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Title: The Elements of Qualitative Chemical Analysis, vol. 1, parts 1 and 2.

Author: Julius Stieglitz

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*** START OF THE PROJECT GUTENBERG EBOOK THE ELEMENTS OF QUALITATIVE CHEMICAL ANALYSIS, VOL. 1, PARTS 1 AND 2. ***

THE ELEMENTS OF QUALITATIVE CHEMICAL ANALYSIS

WITH SPECIAL CONSIDERATION OF THE APPLICATION OF THE LAWS OF EQUILIBRIUM AND OF THE MODERN THEORIES OF SOLUTION
BY JULIUS STIEGLITZ Professor of Chemistry in the University of Chicago
VOLUME I PARTS I AND II FUNDAMENTAL PRINCIPLES AND THEIR APPLICATION
NEW YORK THE CENTURY CO. 1920
Copyright, 1911, by THE CENTURY CO.



Printed, October, 1911
Reprinted, August, 1912
Reprinted, October, 1913
Reprinted, October, 1915
Reprinted, August, 1917
Reprinted, January, 1919
Reprinted, August, 1919
Reprinted, November, 1919
Reprinted, July, 1920

PREFACE

In venturing to add another book on Qualitative Chemical Analysis to the long list of publications on this subject, the author has been moved chiefly by the often expressed wish of students and friends to have his lectures on qualitative analysis rendered available for reference and for a wider circle of instruction. Parts I and II of the present book embody these lectures in the form to which they have developed in the course of the last sixteen years, since, in 1894, the teaching of analytical chemistry, along the lines followed, was first suggested by Ostwald's pioneer "Wissenschaftliche Grundlagen der Analytischen Chemie."

The author believes that instruction in qualitative analysis, besides teaching analysis proper, should demand of the student a very distinct advance in the study of general chemistry, and should also, consciously, pave the way for work in quantitative analysis, if it is not, indeed, accompanied by work in that subject. The professional method of work, whether routine or research work of the academic or the industrial laboratory is involved, inevitably consists in first making an exhaustive study of the general chemical aspects of the subject under examination: it includes a thorough study of books of reference and of the original literature on the subject; and when the experimental work is finally undertaken, it is carried out with a critical, searching mind, which questions every observation made, every process used. The method of instruction in this book aims at developing these habits of the professional, productive chemist. For the reasons given, a rather thorough and somewhat critical study is first made (in Part I) of the fundamental general chemical principles which are most widely involved in analytical work. The applications of these principles to the subject matter of elementary qualitative analysis are then discussed (in Part II), in closest connection with the laboratory work covering the study of analytical reactions (in Part III). The material is presented, not as a finished subject, but as a growing one, with which the present generation of chemists is still busy, and which contains many important, unsolved problems of a fundamental character. Numerous references to standard works and to the current literature are given, of which those suitable for reading by the young student are specially designated. The obvious demand is thereby made on the student to aim to remain in touch with the growth of the science, after he has completed his studies under the guidance of an instructor. Finally, to arouse and develop the critical, questioning attitude of the professional chemist, referred to above, the subject matter of the laboratory work, given in Part III, is put very largely in the form of questions, which demand not only careful observation on the part of the student, but also a thoughtful interpretation of the observations made.

In the experience of the author, although the majority of students attending his lectures had already acquired some knowledge of chemical and physical equilibrium, of the theories of solutions and of ionization and of their applications, the more exhaustive treatment of parts of these subjects and of related topics, to which a course in qualitative analysis lends itself, has been of particular benefit to them, bringing them into closer touch with the method of detailed study of a chemical topic, than the broader, more varied work of general chemistry courses usually does. Throughout the theoretical treatment of the subject, the attempt is made to prepare the student for a more general quantitative expression of chemical relations. For this reason, chemical and physical equilibrium constants are given and used, wherever it is possible. The author is aware that these "constants" have, in part, only a temporary standing; that more exact work will continually modify their numerical values and, probably, limit the field for their rigorous application. The latter facts can be impressed on the student and still the invaluable principle be inculcated in his mind, that chemistry is striving to express its relations, as far as possible, in mathematical terms, exactly as its sister science, physics, has long been doing. At the same time the treatment of physicochemical topics has been kept within the bounds set by the subject matter, and by the chemical maturity of the students addressed: it is elementary in form, and quantitative relations are used, in the main, only to elucidate qualitative facts. The rigorous development of the subjects presented and their elaboration from a purely physicochemical standpoint are left to advanced courses. It has been found that this method interests the better class of students in seeking such advanced courses.

