Feb., 1956
23 1
HEATCAPACITY AND HEATCONTENT O F A L ~ O AND ~ MoS12
Viscosity Increment in the Complete Absence of Salt.-Table I shows that a small increase in [ q ] occurs not only as the charge is increased, but also at the isoionic point in the complete absence of ,salt. This effect may also be interpreted as an electroviscous effect for while the average charge a t the isoionic point is zero, the average value of Z2 is not zero,*Qa fact responsible for a number of physical phenomena of isoionic proteins a t low ionic strength.42 Assigning a value of 10 to for serum albumin at the isoionic point, and assuming that the only inorganic ions present are the hydrogen ions required to produce the equilibrium pH of 5.0, we may again apply Booth’s equation and calculate an increase in [77] of 0.0009. This is somewhat smaller than the observed increase of 0.0035, but the difference is much less than. the difference between results calculated and observed for ovalbumin in the absence of salt. Booth4 states that his equation is not strictly applicable t o very low values of
there might be significance in expressing the concentration dependence of the viscosity of macromolecular solutions by a power series of the form44 +
q/qo = 1
+ [SIC + KItll2c* + . . ,
Concentration Dependence.-It was pointed out in connection with Fig. 2 that the concentration dependence of reduced viscosity, as reflected in the slopes of plots such as those of Fig. 1, appears to contain two factors,a non-electrostaticone independent of charge or ionic strength, and an electrostatic factor depending strongly on these variables. The expanded form of Einstein’s equation, or the corresponding equations of G ~ t h suggest , ~ ~ that
if we use this equation to describe our results, we should conclude that K is the sum of two terms, K = KO K1, KOrepresenting the non-electrostatic interaction between the dissolved particles and K I , the electrostatic interaction. K1 should be a function of charge and ionic strength, and should vanish when = 0, or, at any value of 2, where EL is sufficiently large. Rough empirical values of KC,and K1may be obtained from Fig. 2. One obtains for KO the value of 1.88 f 0.13, while K 1is given approximately as 2 x 10-6 B / p * / z . It is of interest that the value of K Ois essentially the same as that found in this Laboratory for another protein, ribonuclease, for which we obtained K O = 1.92 f 0.12. It is also close to the value, KO = 2.26, predicted by the equation of Guth and Gold.43 An examination of literature data does not suggest, however, that this is a universal constant applicable to all proteins.45 Acknowledgment.-This investigation was supported by research grant NSF G-326 from the National Science Foundation, by research grant H-1619 from the National Heart Institute, of the National Institutes of Health, Public Health Service and by a grant from the Research Corporation.
(42) J. G. Kirkwood and J. B. Shumaker, Proc. N u l l . Acad. Sci. U.S., 38, 863 (1952). (43) E. Guth, K o l l o i d - Z . , 74, 147 (1936); E. G u t h and 0. Gold, Phw. Revs., 65, 322 (1938).
(44) J. 0. Buzzeil, Ph.D. Thesis, State University of Iowa, 1955. (45) The data of Polson,m for example, yield considerably smaller values of KOfor a number of proteins, but a value near 2.0 is obtained from his data for serum globulin in 0.81 M NaC1.
z2
Ka.
+
HIGH TEMPERATURE HEAT CONTENT A N D HEAT CAPACITY OF A1203 A N D MoSi; BY B. E. WALKER, J. A. GRANDAND R. R. MILLER Chemistry Division, Naval Research Laboratory, Washington, D.C. Received July 81,1966
The heat capacity of ALOa and MoSil were derived from heat content measurements made over the range 30 to 700” for AI& and 30 to 900” for MoSis. The changes in enthalpy were determined by the ‘‘drop” method and a copper-block caloriheter. The calorimeter is a modified version of one previously used and described by J. C. Southard.2 The furnace for heating the samples is specially constructed for high temperature heat capacity work.
