INDUSTRIAL AND ENGINEERING CHEMISTRY
3 14
8. While results on quadruplicate untreated blocks (Table 11) and duplicate treated blocks show good agreement, data on reproducibility of this technic in other hands are not available at the present time, and definite claims for the true reproducibility of the method must await trial by other workers. Literature Cited 11) Gillander, H. E., King, C. G., Rhodes, E. O., and Roche, J S , IND.EXG CHEV. 26, 175-83 (1934).
VOL. 10, NO. 6
(2) Llese. J . , et al., Z . angew. C h e m 48,21 (1935). (3) Lumsdenl G. (2.1Bell Labs. Record, 20 9-14 (1932) (4) Richards, C.A., Proc. Am. Wood Preservers' Assoc., 19, 127-35
(1923). Schmltz, H., IND.E K G . CHEX.,Anal. Ed., 1, 76-9 (1929). 6) Waterman, R. E., Leutritz, J., and Hill, C. M., Bell Syetem Tech. J., 16,194-211 (1937). t i ) Waterman, R. E.. and \Tilliams, R. R., IND. ENG.C H m f . , AnalE d , 6,413-18 (1934). cj)
RECEIVEDFebruary 9, 1978
Thermal Conductivity of Liquids U
Binary Mixtures of Water-Methyl Alcohol and Water-Ethyl Alcohol OSCAR KENNETH BATES, GEORGE H..IZZARD, A \ D GERALD PALMER St. Lawrence Unibersitj. Canton, N. Y.
The paper presents improvements in the operation of the apparatus previously reported ( 1 , 2), and the results of the determinations of the thermal conductivity and temperature coefficients of thermal conductivity for water-methyl alcohol and waterethyl alcohol binary mixtures.
B
ATES reported in detail the method of determining the thermal conductivity of liquids, a description of the apparatus, and the calculation of the coefficients in previous papers (1, 2 ) . Figure 1 gives a general view of the present setup. However, two changes have been made in the operation of the apparatus from that previously reported. To minimize conduction from the room to the calorimeters, thecalorimeterwater must bekept at room temperature, besides insulating heavily with rock wool and magnesia insulation. During the winter months electrical heating of the calorimeter cooling water from 5' to 20' C. requires the continuous use of about 2 kilowatts. To reduce the power consumption and eliminate the necessity for thermostatic controls, the authors recirculated the cooling 8 water, taking special care t o keep the temperature constant. A small centrifugal pump ( B , Figure 2) delivered the cooling water from the calorimeterback to the constant-head tank, located some 2 meters (6 feet) above the apparatus. To prevent vibration from reaching the apparatus, the pump was cushioned by several inches of sponge rubber, and all piping insulated from the wall. by sponge rubber. Cold water from the serondary constant-head tank (C, Figure 2) was added to the circulating water at an open tank at the inlet to the pump, to balance the heat picked up in passing through the calorimeter. A specially constructed needle valve in the outlet of the secondary constant-head tank accurately controlled the amount of water added In this manner, the temperature of the tebt calorimeter was maintained very steadily. Since the work requires equilibrium temperature conditions, this method of controlling the temperature of the water flmying through the calorimeters seemed superior to electrical heating and thermostatic control. The line voltage must be controlled ver) closely to eliminate fluctuations of the heater temperature. A 250-watt Raytheon voltage
regulator ( A , Figure 2) provided a completely constant voltage and, with the recirculating water system described above, virtually rliminatpd temperature fluctuations of the apparatus.
Procedure A previous paper (1) explained in detail the experimenta! procedure and method of calculation of the various coefficients. The values of the several coefficients were calculated from the temperature gradient curves drawn for each series of runs. I n this case, a series of tests was made for liquid mixtures of the following compositions (in per cent by weight): Methanol- Water Distilled water 9.0 per cent methanol-91.0 per cent water 18.4 per cent methanol-81.6 per cent water 35.8 per cent methanol-64.2 per cent water 58.0 per cent methanol-42.0 per cent water 77.1 per cent methanol-22.9 per cent water 89.2 per cent methanol-10.8 per cent aater 99.4 per cent methanol- 0.6 per cent water The methanol was received from E. I. du Pont d e Neinours & Go., Inc. T h e composition was reported as 99.85 per cent or better, and the specific gravity given as 0 79620 a t
FIGURE 1.
