George T. Armstrong
National
of Standards Washington, D. C.
Bureau
J The Calorimeter and Its Influence on the Development of Chemistry
compared with many techniques of current interest in chemistry, the measurement of heat is quite old. The phenomenon of heat is, of course, one of the common attributes of nature sensed by man. Even so, several centuries ago the explanation of this phenomenon was among the most obscure problems to which scientists addressed thenlselves. A considerable amount of effort was devoted to attempts to interpret and understand it.' Without going into the details of this search for understanding, which are not directly relevant to our subject, we can say with considerable conviction that Kelvin's well-known saying (2) is applicable to heat: "When you can measure what you are speaking about, and express it in numbers, you know something about it; and when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." For a long time in the attempt t o understand heat, it was not a t all clear to investigators what properties associated with it could be measured. Aside from the rather more readily observed temperature effects, for instance, weight changes were observed and much effort was expended in attempts to associate them with heat effects. While we now know that weight changes associated with heat evolution or absorption are so minute as to be undetectable by gross weighing techniques, this fact was not known two hundred and fifty years ago. The situation was complicated by the fact that in the typical process-combustion-in which a quantity of heat was involved, a weight change observed by the experimenter was almost as prominent as the heat effect. After erroneous conclusions by other investigators, it required very careful experiments by Kunckel (1716) (S),Boerhaave (1732) (4), Lomonosov (1756) (6),Lavoisier (1774) (O), Priestley (1774) (7), and others (8) to demonstrate with reasonable accuracy the absence of weight change in a heat process occurring in a closed system. Even Boyle (1744) (9)arrived a t an erroneous result because of an obvious experimental error. After carrying out an oxidation of a metal in a closed system, he opened his reaction vessel to the air before the final weighing, and thus included additional air. It was during the 18th century that calorimetry was devised as a scientific procedure. Awareness of the variables and methods of handling them developed Presented as part of the Symposium on History of Equipment and Inatrumentation before the Division of History of Chemistry at the 145th Meeting of the American Chemical Society, New York, N. Y., September, 1963. 'For information about the early development of the theory of heat and the great soientific detour it followed in the theory of phlogiston, the reader is referred to historical work on science, as for example, Partington (I).
gradually and understanding of the nature of heat became more definite. At the beginning of the 18th century no methods were known for measuring quantity of heat; a t the end of the century the calorimeter was a working and widely used instrument for investigation. It is interesting to think that in this era when calorimetry was actually in its least developed state it may have played its most prominent role in the development of chemistry. Thus, throughout the 18th century and into the early 19th century, combustion and the nature of heat were among the most intensively investigated areas of chemistry. Because a general understanding of these phenomena was just beginning, their study was in the forefront of the scientific advance. The most prominent chemists of that period concerned themselves in greater or lesser degree with studies of heat, and most did some experimental calorimetry. Of these may be named (as among the better known) Boerhaave, Fahrenheit, Lomonosov, Black, Watt, Crawford, Kirwin, Cavendish, Lavoisier, Gadolin, and Dalton (10). As the passage of years gave increased understanding, the study of heat receded from its dominant position in the frontier of science, and assumed a well-defined position within the general framework. Calorinletry currently contributes data of great value for practicing chemists and for the development of theories of chemical interactions. These data are being measured a t a continually increasing rate, and with increasing confidence for a greater variety of substances and a wider range of physical conditions. Following this introductory material we shall turn first to a few highlights in the development of calorimeters for heat capacity and heat of reaction measurements, and then turn to a few illustrations of the consequences of calorimetric measurements. Development of the Colorimetry of Nonreacting Systems
Even before the question of mass changes had been settled, a comparative method of heat measurement had been adopted. The method used was the heating of water, and the measure originally used was the number of degrees temperature change of a given mass of water caused by the heat. Thus, for example, Cavendish (11) observed the rate a t which the temperature of a given mass of water rose while being heated by a gas burner. When the water reached its boiling point, the temperature stopped rising. He determined the time required for the water to boil away while being heated a t the same rate. From the time required and the observed rate of temperature change of the water before boiling began, he calculated that the temperature of the water would have riser 982" if boiling had not Volume 41, Number 6, June 1964
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occurred. This was an early measurement of the latent heat of vaporization. Prior experiments by Taylor (1723) (12) using a linseed oil thermometer established a linear relationship between the distance moved by the liquid in the capillary of the thermometer and the amount of hot water added to a given amount of cold water. Black, unaware of Taylor's work, confirmed this relationship (1760) (18) using a mercury thermometer. The method in which the temperature rise of water was used as a measure of the amount of heat was thus given a foundation.