Introduction The purpose of this investigation was to check the accuracy of this Laboratory’s apparatus through enthalpy and heat capacity measurements on a calorimetric standard material, AI2O3,and to provide some useful and accurate high temperature data on a relatively new and little known material, MoSiz, for another agency. Experimental Apparatus The apparatus used in these determinations is a modified version of Southard’s apparatus2 in which a capsule is heated to a desired temperature and a t a given moment ifi dropped into a calorimeter of known heat capacity. The modifica. ( 1 ) This work was sponsored by the Materials Lab., Research Division, Wright Air Development Center. (2) J . C. Southard, J . Am. Chem. Soci. 63,3142 (1941):
tions described below were introduced principally to attain greater accuracy and ease in operation. The copper-block calorimeter is immersed in an oil-bath, which is well insulated to prevent excessive heat leakage. The bath is controlled a t 30” by a Magna-set precision thermostat, which, when used in conjunction with two motordriven stirrers, a. 50-watt nichrome heater and a coppercooling coil, maintains the bath temperature to within =t0.005O The calorimeter consists of three separate copper parts, which were machined from the same bar and assembled by shrinking the inner parts into position. The calorimeter thermometer, which IS a transposed bridge arrangement of two copper and two manganin resistances (270 n each), as suggested by Maiera and used by Southard,2 is wound on the central copper piece. The heater for electrical calibration purposes is wound on the copper block that forms the receiving well. The calorimeter is protected from furnace
.
(3) C . G. Maier, THIE JOIJRNAI.,84, 2860 (1930).
232
B.E.WALKER,J. A. GR.4ND AND R. R. MILLER
radiation by a double cam arrangement, which permits both cams to be opened simultaneously durin a bucket dro The thermometer current is controlfed by a N d calibrated standard resistance and heliopot and is read on a Type B Rubicon millivolt potentiometer. The relative temerature of the calorimeter is read to 0.0002° on ashielded Fype C Rubicon micro-volt potentiometer. The heat exchange rate of the calorimeter is 0.00106° per mindte-degree and is reproducible from day to day to 10.00002' per minute-degree. The heat capacity of the calorimeter was determined in the standard manner b supplying a known quantity of heat to the calorimeter an8 observing the rise in temperature. The heat ca acity was obtained from about thirty calibrations made Eefore and during the enthalpy measurements and found to be 2049.35 cal./mv. with an average deviation of f0.03010. (In this system 1 mv. is equivalent t o 0.963O.) The furnace is specially constructed for this work so that there will be an isothermal zone of considerable length and the temperatures of the containers will be accurately known. The Alundum furnace core (2.5in. bore and 48 in. long) is wound with three pIatinum-lO% rhodium heating elements 80 that a desired temperature can be obtained more quickly and to provide the long isothermal zone mentioned above Power for the heaters is sup lied and controlled by several cascaded constant-voltage &la transformers, in conjunction with a variable transformer for each heater. A 60 in. McDanel porcelain tube fits inside the Alundum core and the thermocouples inside this tube are shielded from induced electromotive forces by a nickel screen placed between the core and the McDanel tube. Platinum-platlnum-10% rhodium thermocouples are peened into the center of five high conducting gold tubes 1, 6, 1/2 and 1 in. long. The gold tubes are spaced at equal intervals by porcelain tubes and located so that the temperature in the urnace may be read at several points. The central gold piece has two additional thermocouples attached a t each end and a gold disc has been pinned to this tube so that the sample container, when drawn up into the furnace, will OCCUPY the center and most nearly isothermal region of the furnace. The porcelain spacers and the gold tubes are grooved on their outer surfaces to allow clearance for the seven in. diameter double-bore porcelain tubes, which contain the thermocouple leads. By suitable adjustment of the three heaters the temperature gradient of the central gold piece can be controlled within O.lo/cm. The thermocouples were calibrated a t this Laboratory a ainst several primary standard thermocouples from the 8ational Bureau of Standards. The furnace temperatures are read on a Type B millivolt potentiometer and are calculated to be accurate t o about 10.05%.
.
Experimental Method I n brief, the method consists in heating the sample to a known temperature in the furnace; then dropping i t into the calorimeter and measuring the temperature rise of the calorimeter. The furnace is considered to be a t equilibrium when the change in temperature of the three thermocouples on the central gold tube is less than O.Ol'/min. The temperature rise of the calorimeter 1s determined by the method of least squares and extrapolation back to a "zero" time computed by Dickinson's method.' These procedures are repeated at a number of furnace temperatures and the heat capacity can be derived by the usual methods. The calorimeter and furnace tube are subjected to a continuous flow of argon gas t o minimize the oxidation of the type 347 stainless steel containers. The effectiveness of the argon is evident from the fact that less than 6.0 mg. of oxygen were gained during the entire series of runs on the sample container. I n addition to the enthalpy measurements for the bucket containing the sample, the method a h o requires that measurements be made for the empty container. The heat content data obtained from type 347 stainless steel, varies slightly from thetrue heat content, especially a t high temperatures, due to heat loss by radiation and convection during a drop and the heat content of the nichrome wire, which is attached to the container and included in a drop. When these corrections are applied, the heat content values for 347 stainless steel have an average deviation of only 10.25% (4) W. P. White, "Modern Colorimeter," Chemical Catalog Co., Zw., New York, N . Y., 1928, PP. 53-57.