The relations of qualitative to quantitative analysis are touched upon in the theoretical treatment, where it has been feasible to do so. The laboratory methods aim also at beginning the training of students in the habit of accuracy demanded by quantitative analysis, by laying special emphasis on the methods of detecting traces of a number of the common elements and by requiring a report on the relative quantities of components found. The study of reactions is carried out, almost wholly, with solutions of known and uniform molar concentration. However, the actual development of quantitative accuracy is left to the instruction in the courses in quantitative analysis, in which a successful training in this direction is far more readily attained. Simultaneous courses in the two branches of analysis seem to the author to be highly desirable, whenever practicable. The study of quantitative analysis adds neatness of manipulation and accuracy to the work in qualitative analysis; and the latter supplies the opportunity for the further development of a student's knowledge of general chemistry, for which there is a much smaller scope in quantitative analysis courses, and thus relieves a condition where a serious pedagogical defect is likely to exist in the development of our students.

Parts III and IV of this book are published in a separate volume, as a laboratory manual for qualitative analysis. They comprise the instructions for laboratory work introductory to systematic analysis (the study of reactions and of the analysis of groups, in Part III) and an outline for elementary systematic analysis (Part IV). The attempt has been made, in particular, to bring the laboratory work, which otherwise follows the usual lines of instruction in systematic analysis, also into closest relations to the development of the scientific foundations of analytical chemistry, as represented in Parts I and II. It is believed that the subject matter lends itself especially well to such a close interweaving of the two sides of the study, without any special loss of time to the student, and with the result, it is hoped, of a greatly increased interest on his part and an increased stimulus of the habit of scientific thought.

The following plan of work is used by the author with his classes: The first section (lasting eleven weeks) of the course in qualitative analysis is started with some seven to ten (according to the ability of the class) lectures or classroom exercises, given daily, and covering the first seven or the eight chapters of Part I. At the end of the second week the laboratory work is started. During the remainder of this section of the course, two hours of classroom work and eight hours of laboratory work per week are required, and, in this period, Part III, comprising the first half of the laboratory manual, is studied in the laboratory in closest connection with the classroom work on Part II of the book. As far as possible, the laboratory work on a given topic precedes the classroom work. This first course is followed by an eleven weeks' course in systematic analysis, covering Part IV of the book. A third (graduate) course, optional for students specializing in chemistry, is offered, in which very complex commercial and natural products are analyzed and in which special attention is also given to rare elements. During this course, particular care is taken to familiarize students with other works on qualitative analysis, such as the outlines of A. A. Noyes and Bray, and the special parts of Fresenius's manual.

Students who have been prepared in general chemistry along physicochemical lines, as represented, for instance, by Smith's textbooks, make more rapid and more easy progress in the first course than do students otherwise prepared. But the treatment of the subject is intended to make it possible for students, who have not paid particular attention to chemical equilibrium and to the modern theories of solution in their general chemistry course, to complete the course within the time limit indicated. Perhaps one-third of the students in an average class, in the past, have taken the course under these conditions and no special difficulty was encountered by them.

In the theoretical treatment the author is particularly indebted to the original articles and to the larger works of Arrhenius, van 't Hoff, Nernst, A. A. Noyes, Ostwald, and Walker. For the systematic analytical material acknowledgment is due, in particular, to Fresenius's "Qualitative Chemical Analysis," and to the important publications by A. A. Noyes and Bray in the Journal of the American Chemical Society. Some of the excellent methods of the latter authors have been adopted outright, as indicated in the text. For some special matters the author is indebted to the texts of W. A. Noyes and of Böttger. Constant references to his sources of information have been made by the author, partly as a matter of acknowledgment, and more particularly to give students and teachers the opportunity for more extended, first-hand reading on any topic of interest. References suitable for college students are indicated by the addition of (Stud.). In two or three instances, the original source of information has been forgotten and diligent search has failed to trace it. For use in preparing any future edition of the book, the author will be glad to have his attention called to the facts by authors.