GENERllL
LAYOL-T OF
APPAR4TC.4
AIV.4LYTICAL EDITION
JUNE 15, 1938 TABLE MethaWater no1 % by weight 100
(Pure water) 95 5 90 10 85 15 80 20 75 25 70 30 65 35 60 40 55 45 50 50 45 55 40 60 35 65 30 70 25 75 20 80 15 85 90 10 5 95 100 (Pure methanol) a
I. TRUECOEFFICIENT
OF
THERMAL CONDCCTIVITY (Kr)
Values of Kt
0,00138
30'C. 4OOC. 50OC. 60" C. Gram calories, second-', cm.-2, C. -1, cm.a 0.00141 0.00145 0.00149 0.00152 0.00156
0.00132 0 00126 0,00120 0.00115 0,00110 0.00105 0,00100 0.00096 0,00091 0,00088 0.00083 0.00079 0,00076 0.00072 0,00069 0.00065 0,00062 0.00059 0,00055 0.00053
0,00135 0,00129 0,00123 0,00117 0,00112 0,00107 0.00101 0,00096 0.00092 0.00088 0.00083 0.00079 0,00075 0,00071 0,00067 0.00064 0,00060 0.00057 0.00054 0.00051
10" C. I
20OC.
0.00139 0,00132 0,00126 0,00120 0.00114 0,00108 0,00103 0.00097 0.00092 0.00088 0.00083 0.00078 0.00074 0.00070 0.00066 0.00062 0.00059 0.00056 0.00052 0.00050
0.00142 0.00135 0,00129 0.00122 0.00116 0,00110 0,00104 0.00098 0.00093 0.00088 0.00082 0.00078 0.00073 0.00069 0.00065 0.00061 0.00058 0.00054 0.00051 0.00048
0.00146 0.00139 0,00132 0.00125 0.00118 0.00112 0.00105 0.00099 0.00093
0.00088 0.00082 0.00077 0.00072 0.00068 0.00064 0.00060 0.00056 0.00053
315
0.00149 0.00142 0.00134 0.00127 0.00120 0.00113 0.00106 0.00100 0.00094 0.00088 0.00082 0.00077 0.00072 0.00067
... ... ... ... ...
0.00050
...
0.00047
70'C.
. %,
Equations for True Coefficient o f Thermal Conduotivity
a d
c.-i
0.00160
0.27
K;=
0.00151 0.00145 0.00137 0.00129 0.00122 0.00115
0.26 0.25 0.22 0.21 0.18 0.14 0.12 0.10 0.06 0.00
Kt = 0.00128 KI 0.00123 KI 0.00118
... ... ...
... ... ... ... ... ... ... ... ... ... ...
0.00134 f 0.00000365 ( t )
++ 0.00000350 (t) 0.00000315 (ti + 0.00000275 Kt 0.00113 + 0.00000225 ( t ) Kt = 0.00108 + 0.00000200 ( t ) Kt = 0.00103 + 0.00000175 ( t ) Kt = 0,00099 + 0.00000125 ( 1 ) K t = 0.00095 + 0.00000075 ( 1 ) Kt = 0,00091 + 0,00000050 ( 1 ) KI 0.00088
--
-0.03
Kt Kt
-0.06 -0.10 -0.11 -0.11 -0.16 -0.17 -0.18 -0.19 -0.20
Kt
Kt
-
0.00083 0.00080
= 0.00076
K; = KI KI
KI =
K ;= Ki =
0,00073 0.00070 0.00066 0.00063 0.00060 0.00057 0.00054
(tj
-- 0.00000025 (t, 0.00000050 ( t ) -- 0.00000075 0.00000100 - 0.00000125
(1)
(t) (t)
- 0.00000125 ( t )
-- 0.00000125 (t) 0.00000150 i t ! - 0.00000150 -
(1)
0.00000150 ( 1 )
C.-l. cm.: 2900 = K t ( B . t. u . , Kt(cal., sec.-l, cm.-2. C. g. s. system, defined by Kt = Kzo[l o w f - 20)).
