The use of oil in the bath is preferred to water. Oil decreases the errors caused by (1) capacitance bypaths between parts of the cell, (2) capacitance between the cell and the walls of the bath, and (3) electrical eddy currents in the liquid outside the cell. These errors may amount to 0.5 percent or more [11,12].

3. PROCEDURE

(a) EQUILIBRIUM WATER

All solutions on which conductivity determinations are to be made should be prepared from water of low specific conductance. It is possible to obtain water which has a specific conductance of 0.043 × 10-6 mho cm at 18° [25]. However, the instant water comes in contact with the air, CO2 is absorbed and the conductivity increases. When it is brought into equilibrium with the CO2 in the air, preferably by rapid aeration [26], and has no other impurities, it has a specific conductance of about 0.85X10-6 [27]. It also has the pH value 5.7, which can be readily checked with isohydric indicators [26]. (A diaphragm pump of suitable construction is very convenient for spraying outdoor air through a porous Alundum or fritted Pyrex aspirator immersed in the water. Laboratory compressed air generally carries along a spray of oil and impure water.) Such water is known as "equilibrium water." Water having a specific conductance greater than 3X10-6 mho cm-1 at 25° C may produce a precipitate in the sugar solution, which would alter its conductivity. However, it is possible to secure water of this or lower conductivity from an ordinary laboratory still. If such water is not available, equilibrium water may be prepared directly from tap water [27], but preferably from distilled water, by distillation in a Jena- or Pyrex-glass vessel to which a few milliliters of Nessler solution or alkaline permanganate [28] has been added, and condensing the vapors in a block tin condenser. This water is then thoroughly aerated (overnight generally sufficing) and should be stored in thoroughly steamed and seasoned Pyrex glass-stoppered bottles. It is quite stable over a period of several weeks.

(b) PREPARATION OF POTASSIUM CHLORIDE SOLUTION

The potassium chloride should be selected from the purest material available, recrystallized from conductivity or equilibrium water, separated by centrifugal drainage, fused in a platinum crucible, poured into a platinum dish, and transferred to a closed bottle while still hot. Solutions made from it should be carefully prepared according to the following procedure:

An approximate cell constant is estimated from a rough measurement of the dimensions of the cell. From this value the concentration of potassium chloride is selected from the recommended value in table 33. The correct amount of potassium chloride is weighed into a Pyrex vessel and equilibrium water is added to bring the weight to 1,000 0.02 g. The correction to be applied to convert both the weight of the potassium chloride and the solution to weight in vacuum is determined according to directions found in table 114, page 632

TABLE 33.-Specific conductance (at 1,000 cycles) of potassium chloride solutions, in reciprocal ohm-centimeter

1 When the corresponding standard solutions are used in cells that have a cell constant lying between the limits given in this column, the measured resistance will be between 1,000 and 50,000 ohms.

The specific conductances of solutions 1, 2, and 3 in table 33 were determined by Jones and Prendergast [29]. The value for solution 4 was calculated from the empirical equations of Davies [30], which are as follows:

A=149.92-93.85√C+50C at 25° C

A=129.67-79.55√C÷35C at 18° C,

(64)

(65)

where A is the equivalent conductance, and C the concentration of the solution in moles per liter. Values calculated from these equations are in agreement with those experimentally determined by Shedlovsky [31], Davies [30], and Johnson and Hulett [32], at 25° C., and with those of Shedlovsky [33], as well as Davies [30], at 18° C. The specific conductance is determined from the equivalent conductance by equation

where k is the specific conductance, and the concentration in equivalents per milliliter (not per liter).

In order to calculate the concentration of solution 4 in grams of potassium chloride per 1,000 g of solution, the density of a 0.001 N KCl solution at 25° C was determined by methods of interpolation from data found in the International Critical Tables. This density is based on a solution which contains 0.074533 g of KCl per liter at 25° C.

(c) DETERMINATION OF CELL CONSTANTS

The resistance, Rsolv., of equilibrium water from the same lot as that used in making the potassium chloride solutions is checked in a clean cell [12, 34]. The cell is rinsed two or three times with the potassium chloride solution and then filled therewith. It is allowed to remain 15 or 20 minutes in the constant-temperature bath. The resistance of the solution is then determined, and redetermined at the end of 5 minutes. If the two resistances check, the solution has reached thermal equilibrium. To verify the cleanliness of the cell, a second determination should be made after rinsing and filling it with fresh solution. The final value of the resistance, Roln., is used to determine the cell constant (uncorrected for solvent conductivity) by means of the equation

uncorrected kRgoln.,

=

(67)

in which k is the specific conductance of a standard potassium chloride solution (from table 33); C, the concentration in grams of potassium chloride per 1,000 g of solution corresponding to this specific conductance; and C1, the actual concentration of the solution. Both C and C are expressed in grams of potassium chloride per 1,000 g of solution, corrected to weight in vacuum. Since the change in specific conductance of a potassium chloride solution with concentration is not constant, the value of C should be made as nearly equal to C as possible.