Vol. 60
from those found by the National Bureau of standards.' The heat loss and the heat contributed by the nichrome wire, however, do not have to be accounted for in the sample runs because a bucket of similar shape, mass and composition is used, as well as the same dropping technique. The method further requires that other conditions be nearly, the same for the empty container runs as for the sample runs, such as the rate of flow of argon through the system, the thermal equilibrium of the furnace, and the time of fall of the containers from the furnace into the calorimeter. The buckets were allowed to fall freely, but due to the piston-like effect of the containers in falling, the heavier sample containers fell faster than the empty buckets. This was adjusted by attaching weights to the opposite end of the wire holding the container with sample in such a manner that its time of fall would be the same as an empty container. The heat content measurements were all adjusted to the same temperature (30'). Small corrections, a maximum of 0.05% of the total heat measured, were made to account for the oxide formation on the bucket and for the argon gas in the bucket.
Experimental Results In order to check the performance of the system, initial heat content and heat capacity measurements were made on the calorimetric standard material, AlzOs. The AlzOs crystals were furnished by the National Bureau of Standards and stated to be 99.97% pure, The results were obtained from 30 to 700" over 100" intervals and are listed and compared to those attained a t the National Bureau of Standards6 in Tables I and 11. The sample weighed 20.6987 g., in vacuo, and the type 347 stainTABLEI HEATCONTENT OF AlzOa Temp., OC.
98.12 98.61 197.20 207.63 296.86 298.26 404.81 416.51 511.30 503.01 595.05 598.17 705.23 702.36
H,
NRL
- H,,,
NBS
H, - Ha0, Csl./g. dev.
csl./g.
cal./g.
13.84 13.95 36.71 39.25 61.81 62.17 90.57 93.76 120.06 117.74 143.83 144.72 175.68 174.84
13.74 13.88 36.63 39.18 61.83 62.12 90.63 93.68 120.10 117.68 144.05 144.69 175.89 175.03
NRL-NBS
% Dev. NRGNBS
-0.73 .50 - .22 .18 .03
-0.10 - .07 - .08 - .07 .02 - .05 .06
-
+ + - .08 + .04 - .06 + .22 - -03 + .21 + .19
+
-
:08
+ .07 - .09 + .03 - .05 + .15 - .02 + .12 + .ll
Mean
* O . 17%
TABLE I1 HEATCAPACITY OF AlzOs Tyw., C.
NRL Cp cal./g., 06.
NBS CP, cai./g., o c .
?To Dev. NRL-NBS
64.2 150.4 250.0 354.1 458.9 551.9 650.2
0.2020 .2315 .2530 .2669 .2771 .2848 .2900
0.2038 .2319 .2527 .2671 .2771 ,2838 .2892
-0.89 -0.17 +os 12 -0.07 0.00 +0.35 + O . 28
Mean
&0.29%
(5) T.B. Douglaa and J. L. Dever. NBS Report 2302,1953. (6) D . C. Ginnings and R. J. Corruccini, J . Research Nutl. Bur. Standards, 38, 593 (1947).