+
b a20 as
T.IBLE11. TRUECOEFFICIENT OF THERMAL CONDUCTIVITY (Kt) Ethyl
Kater Alcohol yo b y weight 100 (Pure water) 95 5 90 10 85 15 80 20 75 25 70 30 65 35 60 40 55 45 50 50 45 55 40 60 65 35 30 70 25 75 80 20 15 85 10 90 5 95 (Pure ethyl) 100
7
100
c.
200
T'alues of Kt 30" C . 40' C . 50' C. Gram calories, second-', cm.-2, C.-i, cm.o
c.
aid
%,
0.00141
0.00145
0.00149
0.00152
0.00156
0.27
0.00131 0.00125 0,00119 0.00113 0.00108 0,00102 0.00097 0.00092 0.00087 0.00082 0.00078 0.00073 0.00069 0.00065 0.00062 0.00058 0,00055 0.00052 0.00049
0.00135 0,00128 0.00122 0.00116 0.00110 0.00104 0,00098 0.00093 0.00087 0,00082 0.00077 0.00073 0.00068 0.00064 0.00061 0.00057 0.00053 0.00050 0.00047
0.00139 0.00132 0.00125 0,00119 0,00112 0.00106 0,00099 0.00093 0.00088 0.00083 0.00077 0.00072 0.00068 0.00063 0.00059 0.00055 0.00051 0.00048 0.00044
0.00142 0.00135 0.00128 0.00121 0.00114 0.00107 0,00101 0.00094 0.00088 0.00083 0.00077 0.00072 0.00067 0.00062 0.00058 0.00054 0.00050 0.00046 0.00042
0.00145 0.00138 0.00130 0.00123 0.00116 0,00109 0,00102 0,00095 0.00089 0.00083 0.00077 0.00072 0.00066 0.00061 0.00057 0.00052 0.00048 0.00044 0.00040
0.00149 0.00141 0.00133 0.00126 0.00118 0.00110 0.00103 0.00096 0.00089 0.00083 0.00077 0.00071 0.00066 0.00060 0.00056 0.00051 0.00046 0.00042 0.00038
0.25 0.23 0.22 0.21 0.16 0.14 0.11 0.08 0.04 0.00 -0.05 -0.10 -0.16 -0.22 -0.25 -0.32 -0.40 -0,48
0 00046
0.00043
0.00041
0.00038
0.00036
0,OOOHY
-0
C.-l, om.) 2900 = K t ( B . t. u . , hr: -1, it. - 2 . English system C. g . s. system defined b y Kt = K?orl w o ' t - 20!1.
F.-1.
Equations for T r u e Coeffioient o Thermal Conductivity
OC.-1
0.00138
a Kt(cal., sec.-l, tin.-*, b a20 as
60' C .
0.18
.54
K t = 0.00134 f 0.00000365 ( f ) = 0.00128
hi = 0,00122
Kf
= Kl = k't = Kt =
Kt K; Kt K; Kr Kt K; Kt Kt
= = = = = =
= = = KI=
K; = Kt =
K; = Kt
0 , 0 0 116 0,00111 0.00106 0.00101 0.00096 0.00091 0.00086 0.00082 0.00078 0.00074 0.00070 0.00067 0.00063 0.00059 0,00066 0,00054 0.00052
= 0,00048
0.00000336 ( 1 ) ++ 0.00000300 (t) ++ 0.00000270 (t) 0.00000245 ( t ) + 00000200 t ) + 00.00000165 it) + 0 00000130 ( t ) + 0.00000100 ( t ) 4- 0 00000070 ( 1 ) + 0 00000030 ( t )
- 0.00000035
- 0.00000115 0.00000070
(t) ( It ))
- 0.00000130 (1) - 0.00000140 ( t ) - 0.00000170 ( 1 ) - 0.00000200 ( t )
- 0 00000235 - 0.00000250
(t)
(f)
inch!
