An Introductory Course of Quantitative Chemical Analysis Part 26

It is a.s.sumed that the Na^{+} ion, for example, differs from the sodium atom in behavior because of the very considerable electrical charge which it carries and which, as just stated, must, in an electrically neutral solution, be balanced by a corresponding negative charge on some other ion. When an electric current is pa.s.sed through a solution of an electrolyte the ions move with and convey the current, and when the cations come into contact with the negatively charged cathode they lose their charges, and the resulting electrically neutral atoms (or radicals) are liberated as such, or else enter at once into chemical reaction with the components of the solution.

Two ions of identically the same composition but with different electrical charges may exhibit widely different properties. For example, the ion MnO_{4}^{-} from permanganates yields a purple-red solution and differs in its chemical behavior from the ion MnO_{4}^{--} from manganates, the solutions of which are green.

The chemical changes upon which the procedures of a.n.a.lytical chemistry depend are almost exclusively those in which the reacting substances are electrolytes, and a.n.a.lytical chemistry is, therefore, essentially the chemistry of the ions. The percentage dissociation of the same electrolyte tends to increase with increasing dilution of its solution, although not in direct proportion. The percentage dissociation of different electrolytes in solutions of equivalent concentrations (such, for example, as normal solutions) varies widely, as is indicated in the following tables, in which approximate figures are given for tenth-normal solutions at a temperature of about 18C.

ACIDS ========================================================================= SUBSTANCE PERCENTAGE DISSOCIATION IN 0.1 EQUIVALENT SOLUTION _____________________________________________ ___________________________ HCl, HBr, HI, HNO_{3} 90 HClO_{3}, HClO_{4}, HMnO_{4} 90 H_{2}SO_{4} <--> H^{+} + HSO_{4}^{-} 90 H_{2}C_{2}O_{4} <--> H^{+} + HC_{2}O_{4}^{-} 50 H_{2}SO_{3} <--> H^{+} + HSO{_}3^{-} 20 H_{3}PO_{4} <--> H^{+} + H_{2}PO_{4}^{-} 27 H_{2}PO_{4}^{-} <--> H^{+} + HPO_{4}^{--} 0.2 H_{3}AsO_{4} <--> H^{+} + H_{2}AsO_{4}^{-} 20 HF 9 HC_{2}H_{3}O_{2} 1.4 H_{2}CO_{3} <--> H^{+} + HCO_{3}^{-} 0.12 H_{2}S <--> H^{+} + HS^{-} 0.05 HCN 0.01 =========================================================================

BASES ========================================================================= SUBSTANCE PERCENTAGE DISSOCIATION IN 0.1 EQUIVALENT SOLUTION _____________________________________________ ___________________________ KOH, NaOH 86 Ba(OH)_{2} 75 NH_{4}OH 1.4 =========================================================================

SALTS ========================================================================= TYPE OF SALT PERCENTAGE DISSOCIATION IN 0.1 EQUIVALENT SOLUTION _____________________________________________ ___________________________ R^{+}R^{-} 86 R^{++}(R^{-})_{2} 72 (R^{+})_{2}R^{--} 72 R^{++}R^{--} 45 =========================================================================

The percentage dissociation is determined by studying the electrical conductivity of the solutions and by other physico-chemical methods, and the following general statements summarize the results:

!Salts!, as a cla.s.s, are largely dissociated in aqueous solution.

!Acids! yield H^{+} ions in water solution, and the comparative !strength!, that is, the activity, of acids is proportional to the concentration of the H^{+} ions and is measured by the percentage dissociation in solutions of equivalent concentration. The common mineral acids are largely dissociated and therefore give a relatively high concentration of H^{+} ions, and are commonly known as "strong acids." The organic acids, on the other hand, belong generally to the group of "weak acids."