The uncorrected value of the cell constant, as determined from eq 67, may be used to determine the approximate specific conductance, Kolv., of the equilibrium water by means of the equation

Ksolv. =(4)

1

uncorrected×Rsolv.

(68)

Since the specific conductance of the solution, Kgoln., is the sum of the specific conductance of the potassium chloride ions, KKC, plus the specific conductance of the ions present in the equilibrium water, Ksolv., a very close approximation of the cell constant may be calculated from the equation

!= (KC + K2olv.
· Kolv.) Rootn..

a

(68a)

A more accurate method would be to make two resistance measurements, R' and R", extrapolated for infinite frequency, on two standard solutions of known specific conductance, K' and K". Then

a

= (K' –

R'

1 R"

(68b)

All measurements should be made at the temperature and frequency corresponding to that at which the conductance values of the standard potassium chloride solution were determined.

The cell constant, (l/a), at any temperature, t, may be computed from the cell constant, (l/a)o, at 0°, according to the following equation [35]:

where a is the linear coefficient of expansion of the glass from which the cell is constructed. For Jena normal 16 III glass, a=8.08×10-6 [36], and for Pyrex glass, a=3.6X10-6 [37].

Cells should be selected which have constants of such values that the total measured resistance of solutions of the electrolytes will lie between the limits of 1,000 and 50,000 ohms [35]. The highest resistance of any of the solutions measured will be that of equilibrium water, which should have a specific conductance not greater than 3.0X10-6 and the lowest resistance, that of molasses, which may have a specific conductance as high as 5×10-2. Three cell constants will cover this range and yet fall within the limits of resistance given above. These are 0.15, 7.5, and 50.0 reciprocal centimeters. specific conductance covers a narrow range, a single cell may suffice.

(d) CHECKING OF CELLS

The best test for the quality of the cells, whether they have bright or platinized electrodes, and for sufficiency of platinization, is to note the change in resistance resulting from a change in frequency of the oscillator current [38].

If electrode polarization reactance be treated as a function of the frequency, it follows that this reactance may be determined by successively measuring the resistance of the solution at two frequencies,

PLATINIZING CURRENT IN COULOMBS PER SQ CM
FIGURE 52.-Polarization reactance versus platinization.

one of which is about four times as great as the other. Whenever the difference between these two measurements is negligible for the purpose of the measurement, then the deposit of platinum black is adequate. (Fig. 52 [17] shows how the platinization of electrodes reduces this reactance.) However, if the two measurements indicate that a correction should be made, the true resistance may be found by extrapolating the data to infinite frequency [12, 15]. This may be done graphically or in the following manner:

Let R and R2 be the resistance measurements at two frequencies, fi and f2, respectively. Then, if the electrode polarization reactance,

AR, is inversely proportional to some function, n, of the frequency

or

AR=k/f" \
k=ARf"

(70)

where k is the proportionality factor. The true resistance, RT, of the solution is equal to the measured resistance minus the electrode polarization reactance or

Early observers have used unity for the value of n [15], but in a recent investigation 1/2 has been used [17]. It must be remembered that the use of the above equations is valid only when other errors in measurement resulting from changes in frequency (such as from the Parker effect) have been eliminated.

When routine measurements, such as those encountered in factory operations, are being made, no correction for electrode polarization reactance need be estimated. The frequency used for the observation should be recorded if it is to be compared with other data.

4. SPECIFIC CONDUCTANCE OF SOLUTIONS OF SUGAR PRODUCTS

(a) ASH DETERMINATION BY THE "C-RATIO" METHOD

"C-ratio" is defined as the ratio of the percentage of ash determined by incineration, as in chapter XVI, p. 263, to the specific conductance. After this factor has been established by averaging the results of several determinations of gravimetric ash and specific conductance, it may then be used to determine the percentage of ash of similar products by substituting its value and measured values of specific conductance in the equation

Percentage of ash=C-ratio Xspecific conductance.

(73)

This method of determining ash is applicable to control work of individual sugar manufacturers and to the ash analysis of granulated and other refined sugars [39]. However, since the specific-conductance value alone may be used to predict the performance of the product, many prefer to use it without conversion to percentage ash for control work.