Henry P. Talbot.

An Introductory Course of Quantitative Chemical Analysis With Explanatory Notes online

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represents the volume of the water in cubic centimeters delivered by
the pipette. Calculate the necessary correction.

[Note 1: A definite interval must be allowed for draining, and a
definite practice adopted with respect to the removal of the liquid
which collects at the end of the tube, if the pipette is designed to
deliver a specific volume when emptied. This liquid may be removed
at the end of a definite interval either by touching the side of the
vessel or by gently blowing out the last drops. Either practice, when
adopted, must be uniformly adhered to.]


!Graduated or measuring flasks! are similar to the ordinary
flat-bottomed flasks, but are provided with long, narrow necks in
order that slight variations in the position of the meniscus with
respect to the graduation shall represent a minimum volume of liquid.
The flasks must be of such a capacity that, when filled with the
specified volume, the liquid rises well into the neck.


It is a general custom to purchase the flasks ungraduated and to
graduate them for use under standard conditions selected for the
laboratory in question. They may be graduated for "contents" or
"delivery." When graduated for "contents" they contain a specified
volume when filled to the graduation at a specified temperature, and
require to be washed out in order to remove all of the solution from
the flask. Flasks graduated for "delivery" will deliver the specified
volume of a liquid without rinsing. A flask may, of course, be
graduated for both contents and delivery by placing two graduation
marks upon it.

PROCEDURE. - To calibrate a flask for !contents!, proceed as follows:
Clean the flask, using a chromic acid solution, and dry it carefully
outside and inside. Tare it accurately; pour water into the flask
until the weight of the latter counterbalances weights on the opposite
pan which equal in grams the number of cubic centimeters of water
which the flask is to contain. Remove any excess of water with the aid
of filter paper (Note 1). Take the flask from the balance, stopper
it, place it in a bath at the desired temperature, usually 15.5°
or 17.5°C., and after an hour mark on the neck with a diamond the
location of the lowest point of the meniscus (Note 2). The mark may
be etched upon the flask by hydrofluoric acid, or by the use of an
etching ink now commonly sold on the market.

To graduate a flask which is designed to !deliver! a specified volume,
proceed as follows: Clean the flask as usual and wipe all moisture
from the outside. Fill it with distilled water. Pour out the water
and allow the water to drain from the flask for three minutes.
Counterbalance the flask with weights to the nearest centigram.
Add weights corresponding in grams to the volume desired, and add
distilled water to counterbalance these weights. An excess of water,
or water adhering to the neck of the flask, may be removed by means of
a strip of clean filter paper. Stopper the flask, place it in a bath
at 15.5°C. or 17.5°C. and, after an hour, mark the location of the
lowest point of the meniscus, as described above.

[Note 1: The allowable error in counterbalancing the water and
weights varies with the volume of the flask. It should not exceed one
ten-thousandth of the weight of water.]

[Note 2: Other methods are employed which involve the use of
calibrated apparatus from which the desired volume of water may be run
into the dry flask and the position of the meniscus marked directly
upon it. For a description of a procedure which is most convenient
when many flasks are to be calibrated, the student is referred to the
!Am. Chem J.!, 16, 479.]


It cannot be too strongly emphasized that for the success of analyses
uniformity of practice must prevail throughout all volumetric work
with respect to those factors which can influence the accuracy of the
measurement of liquids. For example, whatever conditions are imposed
during the calibration of a burette, pipette, or flask (notably the
time allowed for draining), must also prevail whenever the flask or
burette is used.

The student should also be constantly watchful to insure parallel
conditions during both standardization and analyst with respect to the
final volume of liquid in which a titration takes place. The value
of a standard solution is only accurate under the conditions which
prevailed when it was standardized. It is plain that the standard
solutions must be scrupulously protected from concentration or
dilution, after their value has been established. Accordingly, great
care must be taken to thoroughly rinse out all burettes, flasks, etc.,
with the solutions which they are to contain, in order to remove all
traces of water or other liquid which could act as a diluent. It is
best to wash out a burette at least three times with small portions of
a solution, allowing each to run out through the tip before assuming
that the burette is in a condition to be filled and used. It is, of
course, possible to dry measuring instruments in a hot closet, but
this is tedious and unnecessary.