could be placed a hot object. Water formed by the melting ice was drained off and weighed when the hot object had cooled to ice temperature. From a knowledge of the heat of fusion of ice, one could calculate the heat liberated by a given process. This calorimeter suffered from failure of the water to drain in a consistent way from the ice and also from inadequate protection against room temperature influence. Lavoisier and Laplace cautioned that it worked well only if the room temperature was within 4' of freezing. It is not surprising that some users had difficulty getting consistent results with it. This calorimeter was used for both specific heat and reaction-heat measurements.
Figure 1. Calorimeter used by Covendish for determining heot of vaporization of water ( 1 I ) . The burners (b) were prervmed to provide heot at a constant rote. The rate of temperature rise of the water prior to boiling and the rate of weight loss of woter during boiling were measured. The observations were used toeolcvlate the number of degrees temperature rise of 0 given weight of water thot would be caused by the some amount of heot or was needed to evaporate that weight d woter.
Tho very earliest heat capacity measurements were strictly specific heat measurements made by the method of mixtures, in which a measured amount of a hot substance and a measured amount of a cold suhstance (one of which was usually water) were mixed. The initial temperatures of the separate substances and the final temperature of the mixture were observed. After qualitative measurements of this type by Boerhaave and Fahrenheit (ca. 1732) (14) and by Lomonosov (5), Black (1760) is believed (14) to have made the first quantitative studies in which he measured "capacity for the matter of heat." At about the same time (1757-64), Black, assisted by Irvine (15), measured the heat of fusion of ice and the heat of vaporization of water, to which he gave the name latent heat. The calorimeters used in these studies are obscure, as Black did not publish the work (14). However, Cavendish (If), who also did not publish his work, left a number of manuscripts on similar measurements, including sketches of his calorimeters and notes indicating that the studies were made prior to 1764. Figure 1 shows one of his calorimeters. Measurements were very soon made in several other laboratories on specific heats and on the latent heats of fusion and vaporization of water. The first table of specific heats was published in 1780; it consisted of 43 values compiled by K h a n (16). Lavoisier and Laplace (1784) (17) published a description of an ice calorimeter (Fig. 2) which contained ice in an inner vessel surrounded by an outer vessel also filled with ice. I n the innermost cuplike container 298
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Figure 2.
Ice calorimeter of Lovoirier and Laploce (17).
It is of passing interest to note that as early as 1788 twin calorimeters were introduced. Partington (18) says, "Crawford (19) was the first to determine the specific heat of gases, in 1779 using bladders as containers, and in 1788 two thin brass cylinders, one vacuous and the other filled with the gas, which were heated in boiling water and then immersed in two identical water calorimeters." Petit and Dulong (1819) ($0)determined specific heats by the method of cooling in air from a temperature 5 to 10" above the temperature of the surrounding air. Joule (21) began in about 1840 and continued for several years the determination of the mechanical and electrical equivalents of heat. This work was perhaps the most important calorimetric study ever made. It revealed the interconvertibility of various forms of energy, and established for the first time the relationships anlong them. As a side effect it opened the way for electrical calibration of calorimeters and the ultimate replacement of the calorie by the Joule as the calorimetric unit, many years later. An indication of the importance attached to this work by scientists is the fact that the international unit of energy is named for its author. See refs. (22, 23) for a more complete discussion.