The author wishes to express here his particular appreciation of the generous assistance given him by his former colleague, Prof. Alexander Smith of Columbia University, whose suggestions and advice, especially in the editing of the manuscript and proof, have been invaluable. He also wishes to make grateful acknowledgment to his colleagues, Profs. H. N. McCoy, H. Schlesinger, and Dr. Edith Barnard, to Prof. L. W. Jones of the University of Cincinnati, Prof. E. P. Schoch of the University of Texas, Prof. B. B. Freud of Armour Institute, and Prof. W. J. Hale of the University of Michigan, who have assisted him by reading the proofs or the manuscript, or by carrying out experimental studies underlying part of the work, or in other ways. Corrections of his mistakes of omission and commission, and suggestions, will be gratefully received by the author.

JULIUS STIEGLITZ.

Chicago, September, 1911.

CONTENTS

PART I
FUNDAMENTAL PRINCIPLES
CHAPTER PAGE
I. Introduction 3
II. Osmotic Pressure and the Theory of Solution, I 8
III. Osmotic Pressure and the Theory of Solution, II 21
IV. The Theory of Ionization: Ionization and Electrical Conductivity 33
V. The Theory of Ionization, II: Ionization and Osmotic Pressure; Ionization and Chemical Activity 67
VI. Chemical Equilibrium. The Law of Mass Action 90
VII. Physical or Heterogeneous Equilibrium.—The Colloidal Condition 118
VIII. Simultaneous Chemical and Physical Equilibrium.—The Solubility- or Ion-Product 139
PART II
SYSTEMATIC ANALYSIS AND THE
APPLICATION OF FUNDAMENTAL PRINCIPLES
IX. Systematic Analysis for the Common Metal Ions. The Ions of the Alkalies and of the Alkaline Earths. Order of Precipitation of Difficultly Soluble Salts with a Common Ion 157
X. Aluminium; Amphoteric Hydroxides; Hydrolysis of Salts. The Aluminium and Zinc Groups 171
XI. The Copper and Silver Groups. Precipitation with Hydrogen Sulphide 199
XII. The Copper and Silver Groups (Continued). The Theory of Complex Ions 216
XIII. The Arsenic Group. Sulpho-acids and Sulpho-salts 242
XIV. Oxidation and Reduction Reactions, I 251
XV. Oxidation and Reduction, II. Oxidation by Oxygen, Permanganates, etc.; Oxidation of Organic Compounds 277
XVI. Systematic Analysis for Acid Ions 299

LIST OF REFERENCES AND THEIR ABBREVIATIONS

Note.—(Stud.) affixed to a reference indicates that the original article is recommended as suitable reading for college students taking their second year of work in chemistry.

QUALITATIVE CHEMICAL ANALYSIS PART I FUNDAMENTAL PRINCIPLES

CHAPTER I INTRODUCTION

Qualitative chemical analysis is concerned with the determination of the kinds of matter present in any given substance. In its broadest sense it includes the determination of all kinds of matter, the elements, rare as well as common, and all their combinations, organic compounds as well as inorganic. The recognition of the presence of rare elements, such as radium, uranium, thorium, tungsten, cerium, etc., is becoming a matter of growing importance with the modern development of the subject of radioactivity and the technical exploitation of the rarer elements, and it is a common experience for an analytical chemist to be called upon to determine the presence or absence of alcohol in beverages, of formalin in milk or other foods, and not a rare experience to be obliged to make tests for the presence of alkaloids like strychnine, morphine, cocaine, or for the presence of numerous other organic compounds. In this book, however, we shall limit our material to the more common elements and their most important inorganic combinations, including only a few typical organic acids. The limitation of our experimental material will make it possible to devote special attention to the scientific principles underlying analysis, to secure a clear and definite grasp of them, and to impart with simple material such experience in the technique and methods of analysis as will train the student to apply both his theoretical and practical knowledge to any field of analysis occasion may require. Accurate qualitative analysis, [p004] in any field, will depend on the care taken in mastering the theoretical significance and the technique of the methods recommended for the specific problem before the analyst; the details of the methods themselves, in any problem involving more than elementary analysis, are sought and found by him as a matter of practice in suitable larger works, in monographs and in the original literature. With the object of suggesting this broader application of the training acquired and of cultivating the invaluable habit of the professional chemist of consulting larger works and the literature, frequent reference will be made to such larger works, and to original papers in which more special subjects of analysis or theory are elaborately treated.

To recognize, in a substance, the presence of any element or compound, one must know its characteristic reactions, which will make it possible to distinguish it from all other elements or compounds. Further, in order to reach conclusions with the greatest possible speed, directness, and conclusiveness, it is usually best to carry out an examination in some systematic way, rather than in a haphazard and irregular fashion. We distinguish, accordingly, two parts in our laboratory work: first, the study of characteristic tests or reactions of the common elements and such of their compounds as are of importance in elementary analysis (Part III), and, secondly, practice in a systematic method of analysis (Part IV). In the study of the reactions, the way will be paved for systematic analysis, by taking the elements in the groups, which form the basis of the system of analysis employed, and by analyses of mixtures of the elements of a group immediately after the group has been studied.