!Bases! yield OH^{-} ions in water solution, and the comparative strength of the bases is measured by their relative dissociation in solutions of equivalent concentration. Ammonium hydroxide is a weak base, as shown in the table above, while the hydroxides of sodium and pota.s.sium exhibit strongly basic properties.

Ionic reactions are all, to a greater or less degree, !reversible reactions!. A typical example of an easily reversible reaction is that representing the changes in ionization which an electrolyte such as acetic acid undergoes on dilution or concentration of its solutions, !i.e.!, HC_{2}H_{3}O_{2} <--> H^{+} + C_{2}H_{3}O_{2}^{-}. As was stated above, the ionization increases with dilution, the reaction then proceeding from left to right, while concentration of the solution occasions a partial rea.s.sociation of the ions, and the reaction proceeds from right to left. To understand the principle underlying these changes it is necessary to consider first the conditions which prevail when a solution of acetic acid, which has been stirred until it is of uniform concentration throughout, has come to a constant temperature. A careful study of such solutions has shown that there is a definite state of equilibrium between the const.i.tuents of the solution; that is, there is a definite relation between the undissociated acetic acid and its ions, which is characteristic for the prevailing conditions. It is not, however, a.s.sumed that this is a condition of static equilibrium, but rather that there is continual dissociation and a.s.sociation, as represented by the opposing reactions, the apparent condition of rest resulting from the fact that the amount of change in one direction during a given time is exactly equal to that in the opposite direction. A quant.i.tative study of the amount of undissociated acid, and of H^{+} ions and C_{2}H_{3}O_{2}^{-} ions actually to be found in a large number of solutions of acetic acid of varying dilution (a.s.suming them to be in a condition of equilibrium at a common temperature), has shown that there is always a definite relation between these three quant.i.ties which may be expressed thus:

(!Conc'n H^{+} x Conc'n C_{2}H_{3}O_{2}^{-})/Conc'n HC_{2}H_{3}O_{2} = Constant!.

In other words, there is always a definite and constant ratio between the product of the concentrations of the ions and the concentration of the undissociated acid when conditions of equilibrium prevail.

It has been found, further, that a similar statement may be made regarding all reversible reactions, which may be expressed in general terms thus: The rate of chemical change is proportional to the product of the concentrations of the substances taking part in the reaction; or, if conditions of equilibrium are considered in which, as stated, the rate of change in opposite directions is a.s.sumed to be equal, then the product of the concentrations of the substances entering into the reaction stands in a constant ratio to the product of the concentrations of the resulting substances, as given in the expression above for the solutions of acetic acid. This principle is called the !Law of Ma.s.s Action!.

It should be borne in mind that the expression above for acetic acid applies to a wide range of dilutions, provided the temperature remains constant. If the temperature changes the value of the constant changes somewhat, but is again uniform for different dilutions at that temperature. The following data are given for temperatures of about 18C.[1]

========================================================================== MOLAL FRACTION MOLAL CONCENTRA- MOLAL CONCENTRA- VALUE OF CONCENTRATION IONIZED TION OF H^{+} AND TION OF UNDIS- CONSTANT CONSTANT ACETATE^{-} IONS SOCIATED ACID ______________ __________ __________________ __________________ __________ 1.0 .004 .004 .996 .0000161 0.1 .013 .0013 .0987 .0000171 0.01 .0407 .000407 .009593 .0000172 ===========================================================================

[Footnote 1: Alexander Smith, !General Inorganic Chemistry!, p. 579.]

The molal concentrations given in the table refer to fractions of a gram-molecule per liter of the undissociated acid, and to fractions of the corresponding quant.i.ties of H^{+} and C_{2}H_{3}O_{2}^{-} ions per liter which would result from the complete dissociation of a gram-molecule of acetic acid. The values calculated for the constant are subject to some variation on account of experimental errors in determining the percentage ionized in each case, but the approximate agreement between the values found for molal and centimolal (one hundredfold dilution) is significant.

