached. Consequently it is necessary to avoid, as much as possible, the formation of the foam, and especially to take care never to take the drop for test after agitation except in the middle of the liquid where the foam does not exist.
Suppose the titration has been made upon ten cubic centimeters of the normal solution of phosphoric acid in the conditions which we have just indicated, and the figure for the uranium obtained is 10.2 cubic centimeters; if now the correction, which may be supposed to amount to two-tenths cubic centimeter, be subtracted there will remain ten cubic centimeters of the uranium solution which would have precipitated exactly fifty milligrams of phosphoric acid.
The quantity of phosphoric acid which precipitates one cubic centimeter of the solution will be consequently expressed by the proportion ⁵⁰/₁₀ = five milligrams, which is exactly the strength required. In the example which has just been given, the inscription upon the flask holding the standard solution would be as follows: Solution of uranium, one cubic centimeter equals five milligrams of phosphorus pentoxid; correction, two-tenths cubic centimeter.
99. Titration of the Sample.—The strength of the solution of uranium having been exactly determined, by means of this solution the strength of the sample in which the phosphoric acid has been previously prepared as ammonium magnesium phosphate is ascertained. In this case the quantity of phosphoric acid being unknown, it is necessary to proceed slowly and to duplicate the tests in order not to pass beyond the point of saturation. From this there necessarily results a certain error in consequence of the removal of quite a number of drops of the solution of the sample before the saturation is complete. It is therefore necessary to make a second determination in which there is at once added almost the quantity of the solution of uranium determined by the first analysis. Afterwards the analysis is finished by additions of very small quantities of uranium until saturation is reached. Suppose, for instance, that the sample was that of a mineral phosphate, five grams of which were dissolved in 100 cubic centimeters, and of which ten cubic centimeters of the solution prepared as above required 15.3 cubic centimeters of the standard solution of uranium. We then would have the following data:
Mineral phosphate, five grams of the material dissolved in twenty cubic centimeters of hydrochloric acid.
Water, sufficient quantity to make 100 cubic centimeters.
Quantity taken, ten cubic centimeters = 0.50 gram of the sample taken.