INDUSTRIAL AND ENGINEERING CHEMISTRY
180
points of gum N and gum D do not lie on the dotted line of Figure 4; nevertheless the agreement between the calculated and observed values of viscosity is fairly good. On the other hand, treated rosin, although a straight line, does not fit with the formula. Several foreign gums also deviate widely from the calculated values. CONCLUSIONS The equation =
A exp
The constant b of Equation 2 determines the viscosity of the ordinary American gum or wood rosins. From this, an expression may 'be derived which gives the approximate viscosity of a rosin a t any desired temperature. It is: log7 =
where t,
= 1 = log 7 =
(-) b
Vol. 24, No. 2
- 54 - 3.50 - 20
6.05 f,
melting pointb C., as determined by drop method temperature, C., at which viscosity is desired common logarithm of viscosity in poises. LITERATURE CITED
T - 0
fits all rosins investigated (eighteen altogether) with good agreement over the temperature range 100" to 200" C. The constant 8, excepting for French WW, is about the same for all rosins studied, and varies from 273 to 300. The constant log A is approximately the same for most rosins, varying from -3.4 to -3.6 when 0 = 293. Extrapolation of the lines obtained in this way can be extended to the so-called melting point of the rosin, to estimate the viscosity a t this temperature. It appears to be of the order of 5000 poises.
D. H., Nature, 125, 581 (1930). (2) Frenkel, J., Ibid.,-125,583 (1930). (3) Hatchek, E., "Viscosity of Liquids," pp. 63-78, Van Nostrand, (1) Black,
1928.
(4) Iyer, M. P. V . ,Indian J . Phys., 5,371 (1930). (5) Madge, E. W., J. Phys. Chem., 34, 1599-1606 (1930). (6) Peterson, J. M., and Pragoff, E. P., IND.ENG.CHEM.,24, 173 (1932). (7) Porter, A. W., Phil. Mag., 23, 458 (1912).
RECEIVED April 9,1931. Presented before the Division of Paint and Varnieh Chemistry a t the 81st Meeting of the American Chemical Society, Indianapolia, Ind., March 30 to -4pril 3, 1931.
Parallel Scale Charts R. C . STRATTON, J. B. FICKLEN, AND W. A. HOUGH, Chemical Laboratory, The Travelers Insurance Company and The Travelers Indemnity Company, Hartford, Conn.
R
ECEKTLY the authors were called upon to make a large number of calculations of boiler feed-water treatments, employing soda ash and lime as water-softening agents. The calculation of the necessary amounts of soda ash and lime in each case was made by using modifications of equations originally developed by Stabler (1-4). I n the original Stabler formulas the amounts of the various positive and negative radicals, such as calcium, magnesium, carbonate, and bicarbonate found by anaIysis of the water, were expressed in parts per million. The number of parts per million of each positive or negative radical was then multiplied by its own so-called reaction factor, and the algebraic sum of these products was in turn multiplied by a conversion factor to give the amount of soda ash, or soda ash and lime, necessary for softening the water. The result was expressed in ounces per thousand gallons. In the waters analyzed here, iron, aluminum, carbonate, and hydrogen ions were present in such negligible amounts that these radicals were omitted from the calculation, and the formulas were modified as follows: (To be used for a water conSODAASH TREATMENT. taining a large amount of calcium but only a small amount of magnesium). Ounces soda ash per 1000 gallons water
=
7.44 ( G a )
(1)
(To be used for a water LIMEAND SODAASHTREATMENT. containing a moderate or large amount of magnesium in addition to calcium.) Ounces soda ash per 1000 gallons water = 7.44 h C a r * M-g - nHC03) (21 Ounces lime per 1000 gallons water =
+
where Ca
Mg
HCOa
= p. p. = p. p. = p. p.