The figures given also ill.u.s.trate the general principle, that the !relative! ionization of an electrolyte increases with the dilution of its solution. If we consider what happens during the (usually) brief period of dilution of the solution from molal to 0.1 molal, for example, it will be seen that on the addition of water the conditions of concentration which led to equality in the rate of change, and hence to equilibrium in the molal solution, cease to exist; and since the dissociating tendency increases with dilution, as just stated, it is true at the first instant after the addition of water that the concentration of the undissociated acid is too great to be permanent under the new conditions of dilution, and the reaction, HC_{2}H_{3}O_{2} <--> H^{+} + C_{2}H_{3}O_{2}^{-}, will proceed from left to right with great rapidity until the respective concentrations adjust themselves to the new conditions.

That which is true of this reaction is also true of all reversible reactions, namely, that any change of conditions which occasions an increase or a decrease in concentration of one or more of the components causes the reaction to proceed in one direction or the other until a new state of equilibrium is established. This principle is constantly applied throughout the discussion of the applications of the ionic theory in a.n.a.lytical chemistry, and it should be clearly understood that whenever an existing state of equilibrium is disturbed as a result of changes of dilution or temperature, or as a consequence of chemical changes which bring into action any of the const.i.tuents of the solution, thus altering their concentrations, there is always a tendency to re-establish this equilibrium in accordance with the law.

Thus, if a base is added to the solution of acetic acid the H^{+} ions then unite with the OH^{-} ions from the base to form undissociated water. The concentration of the H^{+} ions is thus diminished, and more of the acid dissociates in an attempt to restore equilbrium, until finally practically all the acid is dissociated and neutralized.

Similar conditions prevail when, for example, silver ions react with chloride ions, or barium ions react with sulphate ions. In the former case the dissociation reaction of the silver nitrate is AgNO_{3} <--> Ag^{+} + NO_{3}^{-}, and as soon as the Ag^{+} ions unite with the Cl^{-} ions the concentration of the former is diminished, more of the AgNO_{3} dissociates, and this process goes on until the Ag^{+} ions are practically all removed from the solution, if the Cl^{-} ions are present in sufficient quant.i.ty.

For the sake of accuracy it should be stated that the ma.s.s law cannot be rigidly applied to solutions of those electrolytes which are largely dissociated. While the explanation of the deviation from quant.i.tative exactness in these cases is not known, the law is still of marked service in developing a.n.a.lytical methods along more logical lines than was formerly practicable. It has not seemed wise to qualify each statement made in the Notes to indicate this lack of quant.i.tative exactness. The student should recognize its existence, however, and will realize its significance better as his knowledge of physical chemistry increases.

If we apply the ma.s.s law to the case of a substance of small solubility, such as the compounds usually precipitated in quant.i.tative a.n.a.lysis, we derive what is known as the !solubility product!, as follows: Taking silver chloride as an example, and remembering that it is not absolutely insoluble in water, the equilibrium expression for its solution is:

(!Conc'n Ag^{+} x Conc'n Cl^{-})/Conc'n AgCl = Constant!.

But such a solution of silver chloride which is in contact with the solid precipitate must be saturated for the existing temperature, and the quant.i.ty of undissociated AgCl in the solution is definite and constant for that temperature. Since it is a constant, it may be eliminated, and the expression becomes !Conc'n Ag^{+} x Conc'n Cl^{-} = Constant!, and this is known as the solubility product. No precipitation of a specific substance will occur until the product of the concentrations of its ions in a solution exceeds the solubility product for that substance; whenever that product is exceeded precipitation must follow.

It will readily be seen that if a substance which yields an ion in common with the precipitated compound is added to such a solution as has just been described, the concentration of that ion is increased, and as a result the concentration of the other ion must proportionately decrease, which can only occur through the formation of some of the undissociated compound which must separate from the already saturated solution. This explains why the addition of an excess of the precipitant is often advantageous in quant.i.tative procedures. Such a case is discussed at length in Note 2 on page 113.