To the same end, all solutions should be kept stoppered and away from
direct sunlight or heat. The bottles should be shaken before use to
collect any liquid which may have distilled from the solution and
condensed on the sides.

The student is again reminded that variations in temperature of
volumetric solutions must be carefully noted, and care should always
be taken that no source of heat is sufficiently near the solutions to
raise the temperature during use.

Much time may be saved by estimating the approximate volume of a
standard solution which will be required for a titration (if the data
are obtainable) before beginning the operation. It is then possible to
run in rapidly approximately the required amount, after which it is
only necessary to determine the end-point slowly and with accuracy.
In such cases, however, the knowledge of the approximate amount to be
required should never be allowed to influence the judgment regarding
the actual end-point.


The strength or value of a solution for a specific reaction is
determined by a procedure called !Standardization!, in which the
solution is brought into reaction with a definite weight of a
substance of known purity. For example, a definite weight of pure
sodium carbonate may be dissolved in water, and the volume of a
solution of hydrochloric acid necessary to exactly neutralize the
carbonate accurately determined. From these data the strength or value
of the acid is known. It is then a !standard solution!.


Standard solutions may be made of a purely empirical strength dictated
solely by convenience of manipulation, or the concentration may
be chosen with reference to a system which is applicable to all
solutions, and based upon chemical equivalents. Such solutions are
called !Normal Solutions! and contain such an amount of the reacting
substance per liter as is equivalent in its chemical action to one
gram of hydrogen, or eight grams of oxygen. Solutions containing one
half, one tenth, or one one-hundredth of this quantity per liter are
called, respectively, half-normal, tenth-normal, or hundredth-normal

Since normal solutions of various reagents are all referred to a
common standard, they have an advantage not possessed by empirical
solutions, namely, that they are exactly equivalent to each other.
Thus, a liter of a normal solution of an acid will exactly neutralize
a liter of a normal alkali solution, and a liter of a normal oxidizing
solution will exactly react with a liter of a normal reducing
solution, and so on.

Beside the advantage of uniformity, the use of normal solutions
simplifies the calculations of the results of analyses. This is
particularly true if, in connection with the normal solution, the
weight of substance for analysis is chosen with reference to the
atomic or molecular weight of the constituent to be determined. (See
problem 26.)

The preparation of an !exactly! normal, half-normal, or tenth-normal
solution requires considerable time and care. It is usually carried
out only when a large number of analyses are to be made, or when the
analyst has some other specific purpose in view. It is, however, a
comparatively easy matter to prepare standard solutions which differ
but slightly from the normal or half-normal solution, and these have
the advantage of practical equality; that is, two approximately
half-normal solutions are more convenient to work with than two which
are widely different in strength. It is, however, true that some of
the advantage which pertains to the use of normal solutions as regards
simplicity of calculations is lost when using these approximate

The application of these general statements will be made clear in
connection with the use of normal solutions in the various types of
volumetric processes which follow.




!Standard Acid Solutions! may be prepared from either hydrochloric,
sulphuric, or oxalic acid. Hydrochloric acid has the advantage of
forming soluble compounds with the alkaline earths, but its solutions
cannot be boiled without danger of loss of strength; sulphuric acid
solutions may be boiled without loss, but the acid forms insoluble
sulphates with three of the alkaline earths; oxalic acid can be
accurately weighed for the preparation of solutions, and its solutions
may be boiled without loss, but it forms insoluble oxalates with
three of the alkaline earths and cannot be used with certain of the

!Standard Alkali Solutions! may be prepared from sodium or potassium
hydroxide, sodium carbonate, barium hydroxide, or ammonia. Of sodium
and potassium hydroxide, it may be said that they can be used with all
indicators, and their solutions may be boiled, but they absorb carbon
dioxide readily and attack the glass of bottles, thereby losing
strength; sodium carbonate may be weighed directly if its purity is
assured, but the presence of carbonic acid from the carbonate is a
disadvantage with many indicators; barium hydroxide solutions may
be prepared which are entirely free from carbon dioxide, and such
solutions immediately show by precipitation any contamination from
absorption, but the hydroxide is not freely soluble in water; ammonia
does not absorb carbon dioxide as readily as the caustic alkalies,
but its solutions cannot be boiled nor can they be used with all
indicators. The choice of a solution must depend upon the nature of
the work in hand.