vantage to he taken of the almost perfect thermal isnIation that can be achieved in their absence a t extremely low temperatures. It permits measurements to be taken for extended periods of time a t temperatures of only a fraction of one degree Kelvin, even though the heat capacities of substances become very m a l l a t these temperatures. The calorimeter with an adiabatic shield containing one or more of the other features mentioned above has become almost standard for low temperature heat capacity studies. With separate heater and thermometer, suitable cryogenic shielding, and a manually or automatically controlled adiabatic shield, it is capable of precision measurements to within about 0.0370 between 300 and 100°K and somewhat more a t lower temperatures (26).
which case the heat measurement is made in terms of the amount of ice melted. While we note that Lavoisier and Laplace iuvented an ice calorimeter, the credit for a practical device is generally given to Bunsen (1870) (28), who devised a sealed system completely filled with ice, liqnid water, and mercury. This design rendered much easier and more accurate the measurement of the amount of ice melted from observation of the displacement of mercury caused by the volume change. After a period of great popularity the Bunsen ice calorimeter fell for a time into disfavor because of the feeling that the density of ice was insufficiently constant and reproducible for measurements of the highest precision. A careful study by Ginnings and Corruccini (20), however, dispelled that notion and allowed the development of a highly precise version of the ice calorimeter.
Figure 6.
Early data on the specific heot of vircovr liquid sulfur (301.
Figure 5. Electricml measuring and control inrtrvmenfotion for o high precision odiobotic calorimeter. INBS
The adiabatic calorimcter has found less favor in high temperature studies because radiation becomes a large heat transfer mechanism at high temperatures, and it becomes difficult to keep such heat transfer small and uniform. Howevcr, recently an adiabatic calorimeter has been devised by West and Ginnings (27) for operation to 500°C. (See Fig. 4 for an illustration of the central features of this calorimeter. Note that it is not a vacuum calorimeter.) A distinguishing feature is the multiple radiation shields on the calorimeter proper and adiabatic shield. This calorimeter, with automatic shield-temperature control, has been found to give heat capacities with a range of about 0.01% in a short series of three or four measurements. The electrical measuring and control instruments associated with this calorimeter are shown (Fig. 5). For temperatures higher than 500°C, the "drop" method is usually used because it permits the heat measurements themselves to be made conveniently in a calorimeter near room temperature. I n this method, the specimen is heated in a furnace to a known high temperature and "dropped" into a calorimeter which measures the total heat given up by the specimen as it cools to calorimeter temperature. The calorimeter is often a metal block of which the temperature rise is measured. However, it may be an ice calorimeter, in 300
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Figure 7. Mearurementr of the speciRc heot d liquid sulfur, mode with on avtomaticolly controlled adiabatic calorimeter (31). Circles represent data point3. The broken line represents the r d i d curve of Figure 6.
Within recent years more or less automatic control of the calorimetric process has become widespread. The most common application of automatic control has been to maintain the adiabatic shield a t the same temperature as that of the calorimeter. This procedure reduces the amount of personal attention that must be paid to the instruments during measurements. The most obvious effect is that measurements can be made by one fewer operator and can be continued easily for long periods of time. A corollary result is that measurements can be made in a painstaking way that would have been essentially impossible without automatic
coirtrol, particularly in cases where a long equilibration period is involved. As an example, me contrast the heat capacity of sulfur obtained with more conventional procedures (SO) (Fig. 6) with that obtained using a calorimeter with automatic shield control (51) (Fig. 7). In the temperature range shown, this substance must stand for hours after a temperature change in order to reach equilibrium. A more elaborate development of automatic control by Stull (52) permits essentially unattended operation of a calorimeter from the lowest temperature to the highest temperature of its range. When more widely used, this type of instrument should supply data on large numbers of compounds, and thus fill in the thermochemical tables mentioned later. Devices for measuring heat capacities of gases have not been discussed here. It is much more difficult to get accurate measurements on gases. On the other hand, the theoretical calculation is so much more certain than with solids and liquids that the experimentalist is hard put to equal the accuracy with which the heat capacity of a gas can he calculated theoretically using structural and energy level data supplied by the spectroscopist. Comparatively few devices have been developed. Those of Osborne, Stimson, and Sligh (SS), and Waddington, Todd, and Huffman (34) may be mentioned. The reader is referred to Sturtevant (55) for a good survey of calorimeters for heat capacity measurements.