+
15" C./4" C. The distillation range did not exceed 1' C. from first drop to dry on a n Engler distillation unit.
z's, true thermal conductivity curves were drawn for every
Ethyl Alcohol-TVater
True Thermal Conductivity, Kt
Distilled water 11.0 per cent ethyl alcohol-89.0 per 20.2 per cent ethyl alcohol-79.8 per 37.4 per cent ethyl alcohol-62.6 per 24.9 per cent ethyl alcohol-35.1 per (9.2 per cent ethyl alcohol-20.8 per 91.7 per cent ethyl alcohol- 8.3 per
cent water
cent water cent water cent water cent water cent water
The ethyl alcohol used was 190 proof industrial alcohol U. S. P., manufactured by the U. S. Industrial Alcohol Co. From the calorimetric determinations and the temperature gradient curves, the true thermal conductivities were determined for the binary liquid mixtures listed above over the range of temperature covered for the particular runs. I n every case, within the accuracy of the tests, the true thermal conductivity was a linear function of the temperature-that is, a straight-line relation. From these curves, composition
10" C. interval.
The final data given in Tables I and I1 and graphically in Figures 3, 4, 5, and 6 were obtained from the conductivitycomposition curves. By means of either the tables or the graphs i t is possible to determine the true thermal conductivity of binary liquid mixtures of both methanol-water and ethyl alcohol-water for any temperature from 10" t o 70" C. and for any composition from distilled water to pure alcohol.
Average or Mean Thermal Conductivity The average thermal conductivity, Kj: between any two temperatures, tz and tl, covered b y the experiments and for any composition, can also be readily determined by using the average or mean temperature from Tables I and I1 and Figures 3, 4,5 , and 6. Since the true thermal conductivity is a linear
V-OL. 10, so. 6
INDUSTRIAL AND ENGINEERING-CHEMISTRY
316
culating the true thermal Conductivity of binary liquid mixtures when the conductivities of the two liquids are known. The equation is K sinh ( 1 0 0 ~ )= K1 sinh (pip)
+ K2 sinh ( p 2 p )
"where pl and p~ are the percentages by weight of the two constituents and p is a constant depending upon the constituents and the temperature." The following is a sample calculation using the above equation: Calculation of the thermal conductivity of a 40 per cent ethyl alcohol40 per cent water binary mixture at 20" C. PI = 40, pz = 60 K I = 0.00043, Kz = 0.00141 (Table 11) loop = 0.94
TABLE111. COMPARISON OF VALUES FOR TRUETHERMAL CoxDUCTIVITY OF WATER,METHYL ALCOHOL,AND ETHYLALCOHOL Liqmd Water Methyl alcohol Ethyl alcohol
Kt"
Tempera- e p o b ture, (%,
Observer I. C T. (3) Bates ( 2 ) Bates, Hazzerd, Palmer
Tear 1929 1936 1938
(True) 0 00138 0 00141 0 00141
I. C. T.
Bates, Hazeard, Palmer
1929 1938
0.00050 0.00051
I. C. T. Bates, Harzard, Palmer Schack (i) Saha and Srivastava ( 4 )
1929 1938 1933 1931
0.000453 0 00043 0.00041 0.00043
O
C.
O C
-1)
20 20 20
0 28 0 26 0 26
20 20
-0.053 -0.20
20 20 40
-0.071 -0.54
26
FIGURE 2. YOLTSGE REGULATOR, A , CESTRIFUPUMP. B , 4 N D SECOSDARY COS'BTAN1HEADTINK,C
GAL
function of the teniperature, the average thermal conductivity between temperatures tz and tl must be the same as the true coefficient at or the average of the t w n temperatures.