A !normal acid solution! should contain in one liter that quantity of
the reagent which represents 1 gram of hydrogen replaceable by a base.
For example, the normal solution of hydrochloric acid (HCl) should
contain 36.46 grams of gaseous hydrogen chloride, since that amount
furnishes the requisite 1 gram of replaceable hydrogen. On the other
hand, the normal solution of sulphuric acid (H_{2}SO_{4}) should
contain only 49.03 grams, i.e., one half of its molecular weight in

A !normal alkali solution! should contain sufficient alkali in a liter
to replace 1 gram of hydrogen in an acid. This quantity is represented
by the molecular weight in grams (40.01) of sodium hydroxide (NaOH),
while a sodium carbonate solution (Na_{2}CO_{3}) should contain but
one half the molecular weight in grams (i.e., 53.0 grams) in a liter
of normal solution.

Half-normal or tenth-normal solutions are employed in most analyses
(except in the case of the less soluble barium hydroxide). Solutions
of the latter strength yield more accurate results when small
percentages of acid or alkali are to be determined.


It has already been pointed out that the purpose of an indicator is to
mark (usually by a change of color) the point at which just enough of
the titrating solution has been added to complete the chemical change
which it is intended to bring about. In the neutralization processes
which are employed in the measurement of alkalies (!alkalimetry!)
or acids (!acidimetry!) the end-point of the reaction should, in
principle, be that of complete neutrality. Expressed in terms of ionic
reactions, it should be the point at which the H^{+} ions from an
acid[Note 1] unite with a corresponding number of OH^{-} ions from a
base to form water molecules, as in the equation

H^{+}, Cl^{-} + Na^{+}, OH^{-} - > Na^{+}, Cl^{-} + (H_{2}O).

It is not usually possible to realize this condition of exact
neutrality, but it is possible to approach it with sufficient
exactness for analytical purposes, since substances are known which,
in solution, undergo a sharp change of color as soon as even a minute
excess of H^{+} or OH^{-} ions are present. Some, as will be seen,
react sharply in the presence of H^{+} ions, and others with OH^{-}
ions. These substances employed as indicators are usually organic
compounds of complex structure and are closely allied to the dyestuffs
in character.

[Note 1: A knowledge on the part of the student of the ionic theory
as applied to aqueous solutions of electrolytes is assumed. A brief
outline of the more important applications of the theory is given in
the Appendix.]


The indicators in most common use for acid and alkali titrations are
methyl orange, litmus, and phenolphthalein.

In the following discussion of the principles underlying the behavior
of the indicators as a class, methyl orange and phenolphthalein will
be taken as types. It has just been pointed out that indicators are
bodies of complicated structure. In the case of the two indicators
named, the changes which they undergo have been carefully studied by
Stieglitz (!J. Am. Chem. Soc.!, 25, 1112) and others, and it appears
that the changes involved are of two sorts: First, a rearrangement
of the atoms within the molecule, such as often occurs in organic
compounds; and, second, ionic changes. The intermolecular changes
cannot appropriately be discussed here, as they involve a somewhat
detailed knowledge of the classification and general behavior of
organic compounds; they will, therefore, be merely alluded to, and
only the ionic changes followed.

Methyl orange is a representative of the group of indicators which,
in aqueous solutions, behave as weak bases. The yellow color which it
imparts to solutions is ascribed to the presence of the undissociated
base. If an acid, such as HCl, is added to such a solution, the acid
reacts with the indicator (neutralizes it) and a salt is formed, as
indicated by the equation:

(M.o.)^{+}, OH^{-} + H^{+}, Cl^{-} - > (M.o.)^{+} Cl^{-} + (H_{2}O).