An important advance was made by Hess (183945) in his thermochemical investigations (56), which were so thorough and so carefully done that some have been inclined to discard all that had gone before and name Hess as the founder of thermochemistry. His calorimeter (Fig. 8) is a remarkable piece of equipment in that mixing of solutions in it was achieved by rotation; and in this way it foreshadowed the rotating calorimeters now coming into more extensive use. The instrument was very simple, hut well designed, and gave results with a range of about 1% as illustrated in Table 1.
Development of Calorimeters for Measuring Heats of Reaction
The ice calorimeter of Lavoisier and Laplace (17) (Fig. 2) was used for measuring heats of reaction as well as specific heats. This device apparently was the first used to measure the energy of a chemical reaction. and thus Lavoisier and Laplace were the founders of thermochemistry although their measurements were of Iov accuracy. I n their early papers describing results obtained with this calorimeter, they enunciated the fundamental law that as much heat is absorbed in the decomposition of a compound as is evolved in its formation. This law apparently was not based on experimental demonstration.
Figure 8. Rotaling calorimeter used by Hers (36, Ortwold's Klarriker No 91. Solutions were held in beakerr lo). When the handle a t the right wor turned, the beokerr tipped over ond their contents were mixed in cylinder (A). Vanes Ibl stirred the water of the calorimeter at the same time. The temperature rise war meowred by a thermometer hanging through the lid. The whole calorimeter war suspended in o larger box to reduce heat tronrfer.
Figure 9. Calorimeter bomb designed by Berthelat (371. The body (B'l has a thin well by present doy standards, but is platinum lined. The lid (81 contains a valve (K,C.Sl and an ignition electrode (fl. The cop (Fl i s screwed on m d tightened by o cop wrench (MI to which con be applied u long hondle. The assembled bomb is in the lower left.
Another extreme advance in reaction calorimetry was the invention by Berthelot (1885) of the calorimeter bomb (57) (Fig. 9). This device, used with slight modifications by investigators ever since, allows reactions to be conducted conveniently in an enclosure so that all products and excess reactants are retained and can be analyzed. The reaction, usually a combustion, can he carried out under pressure, causing it to be more certainly carried to completion. Berthelot's bomb was platinum-lined to inhibit corrosion. A modern calorimeter bomb may be platinum lined or have walls of oxidation resistant alloy, valves for inlet of oxygen and outlet of combustion product gases, electrodes for an ignition device, a support for the combustion reaction, and a gasket for sealing the lid to the body. This type of bomb is applicable to reactions involving a gas and a solid or a gas and a liquid. I t has been used also for reactions involving two gases, though there is less unanimity of opinion that it is suitable for this type of process. Aside from its strictly scientific applications to t,he determination of the properties of pure compounds, this type of calorimeter bomb is widely used commercially in the testing of heating values of solid and liquid fuels and of foods and other agricultural products. Volume 41, Number 6, June 1964
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A thorough study by Dickinson (1915) (38)of the factors involved in making heat measurements with a bomb calorimeter led him to the design of a calorimeter assembly that has been widely copied and has been found to lead to highly reproducible measurements. A schematic diagram of this calorimeter assembly is shown in Figure 10. It consists of an isothermal jacket with a covered cavity in which a calorimeter can is placed. The calorimeter can contains stirred water, and a reaction vessel. The energy of a reaction is determined from the temperature change of the water in the calorimeter can and a knowledge of the energy equivalent of the calorimeter.
The accuracy attainable with this calorimeter in its more refined form, which is about 0.01%, is attributable in part to the careful design of the calorimeter, and in part to the manner of use, which tends to eliminate systematic errors. For instance, while heat transfer occurs between calorimeter and jacket, it is made quite uniform by the design and can be accurately measured. Care is taken to conduct each experiment so far as possible in the same way in both calibration and measurements, i.e., using the same temperature intervals, the same chronological course of the experiment, and so on. Following Dickinson's design, two major developments in bomb calorimetry have occurred: the development of rotating-bomb calorimeters, and the development of aneroid (liquidless) calorimeters. The first of these was found to be desirable to deal with reactions leading, in a. stationary bomb, to an inhomogeneous solution or to a heterogenous mixture of solid and liquid phases in which the energy states of the reaction products are difficult to define. Widely copied styles (Fig. 11) have been developed by Sunner (90)and by Hubbard, Katz, and Waddington (40) for application to organic compounds of sulfur.