Discussion of Results The thermal conductivity values calculated from new tests run on redistilled water checked with the results given by Bates in 1936 ( 2 ) . His investigation was carried on with the same apparatus, but a t the Massachusetts Institute of TechnoloKv, with electrically heated, thermostatically controlled calorimeter water. Results for both binary mixtures (methanolwater and ethyl alcohol-water) show a temperature coefficient which reduces to zero at approximately a 50 per cent solution, going negative for alcohol concentrations higher than 50 per cent. I n other words, the temperature coefficient of thermal conductivity is positive for distilled water (a20 = +0.26%, O C.--I), approaches zero a t 50 per cent methanol-50 per cent water, and is negative for pure methanol (a90 = -0.20%, "C.-l). For ethyl alcohol-water mixtures the zero coefficient occurs around 52 per cent ethll alcohol-48 per cent water, and is negative for pure ethyl alcohol (am = -0.54%, O C.-'). Table I11 gives a comparison of the thermal conductivity values for water, methanol, and ethyl alcohol with those found by other observers. Barratt and Kettleton in the International Critical Tables proposed an equation for cal-
PERCENT METHYL ALCOHOL FIGURE 3. THERMAL CONDUCTIVITY-COMPOSITION CURVESFOR ALCOHOL-WATER SOLCTIONS
METHYL
JUKE 15, 1938
ANALYTICAL EDITION
317
to 10 per cent of the calculated h ' r from the obherved Kt (Table IV). Honever, since the residuals ( A ) were all of the same sign, it seemed necessary to change only p to make the equation fit. When p IS changed to make the wni of the residuals ( A ) as small as possible, the equation fits tlie data very \\ell On the basis of the above calculations, the authors suggest the following values of 100 M at 20" C : eth41 alcohol = 0.94, methyl alcohol = 0.90, glycerol = 0.65
The International Critical Tables suggest that p is a function of the temperature but give only the value a t 20" C. Values of Kt calculated for higher temperatures, the authors' values for 100 p2J suggested above being used, showed fairly good agreement with obserred conductivities a t those temperatures. Since the agreement up to 80" C.is good (Table V), it rrould seem useless t o change p a t higher temperatures, TABLE 1'.
COMPARISOS O F OBSERVED 4 6 D COMPUTED VALUES OF
Ki
(Showing the degree of independence of Water Solutions Composi- Temperaof tion ture Kobe. b y rceighl C. Ethyl alcohol
l00a
= 0.94
hlethyl
alcohol
-
lO0u Glycerol
20 40 60 80 20 40
GO
0 00126 0 0009ci 0,00071 0 00051
50
0,00123
80
o.oon99 0 000i7 0 . ooofio 0.00141 0 00118 0 00096 0 00079
60
0.90
l o o p = 0.65
80 20 40 60 SO
p
n-it11 tempeiature) A X KCSIC.
0 00124 0 00097 0 00073.5 0.00032 0.00124 n.nnioi 0 1000805 0.1)00fi3 0 110140 U iJ0119 0 110101 0 00035
10-5
2 -1 -2.5 -1 1
-2 -3 3 -3 1 -1 -5 -6
FIGURE 4. T H E R V 4 L CONDL-CTIVITY-TEMPERATURE CCRYES FOR METHYL ALCOHOL-KATER SOLUTIONS
Therefore, K =
+
0.00043 sinh (40 X 0.0094) 0.00141 sinh ( G O X 0.00941 sinh (0.94)
From a table of hyperbolic sines! Re get : sinh 0.94 = 1.085, sinh 0.376 = 0.365, sinh 0.504 = 0.594
Substituting these values and solving, R
=
0.000925
Using the authors' values of h'!and values of p given in t h e International Critical Tahles (3),they found variations of 5
CCIMPARISOS OF OBSERVEDTHERMAL COSDUCTIVITIES WITH CONDUCTIVITIES COMPUTED FROJI EQUATIOT K sinh (loop) = K 1 sinh (pip) K2 sinh ( p p )
TABLEIV.
+
Water Solutions of
Composi- Kobs. tion a t 20OC. weight
Roalc.
a t 20OC.a
A X 10-5
5
Kcdo.
I 10-
0.00113 0.000925 0.000735 0 0005i 0.001175 0.00096 0.00079 0.00064 0 001215 O.001OG5 0,00092 0,000795
1.0 0.5 -0.5
at 2 0 ' C . b
yo by Ethyl alcohol
20 40
60 80
Methyl alcohol
20 40 60 80 20 40 60 80
Glycerolc
0.00116 0.00093 0.00073 0 00057
0.00117 0 00096 0.00079 0 00064 0 00124 0 00107 0.00091 0.00078
0.00109 0.00084 0.00066 0 00053 0.00111 0.00068 0.00071 0.00059 0 00125 0.00111 0 00093 0.00081 ~~
6-7 4 6 6 8 5 -1
-4 -4 -3
~
~
~~
0 K C ~ Iis C obtained . from the above equation using values of ethyl alcohol = 1.34, for methyl alcohol = 1.30, and for glycerol given in International Critical Tables. b Kodc. is obtained from the above equation using values of ethyl alcohol = 0.94. for methyl alcohol = 0.90, and for glycerol determined by the authors. C Values for Kt of glycerol were obtained from ( 2 ) .
