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

Since the specific conductance of the solution, Koln., 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, Kolv., a very close approximation of the cell constant may be calculated from the equation

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

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- and the lowest resistance, that of molasses, which may have a specific conductance as high as 5X10-2. 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. If the 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 SQCM
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 fa, respectively. Then, if the electrode polarization reactance,

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

or

AR=k/f" |
k=ARƒ"}'

(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.

Specific-conductance determinations are made in cells of predetermined cell constant at a temperature most convenient for the locality, by measuring, as described above, the resistance of a solution of the product in equilibrium water and substituting this value in eq 63. The value of the specific conductance of the equilibrium water should be subtracted from the value found for the solution before the calculation of the C-ratio is made.

If the solutions are heated or subjected to vacuum, the value of Kolv will be changed from loss of CO2; if high precision is required, the value of Koly should be redetermined on a sample of the equilibrium water treated in the same manner as the solution.

The concentration of the solution recommended by different observers varies from 2.5 g of dry substance per 100 ml to 50 g per 100 ml. Since the conductivity of solutions of beet-sugar products passes through a maximum at 25 g of sucrose per 100 ml of solution [8], measurements made near this concentration will be affected less by slight errors in concentration than at other concentrations [40]. Regardless of what concentration is selected as being the most suitable, it should be the same as that used for the determination of the C-ratio.

(b) ZERBAN AND SATTLER CONDUCTANCE METHOD FOR ASH

Although the C-ratio method may be used to determine the ash content of sugars from the same source in any one season, the ratio determined for one district cannot be used for another district. This fact has resulted in the Zerban and Sattler method for ash determination, based on conductivity measurements under special conditions, and no reference need be made to the gravimetric ash.

In developing this method, they minimize all causes for variability of the C-ratio except that resulting from the composition of the dissolved salts. The inorganic salts in solution in raw sugars are principally sulfates and chlorides. Since the equivalent conductance of solutions containing anions of inorganic salts is considerably higher than that of solutions containing anions of organic salts derived from the same base, it follows that the specific conductance of a solution containing a large percentage of chlorides or sulfates in the ash is relatively greater than that of a solution containing a small percentage. Furthermore, the C-ratio will decrease as the percentage of inorganic anions in the ash increases.

If hydrochloric acid is added to a solution containing only inorganic anions, the specific conductance will increase linearly with the addition of acid. However, if the solution contains both organic and inorganic anions, the specific conductance will increase linearly only after the weaker inorganic anions have been displaced by those of the added acid.

A similar relationship exists between the specific conductance of solutions containing inorganic and organic cations if a solution of potassium hydroxide is added. However, except when the sugar product has received treatment with bone black, this latter relationship is not pronounced and may be ignored.

From these relationships, Zerban and Sattler have developed three general methods for the determination of ash applicable to: 1. Raw cane and soft sugars [41].

2. Refinery sirups and molasses produced without char treatment [42].

3. Raw and refinery sirups and molasses of unknown origin [43]. (1) RAW CANE AND SOFT SUGARS [40].-Twenty-five grams of sugar is dissolved in equilibrium water and the solution diluted to 500 ml at 20° C. The specific conductance, k, of one portion of this solution is determined and likewise, the specific conductance, k1, of another portion to which 5 ml of 0.25 N hydrochloric acid has been added to each 200 ml. Corrections are made for temperature and the conductivity of the water. The corrected specific conductances multiplied by 10 give, respectively, K for the original solution, and K, for the acidified solution. The percentage of ash may then be computed from the empirical equations,

(74) (75)

Raw sugar, percentage of ash=0.001757X (0.913K+193.5-0.1K1) Soft sugar, percentage of ash=0.001695 (0.913K+193.5-0.1K) The temperature corrections for k and k1 are given by the equations (k), (k)20 [1+0.02234(t-20)+0.0000885(t-20)2] (k1);= (k1)20[1+0.01704 (t-20)+0.000062 (t-20)2], in which t is the temperature at which the conductivity determination is made. The correction for (k), is roughly 2.2 percent per degree centigrade if measurements are made near 20° C.

(76)

(77)

The concentration of the acid may be checked by conductivity determinations. When 5 ml of the 0.25 N acid is mixed with 200 ml of equilibrium water the corrected specific conductance is 0.002370 at 20° C.

(2) REFINERY SIRUPS AND MOLASSES PRODUCED WITHOUT CHAR TREATMENT [41].-A solution is made of 100 ml of hot equilibrium water and 25 g of sirup or molasses. It is filtered with vacuum through asbestos and filter-paper pulp into a 200-ml volumetric flask with repeated washing with hot equilibrium water. The filtrate is mixed thoroughly and diluted with equilibrium water to 200 ml at 20° C. To a 20-ml portion of the filtrate is added 22.5 g of pure tablet sugar. This is diluted to 500 ml at 20° C with equilibrium water. This is known as solution A. To 200 ml of solution A, 5 ml of 0.25 N hydrochloric acid is added. This is known as solution B.

The specific conductances are determined in both solutions A and B and are corrected for solvent, specific conductance of the tablet sugar, and temperature. These values multiplied by 106 are respectively K and K1, which may be substituted in the equation

Percentage of ash=0.001757 (9.13K+1935-K1).

(78)

(3) RAW AND REFINERY SIRUPS AND MOLASSES OF UNKNOWN ORIGIN [42]. The procedure is the same as that used for the preceding determinations except that three conductivity measurements are required. Normal orthophosphoric acid is added to solution A to obtain solution B. The specific conductance at 20° C is determined on each of the following solutions:

1. k of solution A, as prepared in the preceding section.