This salt ionizes into (M.o.)^{+} (using this abbreviation for the
positive complex) and Cl^{-}; but simultaneously with this ionization
there appears to be an internal rearrangement of the atoms which
results in the production of a cation which may be designated as
(M'.o'.)^{+}, and it is this which imparts a characteristic red color
to the solution. As these changes occur in the presence of even a
very small excess of acid (that is, of H^{+} ions), it serves as the
desired index of their presence in the solution. If, now, an alkali,
such as NaOH, is added to this reddened solution, the reverse
series of changes takes place. As soon as the free acid present is
neutralized, the slightest excess of sodium hydroxide, acting as
a strong base, sets free the weak, little-dissociated base of the
indicator, and at the moment of its formation it reverts, because of
the rearrangement of the atoms, to the yellow form:

OH^{-} + (M'.o'.)^{+} - > [M'.o'.OH] - > [M.o.OH].

Phenolphthalein, on the other hand, is a very weak, little-dissociated
acid, which is colorless in neutral aqueous solution or in the
presence of free H^{+} ions. When an alkali is added to such a
solution, even in slight excess, the anion of the salt which has
formed from the acid of the indicator undergoes a rearrangement of the
atoms, and a new ion, (Ph')^{+}, is formed, which imparts a pink color
to the solution:

H^{+}, (Ph)^{-} + Na^{+}, OH^{-} - > (H_{2}O) + Na^{+}, (Ph)^{-}
- > Na^{+}, (Ph')^{-}

The addition of the slightest excess of an acid to this solution, on
the other hand, occasions first the reversion to the colorless ion and
then the setting free of the undissociated acid of the indicator:

H^{+}, (Ph')^{-} - > H^{+}, (Ph)^{-} - > (HPh).

Of the common indicators methyl orange is the most sensitive toward
alkalies and phenolphthalein toward acids; the others occupy
intermediate positions. That methyl orange should be most sensitive
toward alkalies is evident from the following considerations: Methyl
orange is a weak base and, therefore, but little dissociated. It
should, then, be formed in the undissociated condition as soon as even
a slight excess of OH^{-} ions is present in the solution, and there
should be a prompt change from red to yellow as outlined above. On the
other hand, it should be an unsatisfactory indicator for use with weak
acids (acetic acid, for example) because the salts which it forms
with such acids are, like all salts of that type, hydrolyzed to a
considerable extent. This hydrolytic change is illustrated by the

(M.o.)^{+} C_{2}H_{3}O_{2}^{-} + H^{+}, OH^{-} - > [M.o.OH] + H^{+},

Comparison of this equation with that on page 30 will make it plain
that hydrolysis is just the reverse of neutralization and must,
accordingly, interfere with it. Salts of methyl orange with weak acids
are so far hydrolyzed that the end-point is uncertain, and methyl
orange cannot be used in the titration of such acids, while with
the very weak acids, such as carbonic acid or hydrogen sulphide
(hydrosulphuric acid), the salts formed with methyl orange are, in
effect, completely hydrolyzed (i.e., no neutralization occurs), and
methyl orange is accordingly scarcely affected by these acids. This
explains its usefulness, as referred to later, for the titration of
strong acids, such as hydrochloric acid, even in the presence of
carbonates or sulphides in solution.

Phenolphthalein, on the other hand, should be, as it is, the best of
the common indicators for use with weak acids. For, since it is
itself a weak acid, it is very little dissociated, and its nearly
undissociated, colorless molecules are promptly formed as soon as
there is any free acid (that is, free H^{+} ions) in the solution.
This indicator cannot, however, be successfully used with weak bases,
even ammonium hydroxide; for, since it is weak acid, the salts
which it forms with weak alkalies are easily hydrolyzed, and as a
consequence of this hydrolysis the change of color is not sharp.
This indicator can, however, be successfully used with strong bases,
because the salts which it forms with such bases are much less
hydrolyzed and because the excess of OH^{-} ions from these bases also
diminishes the hydrolytic action of water.

This indicator is affected by even so weak an acid as carbonic acid,
which must be removed by boiling the solution before titration. It is
the indicator most generally employed for the titration of organic

In general, it may be stated that when a strong acid, such as
hydrochloric, sulphuric or nitric acid, is titrated against a strong
base, such as sodium hydroxide, potassium hydroxide, or barium
hydroxide, any of these indicators may be used, since very little
hydrolysis ensues. It has been noted above that the color change does
not occur exactly at theoretical neutrality, from which it follows
that no two indicators will show exactly the same end-point when acids
and alkalis are brought together. It is plain, therefore, that the
same indicator must be employed for both standardization and analysis,
and that, if this is done, accurate results are obtainable.

