11. Chemical Factors. The calculation of the weight of constituent in a given precipitate follows directly from the proportion:

MA, nM weight of precipitate : x

where MA, represents the molecular weight of the precipitate; M the atomic weight of the constituent or radical desired; and n the number of atomic weights of M in the molecular weight M„A,. Thus, suppose it is required to calculate the weight of iron in 0.6523 g. of ferric oxide. We would have from the stoichiometrical equation that

Fe2O32 Fe: 0.6523 gram :x
159.68 2 (55.84)

which, upon solving, gives, x = 0.4562 g. Fe.

Instead of evaluating proportions like the above each time, we can arrive at the result by one multiplication, if we multiply the weight of precipitate by that number which represents the weight of constituent corresponding to one gram of precipitate. Such a number is called a "chemical factor." For instance, the factor for Fe in Fe2O3 is 0.6994 and if, in the above example, we multiply 0.6523 by this number, we get 0.4562, which is the same. result we obtained by evaluating the proportion.

As an example to show how we calculate a chemical factor, let us calculate the factor of Na which is sought, in terms of NaCl found. We have by virtue of the stoichiometrical relationship between Na and NaCl, that

23.00

=

Atomic weight of Na
Molecular weight of NaCl 58.46

which upon solving gives 0.3934 as the value of the ratio, and this value is the chemical factor. It will be seen that the factor, multiplied by 100, gives the percentage of Na in NaCl, viz., 39.34%.

2. Calculate the percentage composition of the following compounds:

3. The combined weight of the sodium and potassium chlorides from 0.6066 g. of a sample of rock was 0.0318 g. The weight of the potassium chlorplatinate from the combined chlorides was 0.0681 g. What was the percent of potassium oxide and sodium oxide in the rock?

4. 1.0001 g. of a sample of disodium phosphate yielded 0.6172 g. of magnesium pyrophosphate. What was the percentage of PO4 in the sample? Ans. % PO 52.70%

=

5. The weight of magnesium pyrophosphate obtained from 1.1546 g. of sample of rock was 0.0432 g. Find the percentage of MgO.

6. In the analysis of a zinc-base alloy, 0.5280 g. of sample was dissolved in acid, and the solution submitted to analysis. Using all of the solution the following results were obtained: copper (electrolytically) 0.0044 g.; PbSO 0.0078 g.; SnO2 0.0376 g. The solution was then divided into two aliquots, the one giving Al2O3, 0.0679 g.; the other giving ZnSO4, 0.5143 g. The iron was determined in a separate sample and found to be 0.10%. Calculate the respective percentages of the metals determined.

Ans. Pb, 1.01%; Cu, 0.83%; Sn, 5.60%; Fe, 0.10%; Al, 13.64%; Zn, 78.88%

7. 1.0005 g. of a mixture of salts containing potassium sulphate, sodium chloride and sodium carbonate yielded 0.5380 g. barium sulphate. A separate portion of the sample lost 1.46% of its weight when dried at 105°-110°. What was the percentage of potassium sulphate on the original and on the moisture-free basis? Ans. 40.14%. 40.74%

8. A sample of ore contained 18.34% of lead, 12.68% of zinc, and 15.22% of water. What were the percentages of lead and zinc on the moisture-free

basis?

Ans. Pb
Zn =

=

21.63% 14.95%

Upon analysis, this 1.36% of sulphur.

9. A sample of coal yielded 8.36% of water at 85°. partially dried sample yielded 2.32% of moisture and What were the percentages of water and sulphur in the original sample?

10. 1.000 g. of a sample of moist marble lost 0.0210 g. at 110° and 0.4390 g. more on ignition at red heat. What is the probable percentage of water in the original sample?

Ans. 2.1%

13. References.

Textbooks

1. Blasdale, W. C. Principles of Quantitative Analysis. An Introductory Course. D. Van Nostrand Co., New York, 1917, 2nd ed., 70 illustrations, 402 pp.

2. Clowes, F. and Coleman, J. B. Quantitative Chemical Analysis. Adapted for use in the Laboratories of Colleges and Technical Institutes. Churchill, London, 1918, 11th ed., 580 pp.

3. Fay, H. An Advanced Course in Quantitative Analysis with Explanatory Notes. John Wiley & Sons, New York, 1922, 2nd ed., 115 pp.

4. Foulk, C. W. Introductory Notes on Quantitative Chemical Analysis. McGraw-Hill Book Co., New York, 1910, 250 pp.

5. Hamilton, L. F. and Simpson, S. G. Calculations of Quantitative Chemical Analysis. McGraw-Hill Book Co., New York, 1922, 200 pp.

6. Lincoln, A. T. and Walton, J. H. Exercises in Elementary Quantitative Chemical Analysis. The Macmillan Co., New York, 1912, 218 pp. 7. Mahin, E. G. Quantitative Analysis. McGraw-Hill Book Co., New York, 1919, 2nd ed., 605 pp.

8. Miller, E. H. The Calculations of Analytical Chemistry. The Macmillan Co., New York, 1906, 3rd ed., 201 pp.

9. Olsen, J. C. Quantitative Chemical Analysis. A textbook of Gravimetric, Electrolytic, Volumetric and Gasometric Methods with laboratory exercises giving the analysis of pure salts, alloys, minerals and technical products. D. Van Nostrand Co., New York, 1919, 5th ed., 555 pp.

10. Popoff, S. Quantitative Analysis. Containing Theory, Laboratory Directions, Problems, Explanations of Calculations, and Special Topics in Analytical Chemistry. P. Blakiston's Son & Co., Philadelphia, 1924, 342 pp.