Reliable and intelligent analysis is possible only with a clear knowledge of the chemistry of the reactions used, and the chemistry of the most important typical reactions will therefore be considered (in Part II), simultaneously with the laboratory study of the reactions and of systematic analysis.

The reactions for identifying an element or compound must bring physical evidence which can be recognized by our senses. The sense of touch is scarcely ever appealed to; perhaps the numbness or paralysis of the sense of touch imparted to the tongue or eyelid by the alkaloid cocaine and a few modern substitutes for it, and the tingling sensation produced on the tongue [p005] by aconite and its preparations, are the most important, but rare, instances of an appeal to this sense in analytical work. The sense of taste is also rarely used, and always with the greatest care to prevent poisonous effects. Acids and bases, bitter alkaloids, such as strychnine and brucine, sweet substances, such as cane sugar, glucose, glycerine, are instances of compounds which affect our sense of taste. In all these cases the taste is used rather as a confirmative test than as a conclusive proof of the identity of a suspected substance.

The sense of smell is rather more useful in qualitative analysis than that of taste or of touch. Hydrogen sulphide and ammonia, unless present in traces only, readily reveal themselves by their odor. Every chemist should be familiar with the faint but very characteristic odor of hydrocyanic acid,1 which should instantly and automatically warn him of the presence of this potent poison. Owing to partial decomposition by the moisture and carbonic acid absorbed from the atmosphere, alkali cyanides also give this important warning signal. Tests based on the odors of compounds are particularly valuable in the field of organic chemistry, where the sense of smell is extensively used for qualitative purposes; for instance, the pleasant smell of acetic ester, and the nauseating odor of an organic arsenic derivative, cacodyl oxide, may be used with advantage in identifying acetic acid.

But the evidence of touch, taste, and smell is, on the whole, only occasionally available in chemical analysis—almost all the tests employed are visual ones. A small proportion of these are color tests. The color of iodine vapor or of the solution of iodine in chloroform, the colors of metallic copper or gold, of copper salts in ammoniacal solutions, of sulphides, such as the orange sulphide of antimony (exps.), may be mentioned as instances, in which a test of identity depends on the observation of some characteristic color. But the great majority of analytical tests depend on observations of changes of state; evidence consisting in the solution of solids, the formation of precipitates, the evolution of gases, forms the most important part of the observations, [p006] on which our conclusions are based. In organic chemistry, determinations of melting-points and of boiling-points, which are very commonly used for the qualitative identification of compounds, form further instances of the application, to qualitative purposes, of observations based on changes of state.

In very many cases, where the formation or nonformation of a precipitate is intended to be used as an indication of the presence or absence of a given substance, the precipitating agent may throw down one or more of several different precipitates, which, seen without the aid of a microscope, cannot be identified without further examination. It is, thus, commonly necessary to use a sequence of such tests for the complete identification. For instance, the addition of hydrochloric acid to a solution of lead, mercurous or silver nitrate will produce a white precipitate. The precipitates may be distinguished by a further examination of their solubilities: hot water will dissolve the lead chloride, ammonia readily dissolves the chloride of silver and converts the mercurous chloride into a black insoluble mixture containing finely divided mercury (exps.). By the same means the chlorides, if present together, may be separated from one another and subsequently identified. Systematic analysis consists very largely in the use of a proper, logical sequence of such precipitation and solution reactions, and in the drawing of definite conclusions from the results obtained.

By far the greatest part of the experimental work in qualitative analysis has to do, then, with solution and precipitation. For intelligent and accurate analytical work a clear knowledge of the nature of solution and, in particular, of the simple laws governing chemical action in solution, and of those governing the formation and the solution of precipitates, is indispensable. The discoveries of van 't Hoff, in 1885–8, concerning the nature of solution, and the subsequent discoveries of Arrhenius, Nernst, Ostwald and others, have advanced every branch of chemistry, but perhaps no branch has profited quite so much as the theory of analytical chemistry, which, as a result of these discoveries, for the first time, received a clear, precise and satisfying scientific formulation of its empirical processes.2 [p007]

On account of the fundamental importance of this modern scientific formulation of the principles of analytical chemistry for the proper understanding of our subject, we shall consider first (in Part I) the modern theories of solution, with their experimental foundations, and we shall then develop the simpler fundamental laws governing chemical action and physical changes in solution. The analytical reactions themselves will be utilized as far as possible as the material for developing these general principles, so that this study may lead to the desired grasp of the theory of analysis and yet, at the same time, advance the student's knowledge of the practice of analysis.