The following table (Note 1) illustrates the variations in the volume
of an alkali solution (tenth-normal sodium hydroxide) required to
produce an alkaline end-point when run into 10 cc. of tenth-normal
sulphuric acid, diluted with 50 cc. of water, using five drops of each
of the different indicator solutions.

| | | |
| cc. | cc. | cc. |
Methyl orange | 10 | 9.90 | Red | Yellow
Lacmoid | 10 | 10.00 | Red | Blue
Litmus | 10 | 10.00 | Red | Blue
Rosalic acid | 10 | 10.07 | Yellow | Pink
Phenolphthalein| 10 | 10.10 | Colorless | Pink

It should also be stated that there are occasionally secondary
changes, other than those outlined above, which depend upon the
temperature and concentration of the solutions in which the indicators
are used. These changes may influence the sensitiveness of an
indicator. It is important, therefore, to take pains to use
approximately the same volume of solution when standardizing that is
likely to be employed in analysis; and when it is necessary, as is
often the case, to titrate the solution at boiling temperature, the
standardization should take place under the same conditions. It is
also obvious that since some acid or alkali is required to react with
the indicator itself, the amount of indicator used should be uniform
and not excessive. Usually a few drops of solution will suffice.

The foregoing statements with respect to the behavior of indicators
present the subject in its simplest terms. Many substances other than
those named may be employed, and they have been carefully studied to
determine the exact concentration of H^{+} ions at which the color
change of each occurs. It is thus possible to select an indicator
for a particular purpose with considerable accuracy. As data of this
nature do not belong in an introductory manual, reference is made to
the following papers or books in which a more extended treatment of
the subject may be found:

Washburn, E.W., Principles of Physical Chemistry (McGraw-Hill Book
Co.), (Second Edition, 1921), pp. 380-387.

Prideaux, E.B.R., The Theory and Use of Indicators (Constable & Co.,
Ltd.), (1917).

Salm, E., A Study of Indicators, !Z. physik. Chem.!, 57 (1906),

Stieglitz, J., Theories of Indicators, !J. Am. Chem. Soc.!, 25 (1903),

Noyes, A.A., Quantitative Applications of the Theory of Indicators to
Volumetric Analysis, !J. Am. Chem. Soc.!, 32 (1911), 815-861.

Bjerrum, N., General Discussion, !Z. Anal. Chem.!, 66 (1917), 13-28
and 81-95.

Ostwald, W., Colloid Chemistry of Indicators, !Z. Chem. Ind.
Kolloide!, 10 (1912), 132-146.

[Note 1: Glaser, !Indikatoren der Acidimetrie und Alkalimetrie!.
Wiesbaden, 1901.]


A !methyl orange solution! for use as an indicator is commonly made by
dissolving 0.05-0.1 gram of the compound (also known as Orange III) in
a few cubic centimeters of alcohol and diluting with water to 100 cc.
A good grade of material should be secured. It can be successfully
used for the titration of hydrochloric, nitric, sulphuric, phosphoric,
and sulphurous acids, and is particularly useful in the determination
of bases, such as sodium, potassium, barium, calcium, and ammonium
hydroxides, and even many of the weak organic bases. It can also be
used for the determination, by titration with a standard solution of
a strong acid, of the salts of very weak acids, such as carbonates,
sulphides, arsenites, borates, and silicates, because the weak acids
which are liberated do not affect the indicator, and the reddening of
the solution does not take place until an excess of the strong acid
is added. It should be used in cold, not too dilute, solutions. Its
sensitiveness is lessened in the presence of considerable quantities
of the salts of the alkalies.

A !phenolphthalein solution! is prepared by dissolving 1 gram of the
pure compound in 100 cc. of 95 per cent alcohol. This indicator is
particularly valuable in the determination of weak acids, especially
organic acids. It cannot be used with weak bases, even ammonia. It
is affected by carbonic acid, which must, therefore, be removed by
boiling when other acids are to be measured. It can be used in hot

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Online LibraryHenry P. TalbotAn Introductory Course of Quantitative Chemical Analysis With Explanatory Notes → online text (page 3 of 17)