11. Smith, George McPhail. A Course of Instruction in Quantitative Chemical Analysis for Beginning Students. The Macmillan Co., New York, 1921, 218 pp.

12. Talbot, H. P. Quantitative Chemical Analysis. An Introductory Course with Explanatory Notes and Stoichiometrical Problems. The Macmillan Co., New York, 1902, 3rd ed., 146 pp.

13. Willard, H. H. Laboratory Manual for the Course in Advanced Quantitative Analysis. Ann Arbor, Michigan. Mimeographed by Charles C. Edwards, Ypsilanti, Michigan, 1920, 5th ed., 164 pp.

General Reference Works

1. American Society of Testing Materials (A. S. T. M.). Methods. Philadelphia. Published triennially.

2. Classen, A. Ausgewählte Methoden der Analytischen Chemie. Mit 78 Abbildungen und einer Spectraltafel. Braunschweig F. Vieweg und Sohn, 1901. Erster Band, 940 s. Zweiter Band, 831 s.

3. Dennis, L. M.

434 pp.

4. Gooch, F. A.

Gas Analysis. The Macmillan Co., New York, 1913,

Methods in Chemical Analysis. Originated or developed in the Kent Chemical Laboratory of Yale University. John Wiley & Sons, New York, 1912, 1st ed., 536 pp.

McGraw-Hill

5. Griffin, R. C. Technical Methods of Analysis as Employed in the Laboratories of Arthur D. Little, Inc., Cambridge, Mass. Book Co., New York, 1921, 1st ed., 666 pp.

6. Mellor, J. W. A Treatise on Quantitative Inorganic Analysis, being Vol. I of A Treatise on the Ceramic Industries. Charles Griffin & Co., London, 1913, 778 pp.

7. Noyes, A. A. A Course of Instruction in the Qualitative Chemical Analysis of Inorganic Substances. The Macmillan Co., New York, 1922, 9th ed., 190 pp.

8. Prescott, A. B. and Johnson, O. C. Qualitative Chemical Analysis. A Guide in Qualitative Work with Data for Analytical Operations and Laboratory Methods in Inorganic Chemistry. D. Van Nostrand Co., New York, 1918, 7th ed., 436 pp.

9. Scott, W. W. Standard Methods of Chemical Analysis. A Manual of Analytical Methods and General Reference for the Analytical Chemist and for the Advanced Student. D. Van Nostrand Co., New York, 1922, 3rd ed., 2 vols., 1565 pp.

10. Stieglitz, J. The Elements of Qualitative Chemical Analysis. With Special Consideration of the Application of the Laws of Equilibrium and of the Modern Theories of Solution. The Century Co., New

York, 1912. Vol. 1. Parts 1 and 2, Fundamental Principles and
Their Application, 312 pp. Vol. II. Parts 3 and 4, Laboratory
Manual, 151 pp.

11. Sutton, F. A. A Systematic Handbook of Volumetric Analysis, or the Quantitative Estimation of Chemical Substances by Measure Applied

to Liquids, Solids and Gases. P. Blakiston's Son & Co., Philadelphia, 1924, 11th ed., 629 pp.

12. Treadwell, F. P. and Hall, W. T. Analytical Chemistry. John Wiley & Sons, New York, 1924, 6th ed. Vol. I. Qualitative Analysis. Vol. II. Quantitative Analysis.

Special Reference Works

1. Blair, A. A. The Chemical Analysis of Iron. A Complete Account of all the Best Known Methods for the Analysis of Iron, Steel, Pig Iron, Alloy Metals, Iron Ore, Limestone, Slag, Clay, Coal and Coke. J. B. Lippincott Co., Philadelphia, 1918, 8th ed., 319 pp.

2. Clark, W. M. The Determination of Hydrogen Ions. An Elementary Treatise on the Hydrogen Electrode, Indicator and Supplementary Methods with an Indexed Bibliography on Applications. Williams and Wilkins Co., Baltimore, 1922, 3rd ed., 552 pp.

3. Hillebrand, W. F. The Analysis of Silicate and Carbonate Rocks. Bulletin No. 700, U. S. Geological Survey, Department of the Interior, Washington, 1919, 285 pp.

4. Johnson, C. M. Chemical Analysis. Rapid Methods for Special Steels, Steel-Making Alloys and Graphite. John Wiley & Sons, New York,

1920, 3rd ed., 552 pp.

5. Lord, N. W. and Demorest, D. J.

Metallurgical Analysis. McGraw

Hill Book Co., New York, 1913, 3rd ed., 334 p.

6. Meyer, R. J. and Hauser, O. Die Analyse der seltenen Erden und der Erdsäuren, Ceriterden, Ytterden, Zirkonerde und Thorerde, Titansäure,

Niobsäure und Tantalsäure. Verlag von Ferdinand Enke, Stuttgart, 1912, 14 Abbildungen und 31 Tabellen.

7. Moore, R. B. and others. Analytical Methods for Certain Metals. Including Cerium, Thorium, Molybdenum, Tungsten, Radium, Uranium, Vanadium, Titanium and Zirconium. Bulletin No. 212, Department of the Interior, Bureau of Mines, Washington, 1923, 325 pp. 8. United States Steel Corporation, Pittsburgh, Pa.

Methods for the Commercial Sampling and Analysis of Iron Ores, 1914, 2nd ed., 62 pp.

Methods of the Chemists of the United States Steel Corporation for the Sampling and Analysis of Pig Iron, 1922, 40 0 pp.

Methods of the Chemists of the United States Steel Corporation for the Sampling and Analysis of Alloy Steels, 1921, 81 pp.

Methods of the Chemists of the United States Steel Corporation for Sampling and Analysis of Ferro-Alloys and Bearing Metals, 1920, 71 pp.