QUASTITATIVE DIFFERENTIAL THERMAL AXALYSIS
Xov., 1961
continues to decrease and approaches unity. For the light phase, however, the ratio remains essentially constant a t four and the iron concentration decreases. Thus, there is no single value for the number of water molecules associated with the extracting species for all conditions of extraction.
1935
The number varies with the aqueous acid or salt concentration, i.e., with the activity of water in the aqueous phase. Similarly, the formation of two ether phases is governed by the activity of water in the system as controlled by non-extractable salts in the aqueous phase.
QUANTITATIVE DIFFERENTIAL THERMAL AXALYSIS BY CONTROLLED HEATING RATES’ BY EDWARD STURM Department of Geology, Texas Technological College, Lubbock, Texas Received January 26, 1961
The determination of quantities of heat, associated with thermal changes occurring in a sample when investigated by the method of differential thermal analysis, requires difficult evaluations of experimental variables such as the thermal conductivity of the sample and the heat leakage through the thermocouple wires. The method suggested here is based on the experimental determination of the over-all thermal conductivity of the total sample. The over-all thermal conductivity is computed from data obtained when heating the sample a t a rate resulting in a constant thermal gradient. The conductivity thus found is incorporated in a constant of proportionality which relates the heat of the reaction to the area under the differential thermal curve.
Introduction The aini of quantitative differential thermal analysis is the evaluation of heat changes taking place in a substance while it undergoes an exothermic or endothermic reaction. I n the conventional method, the sample substance and a thermally inert substance are heated at a constant rate. By means of a differential thermocouple, the e.m.f.’s developed by the two junctions embedded in the sample and inert substances can be continuously compared. The differential e.m.f., which is proportional to the differential temperature, is plotted against the temperature prevailing in the center of the inert reference substance by means of :m X-Y recorder or two strip-chart recorders. Thermal changes occurring in the sample are recorded as deviations from the base line (Fig. 1). The area under the curve is approximately proportional to the amount of heat liberated or absorbed during the thermal r e a ~ t i o n . ~ -The ~ numerical relationship between the quantity of heat involved and the area under the curve may be expressed as Q
=
Several workers6J made use of the divergence theorem (Green theorem) to obtain an expression for the total heat. Boersma6 derived a general expression (2) for the total heat
where Q’ = quantity of heat per unit volume ( ~ a l . / c m . ~ ) V = volume of sample (cm.3) S = surfwe of sample (cm.z) k, = thermal conductivity of sample (cal./sec. cm. deg.)
For a sample holder of cylindrical shape, whose height (h) equals or exceeds twice its radius ( T ) , Boersma6 derived the relationship
where r
=
radius of the sample holder (cm.)
Although the lower limit of integration should be r = radius of the thermocouple bead, no significant error is introduced by making this limit equal zero. Further, since Q = Q’V, and V = nr2h
$Lf2edt
where Q = quantity of heat (cal.) = differential temperature (deg.) tl, t2 = initial and final time of the reaction (sec.) $ = proportionality constant to be evaluated experinientally (cal./sec. deg.)
e
To evaluate the results of differential thermal analysis quantitatively, one must find the constant of proportionality for the given experimental conditions. (1) This work was supported by a research grant from Texas Technological College, Lubbock, Texas. (2) F. C. Kracek. J . Phys. Chem., 34, 225 (1930). (3) L. G. Berg, Compt. rend. Acad. Sci. U.R.S.S., 49, 648 (1945). (4) S. Speil, et al., U. S. Bureau of Mines Tech. Paper 664, 1945. (5) M .J. Vold, Anal. Chem., 21, 683 (1949).
In practice, the conductivity, k,, is the over-all conductivity of the total sample. This bulk conductivity, henceforth referred to as the effective conductivity, ke, is a function of not only the material under test but also of the effects of the thermocouple mires and the sample holder. The Effective Conductivity In the conventional experimental arrangement, the thermocouple beads are embedded in the center of the sample and inert substances contained in (6) S. L. Boersma, J . Am. Ceram. SOC.,38, 281 (1955). Note: the symbols used here are different from those used by Boersma. (7) C. M. A. deBruijn and W. Van der Marel, Geol. en Mignbouzu, 16, 69 (1954).
EDWAIID STURM
1936
1-01. 65
A value for the effective conductivity of the total sample can be found experimentally by heating the sample a t a rate resulting in almost steadystate conditions of heat flow, that is, a rate a t which the difference between the temperature prevailing outside the sample and that a t the center of the sample (To- Ti) remains constant. Considering the sample holder, the sample, and the enclosed thermocouple wires a single, nonhomogeneous sample, one may write In ( T ) instead of In (r/ro), and k, instead of he in equation 5 . Equating two expressions for total heat, we obtain 27rh ke[To - Ti] [ t z - til &=
Temp. of sample. Area proportional to hcat of reaction.