HEATCAPACITY AND HEATCONTENT OF A L ~ O AND ~ MoSI~
Feb., 1956
less steel container weighed 22.6643 g. No corrections were made for the small amount of impurities in the material. The sample of MoSi2was supplied as a hot-pressed solid block and was machined t o a precision fit with the 347 stainless steel container. This was done so that there would be good heat transfer from the sample to the calorimeter and thermal equilibrium in the calorimeter would be established in a relatively short period of time. The density of the sample was calculated t o be 5.95 g./cc., which is 95% of the theoretical value (6.24 g./cc.). Chemical analysis of the sample material indicated a purity of 97.8%, 1.0% iron and 0.4% excess silicon. Since it seemed most plausible that the impurities would be present as oxides, analysis for oxygen was performed by a vacuum fusion technique by the Metallurgy Division of this Laboratory. The amount of oxygen determined by this method was 0.8%, which satisfied the requirements for the presence of iron as Fez03 (1.4%) and the presence of silicon as Si02 (0.8%). Corrections were applied to the heat content measurements on this basis, since this seemed the most reasonable from the evidence and calculations showed that corrections based on other possible forms of the impurities would be substantially of the same order of magnitude. Heat content and heat capacity results for MoSi2 were completed from 30 to 900" a t 100" intervals. The enthalpy values are shown in Table I11 and the heat capacity is indicated in Fig. 1. The sample weighed 29.6305 g. in vacuo and the 347 stainless steel container, 22.891 1 g. The equations for heat content and specific heat of MoSiz in c.g.s. units are as follows Temperature range 30 to 325" Ht
- H3oo = 0.13321 - 21.83 log ( t + 273.16) -
75.88( 1 0 . 5 % ) ( 1 ) C, = 0.1332
- 9.477 t
+ 273.16
Temperature range 325 to 875" Ht
- H,oo
=
0.1404t
- 31.93 log ( t
+ 273.16) + 50.18(10.5%) (3)
13.864 C, = 0.1404 t 273.16
+
Although two sets of equations are given this does not necessarily indicate a break in the heat capacity curve of MoSiz. This was only done because these two sets of equations best represented the experimental data. It was also determined that the results agreed very well with heat content and heat capacity data for MoSiz, as calculated from K. K. Kelley's data for molybdenum and silicon.' The average deviation of the experimental results from those calculated from Kelley's data was less than 0.3% for both the enthalpy and the heat capacity values. Consequently, the results give additional confirmation of Dulong and Petit's additive law of heat capacities and also provide verification of the heat content and heat capacity data on molybdenum and silicon. (7) K. K. Kelley. Bureau of Mines Bulletin 476, 1949.
233
. 0.12
Y \
0.11
73
" , 0.10
t0.09 0.08 0 100 200 300 400 500 600 700 800 9001000 Temp., O C . Fig. 1.-Heat capacity of molybdenum disilicide.
The results were also compared with those attained at the National Bureau of Standards.8 The results of this investigation are about 2% higher in heat content and heat capacity than the NBS data. This may be due to differences in the samples, which, in both cases, were corrected for impurities, but are not known to be wholly in the form of the compound MoSi2. The agreement, however, is fairly good considering the uncertainties attached to the samples, and either set of data should be applicable to most thermodynamic calculations. TABLE I11
HEAT CONTENT OF MoSi, Temp.,
OC.
110.10 109.61 199.05 197.92 299.67 298.32 419.25 412.49 496.03 495.93 617.86 613.50 697.57 695.80 802.27 787.73 876.15 872.90
H, - H.**cal./g. Obsd. Calcd.
8.41 8.37 18.36 18.20 30.09 29.96 44,08 43.42 53.48 53.33 68.36 67.74 78.56 78.15 91.79 90.17 101.34 100.77
8.37 8.39 18.32 18.19 29.89 29.73 44.06 43.24 53.38 53.36 68.44 67.90 78.45 78.22 91.73 89.87 101.18 100.72
Dev. Obsd. calcd., cal./g.
-
+O. 04 - .02 .04 .01 .20 .23
Dev.
Obsd.
-
calcd.,
%
+O .48 .24 .22 .05 .67 .77 .07 .42 .19 .06 .I2 .24 .14 .09 .07 .33 .16 .01
-
+ + + + + + + + + .03 + + .18 + + .10 +
+ -
+ + + +
.03 .08
.16 .ll .07 .06 .30 .I6 .05 Mean
+ -
+ + + +
&0.24%
The probable error in the present apparatus was calculated to be about &0.3%in the enthalpy measurements and *2% in the heat capacity results. As indicated by the data, however, it appears that the above approximations are somewhat higher than is actually the case. This is probably due to the fact that the probable error was computed from the sum of all the uncertainties attached to the calibration, empty bucket and sample measurements, whereas most of these uncertainties were partially or fully cancelled out by maintaining the same techniques and procedures throughout the investigation. (8) T. B. Douglas and W. Logan, J . Reeca?ch Natl. Bur. Slandarde!
IS, 9 1 (1854).