Chapter I Footnotes

[1] On account of the poisonous character of this and other vapors, the vessel containing a substance whose odor one wishes to test is not brought to the nose, but a little of the vapor is carefully wafted towards one by a motion of the hand, the vapor being thus greatly diluted with air.

[2] We owe the first modern scientific treatment of the principles of Analytical Chemistry to Ostwald's Wissenschaftliche Grundlagen der analytischen Chemie, 1894.

CHAPTER II OSMOTIC PRESSURE AND THE THEORY OF SOLUTION I

[p008] TOC

If a concentrated solution of a substance like sugar or cupric nitrate is allowed to flow into a cylinder of water (exp. with cupric nitrate), we find that the outside forces—gravity—tend to draw the solution, whose specific gravity is greater than that of water, to the bottom of the cylinder. In this method of proceeding there is some inevitable mixing of the solution with the solvent, as the result of friction, but the main portion of the deep Fig. 1. blue solution is drawn to the bottom of the vessel and forms a blue layer under the colorless water. A much sharper line of separation may be obtained by allowing the cupric nitrate solution to enter a cylinder of water from under the water (see Fig. 1), the great density of the nitrate solution causing it to displace the water without perceptible mixing of the two liquids (exp.). If these vessels are left at rest, it may be noted, from day to day, that the copper nitrate diffuses further and further into the pure solvent, and careful examination would show that the solvent, in turn, diffuses also into the copper nitrate solution. The process is a very slow one, but it will continue until a solution of uniform concentration is reached, and this will be the case, whatever the shape of the vessel may be. If, for the moment, only the copper nitrate be considered—and what we are developing for the copper nitrate may be applied equally well, mutatis mutandis, to the diffusion of water into the copper nitrate solution—it is obvious then that copper nitrate in solution diffuses in all directions, even against the force of gravity, and it is plain also, that any object, resisting or arresting such a motion of material particles, must have a force or pressure exerted upon it. Whatever the ultimate [p009] cause of the motion, whether it is the result of inherent molecular velocities of the dissolved copper nitrate, or of an attraction between the solute and the solvent, or both, it is inevitable that a pressure must result from the impact of the moving solute against the solvent.3

Fig. 1.

We have thus phenomena of diffusion of solutes through solvents, exactly as we have the well-known diffusion of gases, and the two phenomena are unquestionably very much alike, the solute, like the gas, tending to diffuse from the place of higher, to that of lower concentration.4 Likewise, if a solution of uniform concentration is heated in one part and not in another, the solute,4 like a gas under similar conditions, will move from the warmer to the colder part of the solution, as was demonstrated by Soret.5 Without committing ourselves for the present to any given reason for the diffusion, we note that the tendency to diffusion is a fact, and we must accept the conclusion that every obstacle to such diffusion must have a pressure exerted upon it.

Now, if a solution is separated from the pure solvent by means of a so-called semipermeable membrane, some of the results of this tendency to diffusion may be demonstrated.

Exp. A concentrated solution of cane sugar in water, colored with some aniline dye, is enclosed in a thimble of parchment paper firmly fastened to a long narrow glass tube (see Fig. 2) and the cell is placed in a vessel of pure water. The parchment is not absolutely semipermeable, but it is approximately so, allowing the solvent, water, to pass, but being practically impervious to the solute sugar. A Schleicher and Schüll diffusion-thimble, No. 579, may be used, with advantage, as the thimble. (Cf. Smith's Introduction to Inorganic Chemistry, p. 284.) [p010]

Fig. 2.

We observe, presently, that the system is not in a condition of equilibrium; water passes through the thimble into the sugar solution and the latter expands, producing a decided difference of level, and consequently a hydrostatic pressure, between the liquid in the cell and the solvent outside of it. We may note two facts: first, that the change includes an expansion of the solute,6 the sugar, in the solution—that is, the tendency of the solute to expand into larger volumes of the solvent is satisfied exactly as in the experiment (Fig. 1) described above. In the second place, like all natural phenomena which proceed spontaneously, the change is in the direction of equilibrium; for when the hydrostatic pressure on the solution in the cell becomes sufficiently great, or if it is made sufficiently great at once by the application of some outside pressure, a point of equilibrium is reached, at which water will pass neither into the cell nor out of it. At that point, the tendency to expansion, both of the solute and of the solvent in the solution, is just overcome by the pressure on the solution.