In r
+ mdc,l[T2- Til
[mace
(6)
where
- ti = the time interval (sec.) 2;, T I = furnace temperatures at times t 2 and
t2
Fig. 1.-Thermogram temperature. of reaction.
of differential temperature versus Shaded area is the area proportional to heat
sample holders of cylindrical shape. The temperature a t the thermocouple bead is due to the heat flow through the sample material as well as that through the thermocouple wires. Ignoring the end effects, the radial heat flow through the sample, under steady-state conditions, may be described as ks27rhtT0 - T,] Q'. = (5) In
t i , respectively ( d g . ) m.. m, = wt. of the samDle and wt. of the Dortion of the thermocoupfe wire embedded ih the sample (g.) e , cw = specific heats of the Sam le and thermocouple wire, respectively (ca1.i. deg.) = over-all or effective conductivity (cal./sec. cm. k, deg.1
Determination of the Proportionality Constant +.-Solving equation 6 for k, and substituting in equation 4,the expression (7) for is now obtained.
+
ro
where Q'. = quantity of heat flowing through the sample per second (cal./sec.) h = height (or length) of the sample holder (cm.) To - I", = the thermal gradient; that is, the difference between the furnace temperature and the temperature a t the center of the sample (deg.) re = the radius of a single, centrally located thermocouple wire whose cross-sectional area equals twice the cross-sstional area of the wire used, that is, ro = r w 4 2 , where rw = the radius of the wire used (em.)
where M
=
an amplification factor depending on the signal amplification employed ( pure number)
The proportionality constant must be evaluated for each analysis in order to allow for differences in sample packing, particle size distribution, and variables due to heat leakage through the thermocouple wires. Care should be taken to use approximately the same volume of sample material for each run. Another implicit assumption is I n differential thermal analysis the thermo- that the thermocouple beads are well centered, couple wires perform the double role of heat de- and that the height of the sample be at least twice tection device and heat sink. Their presence has its radius. Because many substances change significantly the effect of reducing the peak area by an amount related to the ratio of the heat flow through the during the thermal reaction, it is necessary to sample material to that through the thermo- determine $ for temperature ranges before and couple wires. The evaluation of the variables after the reaction (A and B in I?g. 1) and to use affecting the area under the curve poses a number the average value. Excepting weight and specific hcat determinaof experimental difficulties. To mention only one : The sample conductivity, k,, is a function not only t ions, all variable quantities required by equation of the substance itself but also of its porosity which, 7 can be obtained from measurements made with in turn, is a function of its particle size distribution the sample in the holder. This procedure assures and the manner of sample packing. Further, the that the conditions under which y5 is determined conductivity of the sample substance cannot be are the same as those prevailing during the reconsidered a constant in view of the fact that the action. composition of the sample changes during the Suggested Experimental Procedure-In order to dethermal reaction. termine the required variables it is necessary to find the In order to obtain a value for the over-all or heating rate at which the thermal gradient ( T o - T , ) constant for a peiiod of approximately three to effective conductivity, k,, one may consider the remains twenty minutes. The required heating rate can be found sample powder, the sample holder, and the thermo- with the aid of a voltage divider placed between the furnace couple wires a single, non-homogeneous cylindrical control and the furnace, and a third thermocouple placed body. The total sample has an effective conduc- between the sample holders. The furnace is allowed to reach a temperature within the range for which + is to be tivity which is a function of the variables mentioned determined. The voltage divider then is sct so that a low above and others related to the type of sample heating rate is obtained. When the thermal gradient begins holder used and the geometry of the arrangement. to decrease, aa observed on the recorder, the rate of heating
Kov., 19G1
PHOTOCHEMISTRY OF IODIDE Iox
is slowly increased. The latter results in a decrease of the slope of the differential temperature curve. After the slope has been reduced to zero, the measurements of time (ts t l ) and temperature ( T z - TI) and (To - T i ) are made. Although the temperature measurements may be made with the aid of a potentiometer, no substantial loss in accuracy was found when using the recorder. The method was tested by determining the known heats of fusion of KNO,, AgNO3, il’aNOc and KzCr207. Considerable difficulty was encountered when attempting to find the heating rates a t which the thermal gradient remained constant. The difficulty is due to the thermal inertia of
IN
AQUEOUS SOLUTION
1937
the system. Although the heating rate can be changed rapidly, the results of the change can be measured only after a time lag during which the system tends to reach a new state of equilibrium. At the present time, research efforts are directed toward finding a more convenient laboratory technique which either would simplify the procedure for finding the required heating rate or would obviate the need for finding the rate. No limits of accuracy can yet be given. The accuracy is of coursealso a function of the quality of the amplifying and recording equipment and the accuracy of instrument calibration and sample weighing.