Similarly, the ionization of a specific substance in solution tends to diminish on the addition of another substance with a common ion, as, for instance, the addition of hydrochloric acid to a solution of hydrogen sulphide. Hydrogen sulphide is a weak acid, and the concentration of the hydrogen ions in its aqueous solutions is very small. The equilibrium in such a solution may be represented as:

(!(Conc'n H^{+})^{2} x Conc'n S^{--})/Conc'n H_{2}S = Constant!, and a marked increase in the concentration of the H^{+} ions, such as would result from the addition of even a small amount of the highly ionized hydrochloric acid, displaces the point of equilibrium and some of the S^{--} ions unite with H^{+} ions to form undissociated H_{2}S. This is of much importance in studying the reactions in which hydrogen sulphide is employed, as in qualitative a.n.a.lysis. By a parallel course of reasoning it will be seen that the addition of a salt of a weak acid or base to solutions of that acid or base make it, in effect, still weaker because they decrease its percentage ionization.

To understand the changes which occur when solids are dissolved where chemical action is involved, it should be remembered that no substance is completely insoluble in water, and that those products of a chemical change which are least dissociated will first form. Consider, for example, the action of hydrochloric acid upon magnesium hydroxide.

The minute quant.i.ty of dissolved hydroxide dissociates thus: Mg(OH)_{2} <--> Mg^{++} + 2OH^{-}. When the acid is introduced, the H^{+} ions of the acid unite with the OH^{-} ions to form undissociated water. The concentration of the OH^{-} ions is thus diminished, more Mg(OH)_{2} dissociates, the solution is no longer saturated with the undissociated compound, and more of the solid dissolves. This process repeats itself with great rapidity until, if sufficient acid is present, the solid pa.s.ses completely into solution.

Exactly the same sort of process takes place if calcium oxalate, for example, is dissolved in hydrochloric acid. The C_{2}O_{4}^{--} ions unite with the H^{+} ions to form undissociated oxalic acid, the acid being less dissociated than normally in the presence of the H^{+} ions from the hydrochloric acid (see statements regarding hydrogen sulphide above). As the undissociated oxalic acid forms, the concentration of the C_{2}O_{4}^{--} ions lessens and more CaC_{2}O_{4} dissolves, as described for the Mg(OH)_{2} above. Numerous instances of the applications of these principles are given in the Notes.

Water itself is slightly dissociated, and although the resulting H^{+} and OH^{-} ions are present only in minute concentrations (1 mol. of dissociated water in 10^{7} liters), yet under some conditions they may give rise to important consequences. The term !hydrolysis! is applied to the changes which result from the reaction of these ions.

Any salt which is derived from a weak base or a weak acid (or both) is subject to hydrolytic action. Pota.s.sium cyanide, for example, when dissolved in water gives an alkaline solution because some of the H^{+} ions from the water unite with CN^{-} ions to form (HCN), which is a very weak acid, and is but very slightly dissociated. Pota.s.sium hydroxide, which might form from the OH^{-} ions, is so largely dissociated that the OH^{-} ions remain as such in the solution. The union of the H^{+} ions with the CN^{-} ions to form the undissociated HCN diminishes the concentration of the H^{+} ions, and more water dissociates (H_{2}O <--> H^{+} + OH^{-}) to restore the equilibrium.

It is clear, however, that there must be a gradual acc.u.mulation of OH^{-} ions in the solution as a result of these changes, causing the solution to exhibit an alkaline reaction, and also that ultimately the further dissociation of the water will be checked by the presence of these ions, just as the dissociation of the H_{2}S was lessened by the addition of HCl.

An exactly opposite result follows the solution of such a salt as Al_{2}(SO_{4})_{3} in water. In this case the acid is strong and the base weak, and the OH^{-} ions form the little dissociated Al(OH)_{3}, while the H^{+} ions remain as such in the solution, sulphuric acid being extensively dissociated. The solution exhibits an acid reaction.