+
4.16 (mMg T3HC03j rI = 0.0499 rn. of calcium m. of magnesium r2 = 0.0822 m. of bicarbonate T J = 0.0164
(3)
By substituting the numerical vaIues of rl, rz, and r3 in the above equations and multiplying through by the coefficient in front of the parentheses, the following are obtained: Ounces soda ash = 0.371 (p. p. m. Ca) (soda ash treatment) (1) Ounces of soda ash = 0.371 (p. p. m. Ca) 0.612 (p. p. m. Mg) - 0.122 (p. p. m. (2) (soda ash and HCOa) lime treatment) Ounces of Iime = 0.342 (p. p. m. Mg) 0.068 (p. p. m. HCO) (3)
+
+
I
Considering Equation 1, it is obvious that the amount of soda ash is a direct function of the number of parts per million of calcium to be removed, and that a pair of parallel scales can be laid out in which each part per million of calcium will correspond to 0.371 ounce of soda ash. Thus by knowing the amount of calcium in parts per million, one reads directly across to the correct amount of soda ash. Equation 2 is applied visually by using the two scales described above, and in addition a scale for the amount of magnesium and one for the amount of bicarbonate. Each part per million of magnesium is made to correspond to 0.612 of a division of the soda ash scale. On the bicarbonate scale each part per million of bicarbonate corresponds to 0.122 of a division of the soda ash scale. By means of these four scales placed side by side, Equation 2 can now be evaluated as follows: A straight edge is placed upon the amount of calcium and the corresponding amount of magnesium noted. To this amount is added the number of parts per million of magnesium actually found by analysis. The straight edge is then moved upward to the point representing the sum. The amount of bicarbonate corresponding to this sum is noted and from this amount is subtracted the number of parts per million of bicarbonate found by analysis. The straight edge is then moved downward to the point
February, 1932
I N DU ST R I A L A N D E N G I N EER I N G C H EM I STR Y
295 19
18 -40
245 16
- 215 2fO 205 - 200
295 - 185 - 175
-30
190
180
-
14
f3
12
I70 -m5 160 - IO - 155 150
-
I1
- I25 - 8 145 140
135 f30
-
20
9
I20
115
- I05 NO -7 JOO 9s -6 90 85 - 80
-
75 70 65 -60 - 35 -15 - 10 - 5
-fO
55 50
-45
40
-
-
-30 25 20
-
- 0 -0
FIGURE1. CALCULATION FOR FEEDWITH SODAASH WATERTREATMENT
-s 4
-3
-2 -I
-
0
FIGURE 2. CALCULATION FOR F E ED-WA T E R T R E A T M E N T WITH LIME
181
r e p r e a e n t i n g the remainder. The amount of soda ash corresponding to this point is the correct amount to be used with the lime in the soda ash and lime treatment. If the amount of bicarbonate actually found by analysis is greater than the “bicarbonate equivalent” of the calcium and magnesium, no soda ash is necessary. Scales for the application of Equation 3 are constructed in a similar manner and the correct amount of lime is found visually. The various scales described are shown in Figures 1 and 2. The authors realize that the application of these particular formulas is very limited, and that the effect i v e n e s s of the amounts of watersoftening materials c a l c u l a t e d b y their use is a matter of controversy. However, the a u t h o r s do wish to call particular attention to the fact t h a t p a r a l l e l scale charts of the above type can be used to advantage many times in the chemical calculations where the equation is of the general type: Ki(K2X
+ KBY + K Z ....) = U
where K1, KP, KB, and K4 are constants and X, Y , Z, and U are variables.
LITERATURE CITED (1) Foulk, Geological Survey of Ohio, Industrial Water Supplies, Series 4, Bull. 29, 68 et seq. (1925). (2) Rogers, “Industrial Chemistry,” 4th ed., Vol. 1, p. 80, Van Nostrand, 1926. (3) Scott, “Standard Methods of Chemical Analysis,” 4th ed., Vol. 2, p. 1441A, Van Nostrand, 1925. (4) Stabler, U. S. Geol. Survey, Water Szcpply Paper 274 (1911). (Out of print.) RECEIVED September 14, 1931.
An Efficient Gas-Liquid Reaction Tower EDWARDF. I~EGERING, Purdue University, Lujayefte, Ind.
T
H E accompanying figure shows a simple reaction tube which is especially adapted to procedures involving reactions between gases and liquids. To a Buchner type funnel containing a “gerate” glass plate, are sealed the tower and the gas lead. These funnels are available in Jena glass in three standard porosities (3 to 5 p , 5 to 7 p , less than 7 p ) , and under a small gas pressure they give a spray of tiny bubbles. This results in a large reaction surface per volume of gas wed. Since the funnels are obtainable in different sizes, the towers may be small or large,
according to the requirements of the reaction under consideration.
L REACTION TOWER
Towers of this type have proved very satisfactory in oxidation experiments with oxygen gas in this laboratory. RECEIVED January 2, 1932.