THE PHOTOCHEMISTRY OF IODIDE ION I N AQUEOUS SOLUTION1 BY E. HAY ON^ Chemistry Department, Brookhawen National Laboratory, Upton, Long Island, New York Received January SO, 1961
The quantum yield for the formation of IZ on exposure of air-free aqueous solutions of iodide to 2537 A. light is dependent upon tile concentration of iodide and hydrogen ions, as was observed by other workers. I n dilute solutions of iodide at pH > 3, +I* is almost zero. Addition of acceptors for electrons or hydrogen atoms, such as H20zand KNOs, brings about an iodide-induced decomposition of these scavengers in neutral and alkaline solutions. This indicates, contrary t o the postulates of Farkas and Farkas and of Platzman and Franck, that hydrogen ions per se are not essential in the primary photochemical process. The dependence of +I* upon [H+] may be due to the formation of Hz+ as proposed by Rigg and hv
+H
Weiss, or to the scavenging of electrons by the hydrogen ions in solution (I- HzO) +(I- HzO)*and (I-HzO)* I H H:O.
+ +
A number of mechanisms have been postulated for the primary photochemicsl processes occurring in the oxidation of iodide ions in aqueous solutions. As early as 1928 Franck and Scheibe3characterized the absorption bands of iodides as “electron affinity spectra,” and in 1931 Franck and Haber4 proposed that the absorption of energy by iodide ions resulted in the transfer of the electron from the anion t o a water molecule on the hydration sphere. Farkas and F a r k a ~ in , ~ order to explain
+
+
of the quantum yield upon H + and I- concentrations by proposing the formation of Hz+ hv (I- H20) --+ (I- HzO)* (I- HzO)* +I H OHH H + --+ Hz+ H2++I-+I+Hz
+
+ +
More recently Platzman and Franck7,*proposed a model for the excited complex in which the electron transfer process was based on the rate of hv collision between ionic species. To explain the (I- Hz0) --+-( I HzO-) +I H OHdecline in the quantum yield of iodine with dethe dependence of the photooxidation of iodides creasing hydrogen ion concentration, they presumed upon the hydrogen ion concentration, suggested the photolytic process to result from a collision that the transfer of the electron occurred from the of a hydrogen ion with the entity formed by the hydration sphere to a hydrogen ion in solution. absorption act.7 Smith and Symonds,g in trying to explain the dependence of the absorption band hY (I- H20) +(I HzO-) of iodide on temperature and the nature of the ( I &0-) + (I- H20) heat solvent used, have suggested another model based ( I HZO-) + H + +I H Hz0 on a modification of that proposed by Plataman Rigg and Weiss6 investigated the photochemistry and Franck.’J The experiments carried out in this work indicate of iodide solutions over a wide range of iodide and hydrogen ion concentrations, and observed that that hydrogen ions are not essential in the primary the quantum yield was dependent upon both H + photochemical process resulting in the oxidation and I- concentrations. Since the Farkas and of iodide ions, since such an oxidation was obtained Farkas mechanism excluded a dependence of the in oxygen-free neutral or alkaline solutions of iodide quantum yield on iodide concentration, Rigg and in the presence of solutes which can themselves Weiss postulated the formation of H and I atoms scavenge electrons or hydrogen atoms. The hyin aqueous solution, and explained the dependence drogen ion can, however, play the same role as the other solutes used insofar as it too can scavenge (1) Researon performed under the auspices of the U. 8. Atomic electrons or hydrogen atoms, but with much lower Energy Commission. efficiency. Recently, after the completion of (2) Department of Physical Chemistry, Cambridge University,
+ +
+ + +
England. ( 8 ) J. Franck and G. Srheibp. Z. physik. Chem., A159, 22 (1928). ( 4 ) J. Franck and I?. IIaber, S. E . preuss. Akad. Wvisrr. (Phys. M d h . ) , 250 (1931). ( 5 ) A. Farkas and I,. Farkas, Trans. Faraday Soc.. 54, 1113 (1938). (0) T. Rigg and J. Weiss, J. Chem. Soc., 4198 (1952).
(7) R. Platzman and .J. Franck, Research Council of Israel, Bperial Publication No. 1. Jerusalem, 1952, p. 21. ( 8 ) R. Platzman and J. Franck, Z . Physzk, 158, 411 (1954). (9) hl. Smith and M. C. R. Symonds. Trans. Faraday Soc., 64, 346 ( 1958).