Such hydrolytic processes as the above are of great importance in a.n.a.lytical chemistry, especially in the understanding of the action of indicators in volumetric a.n.a.lysis. (See page 32.)

The impelling force which causes an element to pa.s.s from the atomic to the ionic condition is termed !electrolytic solution pressure!, or ionization tension. This force may be measured in terms of electrical potential, and the table below shows the relative values for a number of elements.

In general, an element with a greater solution pressure tends to cause the deposition of an element of less solution pressure when placed in a solution of its salt, as, for instance, when a strip of zinc or iron is placed in a solution of a copper salt, with the resulting precipitation of metallic copper.

Hydrogen is included in the table, and its position should be noted with reference to the other common elements. For a more extended discussion of this topic the student should refer to other treatises.

POTENTIAL SERIES OF THE METALS

__________________________________________________________________ POTENTIAL POTENTIAL IN VOLTS IN VOLTS _____________________ ___________ ____________________ ___________ Sodium Na^{+} +2.44 Lead Pb^{++} -0.13 Calcium Ca^{++} Hydrogen H^{+} -0.28 Magnesium Mg^{++} Bis.m.u.th Bi^{+++} Aluminum A1^{+++} +1.00 Antimony -0.75 Manganese Mn^{++} a.r.s.enic Zinc Zn^{++} +0.49 Copper Cu^{++} -0.61 Cadmium Cd^{++} +0.14 Mercury Hg^{+} -1.03 Iron Fe^{++} +0.063 Silver Ag^{+} -1.05 Cobalt Co^{++} -0.045 Platinum Nickel Ni^{++} -0.049 Gold Tin Sn^{++} -0.085(?) _____________________ ___________ ____________________ __________

THE FOLDING OF A FILTER PAPER

If a filter paper is folded along its diameter, and again folded along the radius at right angles to the original fold, a cone is formed on opening, the angle of which is 60. Funnels for a.n.a.lytical use are supposed to have the same angle, but are rarely accurate. It is possible, however, with care, to fit a filter thus folded into a funnel in such a way as to prevent air from pa.s.sing down between the paper and the funnel to break the column of liquid in the stem, which aids greatly, by its gentle suction, in promoting the rate of filtration.

Such a filter has, however, the disadvantage that there are three thicknesses of paper back of half of its filtering surface, as a consequence of which one half of a precipitate washes or drains more slowly. Much time may be saved in the aggregate by learning to fold a filter in such a way as to improve its effective filtering surface.

The directions which follow, though apparently complicated on first reading, are easily applied and easily remembered. Use a 6-inch filter for practice. Place four dots on the filter, two each on diameters which are at right angles to each other. Then proceed as follows: (1) Fold the filter evenly across one of the diameters, creasing it carefully; (2) open the paper, turn it over, rotate it 90 to the right, bring the edges together and crease along the other diameter; (3) open, and rotate 45 to the right, bring edges together, and crease evenly; (4) open, and rotate 90 to the right, and crease evenly; (5) open, turn the filter over, rotate 22-(1/2) to the right, and crease evenly; (6) open, rotate 45 to the right and crease evenly; (7) open, rotate 45 to the right and crease evenly; (8) open, rotate 45 to the right and crease evenly; (9) open the filter, and, starting with one of the dots between thumb and forefinger of the right hand, fold the second crease to the left over on it, and do the same with each of the other dots. Place it, thus folded, in the funnel, moisten it, and fit to the side of the funnel. The filter will then have four short segments where there are three thicknesses and four where there is one thickness, but the latter are evenly distributed around its circ.u.mference, thus greatly aiding the pa.s.sage of liquids through the paper and hastening both filtration and was.h.i.+ng of the whole contents of the filter.

!SAMPLE PAGES FOR LABORATORY RECORDS!

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CALIBRATION OF BURETTE No.