Definition of Osmotic Pressure.

The hydrostatic pressure which is necessary to bring the solution into equilibrium with the pure solvent, when the two are separated by a semipermeable membrane, may be defined, according to van 't Hoff, as the measure of what is called the osmotic pressure of the solution. We note that this definition still does not commit us to any theory as to the origin of the pressure, but merely formulates an experimental relation.

Measurement of Osmotic Pressure.

—More perfect semipermeable membranes can be produced. These make possible quantitative measurements of the hydrostatic pressure on a solution, when equilibrium between the solution and the pure solvent [p011] has been reached. Such membranes were first used by Pfeffer. They consist of certain gelatinous precipitates, notably copper ferrocyanide. Films of these precipitates may be formed, under proper conditions, which are permeable to water but not to certain solutes, such as cane sugar, glucose and galactose.
Fig. 3.

By precipitating these membranes in the pores of unglazed clay cells, especially by the process devised by Morse,7 we may make them sufficiently strong to resist enormous pressures—some used by the Earl of Berkeley were found to withstand a pressure of 130 atmospheres. The hydrostatic pressure required to produce equilibrium may then be measured in either of two ways. The first method, used originally by Pfeffer and more recently by Morse and Frazer8 and their collaborators in a wonderfully conscientious study of osmotic pressures, consists in allowing the hydrostatic pressure to establish itself by the passage of very small quantities of the solvent, through the membrane, into the tightly closed cell containing the solution. When the resulting pressure produces a condition of equilibrium, it is measured9 by a manometer connected with the solution, much as a gas pressure may be measured (Fig. 3).10 This process requires considerable time for exact measurements—weeks, during which the cell must be kept at a constant temperature. The second method, which has been used by Berkeley and Hartley,11 is very much more rapid and requires only a few hours for the measurement. It consists in having the pure solvent within the cell, instead of outside of it, and in [p012] exerting an external pressure on the solution outside of the cell, until a delicate manometer, communicating with the pure solvent, shows that water does not pass through the membrane in either direction—equilibrium having been reached.

Osmotic Pressure and the Laws of Gases.

—The work of van 't Hoff, which has proved of inestimable value to the development of chemistry, succeeded in demonstrating that, for dilute solutions, the osmotic pressure, as defined above, obeys the common laws of gases,12that, in fact, a substance in a dilute solution has an osmotic pressure equal to the gas pressure which it would exert if it were a gas of the same volume and at the same temperature.13

Space does not permit the presentation of all the details of the evidence confirming this conclusion, but some of the most direct experimental proofs14 will be considered. [p013]

Boyle's Law.

—Boyle's law for gases states that, at a constant temperature, the pressure of a gas changes inversely as its volume, or directly as its concentration. Mathematically we have P : P′ = V′ : V or PV = P′V′ = a constant, and P : P′ = C : C′ or P : C = P′ : C′ = a constant. When van 't Hoff published his first paper on the subject, Pfeffer's results from the direct measurement of the osmotic pressures of cane-sugar solutions were available, and even these, although experimentally not as exact as more recent determinations, showed plainly that, at a given temperature, the osmotic pressure of a sugar solution varies directly as the concentration, or inversely as the volume containing a given weight of the sugar. At 13–16° we have:
Concentration. Osmotic Pressure.
mm. Mercury.
Pressure/
Concentration.
1.00% 535 535
2.00% 1016 508
2.74% 1518 554
4.00% 2082 521
6.00% 3075 513

The ratio of pressure to concentration varies irregularly round a mean value of 526, and is approximately constant. The more recent, exceedingly careful measurements of Morse and Frazer confirm the conclusion, that Boyle's law holds for the osmotic [p014] pressures of dilute solutions; they find that the osmotic pressures of glucose and of cane-sugar solutions vary directly as the concentrations of the solutions, at a constant temperature.15

Gay-Lussac's Law.

—Gay-Lussac's law for gases states that, if the volume of gas is kept constant, its pressure increases by 1 / 273 of its value for every degree above 0° C., or Pt = P0(1 + t / 273).

Expressing the temperature in absolute degrees, we have more simply: