The determination of hardness by the soap method roughly approximates
the amount of calcium and magnesium in a water, though it actually
measures the soap-consuming power of the water.
_Reagents._—1. Standard calcium chloride solution. Dissolve 0.2 gram of
pure calcite (calcium carbonate) in a little dilute hydrochloric acid,
being careful to avoid loss of solution by spattering. Evaporate the
solution to dryness several times with distilled water to expel excess
of acid. Dissolve the residue in distilled water and dilute the solution
to 1 liter. One cc. of this dilution is equivalent to 0.2 mg. of calcium
carbonate.
2. Standard soap solution. Dissolve 100 grams of dry white Castile soap
in 1 liter of 80 per cent alcohol, and allow this solution to stand
several days before standardizing. Pure potassium oleate made from lead
plaster and potassium carbonate may be used in place of Castile soap.
_First method of standardization._—Dilute 20 cc. of the calcium chloride
solution in a 250 cc. glass-stoppered bottle to 50 cc. with distilled
water which has been recently boiled and cooled. Add soap solution from
a burette, 0.2 or 0.3 cc. at a time, shaking the bottle vigorously after
each addition until a lather remains unbroken for five minutes over the
entire surface of the water while the bottle lies on its side. Then
adjust the strength of the stock solution with 70 per cent alcohol so
that the resulting diluted soap solution will give a permanent lather
when 6.40 cc. of it is properly added to 20 cc. of standard calcium
chloride solution diluted to 50 cc. Usually 75 to 100 cc. of the stock
soap solution is required to make 1 liter of the standard soap solution.
The quantity of calcium carbonate equivalent to each cubic centimeter of
the standard soap solution consumed in the titration is indicated in
Table 6.
Table 6.—TOTAL HARDNESS IN PARTS PER MILLION OF CaCO_{3} FOR EACH TENTH
OF A CUBIC CENTIMETER OF SOAP SOLUTION WHEN 50 CC. OF THE SAMPLE IS
TITRATED.
───────────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────
Cubic │ │ │ │ │ │ │ │ │ │
centimeters│ 0.0.│ 0.1.│ 0.2.│ 0.3.│ 0.4.│ 0.5.│ 0.6.│ 0.7.│ 0.8.│ 0.9.
of soap │ │ │ │ │ │ │ │ │ │
solution. │ │ │ │ │ │ │ │ │ │
───────────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────
0.0│ │ │ │ │ │ │ │ 0.0│ 1.6│ 3.2
1.0│ 4.8│ 6.3│ 7.9│ 9.5│ 11.1│ 12.7│ 14.3│ 15.6│ 16.9│ 18.2
2.0│ 19.5│ 20.8│ 22.1│ 23.4│ 24.7│ 26.0│ 27.3│ 28.6│ 29.9│ 31.2
│ │ │ │ │ │ │ │ │ │
3.0│ 32.5│ 33.8│ 35.1│ 36.4│ 37.7│ 38.0│ 40.3│ 41.6│ 42.9│ 44.3
4.0│ 45.7│ 47.1│ 48.6│ 50.0│ 51.4│ 52.9│ 54.3│ 55.7│ 57.1│ 58.6
5.0│ 60.0│ 61.4│ 62.9│ 64.3│ 65.7│ 67.1│ 68.6│ 70.0│ 71.4│ 72.9
│ │ │ │ │ │ │ │ │ │
6.0│ 74.3│ 75.7│ 77.1│ 78.6│ 80.0│ 81.4│ 82.9│ 84.3│ 85.7│ 87.1
7.0│ 88.6│ 90.0│ 91.4│ 92.9│ 94.3│ 95.7│ 97.1│ 98.6│100.0│101.5
───────────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────
This table does not provide for the use of so large volume of soap
solution for a single determination as former ones because the end-point
becomes somewhat obscured in the presence of magnesium if more than 7
cc. is used.
_Second method of standardization._—Dilute 100 cc. of the stock soap
solution to 1 liter with 70 per cent alcohol. This dilute solution
should be of such strength that approximately 6.4 cc. of it will give a
permanent lather when 20 cc. of standard calcium chloride solution
diluted to 50 cc. with distilled water is titrated with it. Determine
the amount of soap solution required to give a permanent lather with 50
cc. of distilled water and with 5, 10, 15, and 20 cc. of standard
calcium chloride solution diluted to 50 cc. with distilled water.
Finally plot on cross-section paper a curve showing the relation of
various quantities of soap solution to corresponding quantities of
standard calcium carbonate solution and therefore to parts per million
of hardness.
_Procedure._—Measure 50 cc. of the water into a 250 cc. bottle and add
to it soap solution in small quantities in precisely the same manner as
described under the standardization of the soap solution. From the
number of cubic centimeters of soap solution used obtain from Table 6 or
from the plotted curve the total hardness of the water in parts per
million of calcium carbonate.
To avoid mistaking the false or magnesium end-point for the true one[35]
when adding the soap solution to waters containing magnesium salts, read
the burette after the titration is apparently finished, and add about
0.5 cc. more of soap solution. If the end-point was due to magnesium the
lather will disappear. Soap solution must then be added until the true
end-point is reached. Usually the false lather persists for less than
five minutes.
If more than 7 cc. of soap solution is required for 50 cc. of the water
take less of the sample and dilute it to 50 cc. with distilled water
which has been recently boiled and cooled. This step reduces somewhat
the disturbing influence of magnesium,[107a] which consumes more soap
than an equivalent weight of calcium.
At best the soap method is not a precise test on account of the
different relative amounts of calcium and magnesium in different waters.
For hard waters, especially in connection with processes for
purification and softening, it is advised that this method be not
exclusively used. If the same water is frequently analyzed it may be of
assistance to standardize the soap solution against a mixture of calcium
and magnesium salts, the relative proportions of which approximate those
found in the water.
The strength of the soap solution should be determined from time to
time, to make sure that it has not materially changed. Record all
results in parts per million of calcium carbonate.
One English degree of hardness, Clark’s scale, is equivalent to 1 grain
per Imperial gallon of calcium carbonate. One French degree of hardness
is equivalent to 1 part per 100,000 of calcium carbonate. One German
degree of hardness is equivalent to 1 part per 100,000 of calcium oxide,
and multiplied by 17.9 gives parts per million of calcium carbonate. The
relations of these various scales are indicated in Table 7.
Table 7.—CONVERSION TABLE FOR HARDNESS.
───────────────────────────┬───────────────────────────────────────────
Unit. │ Equivalent.
───────────────────────────┼──────────┬──────────┬──────────┬──────────
│Parts per │ Clark │ French │ German
│ million. │ degrees. │ degrees. │ degrees.
───────────────────────────┼──────────┼──────────┼──────────┼──────────
One part per million │ 1.00│ 0.07│ 0.10│ 0.056
One Clark degree │ 14.3│ 1.00│ 1.43│ .80
One French degree │ 10.0│ .70│ 1.00│ .56
One German degree │ 17.9│ 1.24│ 1.78│ 1.00
───────────────────────────┴──────────┴──────────┴──────────┴──────────