A = Kobe.
-
Kcalo.
n
-0..5
0 0
0 2.5 0 5 -1.0 -1 5 100~nofor = 0.40 as
lO0r:o for = 0.65 ae THERMAL COXDUCTIVITY-TEMPERATURE CURVES FOR ETHYL ALCOHOL--WTATER SOLUTIONS
FIGURE 5.
INDUSTRIAL AND ENGINEERING CHEMISTRY
318
VOL. 10, NO. 6
FIGERE6. THERMAL CONDUCTIVITY-COMPOSITION CERVES FOR ETHYLALCOHOLw.4TER SOLUTIONs
versity for their cooperation in the general research program. Acknowledgment is also made to E. I. du Pont de Nemours &. Co., Inc., for their permission to publish the data on the thermal conductivity of methyl alcohol-water mixtures.
Literature Cited LO
300
11) Bates, ISD. EKQ.CHEM., 25, 431 (1933). ( 2 ) Ibid., 28, 494 (1936). I 3) International Critical Tables, Vol. V, pp. 227-8,
New York, McGraw-Hi11 Book Co., 1929. 4) Saha and Srilastava, “Text Book of Heat,” p. 327 (taken partly from Landolt and Born-
IO 20 30 40 50 60 7 0 80 90 100 PERCENT ETHYL ALCOHOL
for doing $0 mould not appreciably improve the fit of the equation. The authors wish to express their appreciation to Laurens H. Seeyle and to Ward c. Priest of The St. Lawrence Uni-
stein, “Physikalisch-chemischenTabellen” and partly from Kaye and Laby, “Tables of Physical and Chemical Constants”), Allahabad, The Indian Press, 1931. ( 5 ) Schack, “Industrial Heat Transfer,” tr. by Goldachmidt and Partridge, p. 349 (taken from E. Schmidt, Mitt. Forschungshezm. Warmesh., No. 5, Munich, 19241, Sew York, John Wiley & Sons. 1933.
R~~~~~~~ February 16, l Y 3 S .
Determination of Gold and Silver in Cyanide Solutions W. E. CALDWELL AND L. E. SMITH, Oregon State College, Corvallis, Ore.
R
OUTINE control assays for the gold and silver content
of the alkali cyanide leach solutions from crushed ore, and on the barren solutions after recovery of most of the precious metals therefrom, are made by many methods. The procedures most commonly employed are the copper sulfate method as used in South Africa ( d ) , the evaporation method (2, S ) , and the zinc-lead acetate method ( 3 ) . The work of Yasuda (4), and as extended by Caldwell and McLeod ( I ) , shows that minute quantities of gold may be obtained from large volumes of solution by employing a semicolloidal mercury and mercurous chloride collector. Although their method, as reported, is not applicable to cyanidecontaining solution, it was desired to apply its general principle and procedure to determining the noble metal content of cyanide-containing solutions. T h e problem, then, was to destroy or eliminate the cyanide ion of the samples containing noble metal so that it would not interfere with collection of gold from solution by mercurous precipitate.
A well-known inorganic reaction is the formation of potassium ferrocyanide by the reaction of ferrous sulfate and potassium cyanide. It seemed feasible with the use of ferrous sulfate to eliminate the cyanide ions from the solution that the colloidal mercury fall method should yield good results as a collector of gold and silver from solution. To test the applicability of the semicolloidal mercury fall method in collecting and recovering gold and silver from cyanide-containing solution, if the cyanide ion is converted to ferrocyanide by use of ferrous sulfate, numerous experimental runs were made. Simulated cyanide leach solutions as from gold ores were prepared. Particles of pure gold, weighed to within 0.01 mg., were dissolved in the minimum quantity of aqua regia and transferred to water in 2-liter bottles. A measured volume of standard silver nitrate was introduced. Potassium cyanide was added to yield solutions of various percentages of cyanide, but in general of about 0.025 per cent, which is representative of economic leach solutions.