Figure 10. Schernotic diagram of orrembled Dickenmn calorimeter with iacket. 8, bomb; C, calorimeter verrel; J, jacket wail; P, resistance thermometer; FL. flring leads; CS colorimeter stirrer; JS, iacket stirrer; TV, tube to thermostot volve; H, locket heater; TB, thermostat bulb; TH, tubvlor housing. INBS drawing.)
Figure 12.
Figure 11. Resent rotating-bomb colorimeter. (Rosini, F. D.,"Experimento1 Thermochemirtry." lnterrcience Publishers, 1956, p.
156.1
302
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Aneroid bomb colorimeter 142).
Some sources of scatter in measurements with the Dickinson type calorimeter are suspected to be associated with the water used as a temperature equalizing medium in the calorimeter can. The water is also an inconvenience in operation. Aneroid calorimeters by Keith and Mackle (41), by Meetham (42), and by others, have been developed to avoid these difficulties. Meetham's calorimeter is shown in Figure 12. Note the extremely heavy bomb walls of a high thermal conductivity material required for temperature equalization in the absence of stirred water. With no water present, it also becomes possible to reduce heat transfer
between jacket and calorimeter more readily by evacuating the intewening space, and the way is also opened for insertion of radiation shields or adiabatic shields in the manner used in heat capacity calorimetry. These variations in the design of reaction calorimeters have not yet succeeded in producing an instrument of greater precision than refined versions of the Dickinson calorimeter, but may ultimately be expected to do so. A feature of reaction calorimetry which has been of overriding importance in the development of calorimeters is the great variety of processes which are of interest for study. The variety of processes has led to development of a correspondingly great variety of calorimeters. The proliferation of calorimeter designs is indeed an outstanding aspect of instrumentation for calorimetry. Thus, despite the length of the preceding comments on bomb calorimetry, it is not a universally applicable method; and, in fact, there is nothing approaching a universal instrument applicable with approximately equal facility to measurements of all types of reaction heats. Some major classes of interests which have led to specialized forms of calorimeters and reaction vessels are: Solution processes (heats of solution and of reactions in solution) Extremely slou~reactions Reactions involving very small amounts of heat Reactions involving gases Reactions requiring a sustained high temperature Reactions requiring catalysts -0 ,'L""N
F l a w 13. Diphenyl ether calorimeter (431, lnride an evmcuated space hang* 0 vesrel filled with liquid mercury (gray) above which ir diphenyl ether frozen on many small copper vanes. The chemical procesr being studied MCUII in an inner vessel IF) equipped with a valve (A) for introducing romples, and o stirrer 12). If the process evolves heot some diphenyl ether Is melted, and the resulting change of volume causes mercury to be forced out into the copillory tube la),where the volume of mercury forced out can be measured. The omount of heot con lhen be calculated if a previous mlibrotion has given the amount of energy corresponding to the melBng of rufficient diphenyl ether to cause o given change in volume.
Some studies involve more than one of these special conditions. We are unable in thi space to outline the development of calorimetry in all these areas. Only two examples will be mentioned. One is a modified Bunsen ice calorimeter (Fig. 13) containing diphenyl ether instead of water, developed by Jessup (@), which is conveniently used a t room temperature for measuring small amounts of heat in the range of 1 to 100 joules. The other is the twin calorimeter assembly of Buzzell and Sturtevant which allows measurements of very small amounts of heat, even when the process is very slow. This type of calorimeter is particularly useful for measuring the energy differences of nearly equal pmc-
(a)
e8SeS.
The reader is referred to reviews by Sturtevant (55) and by Roth and Becker (45) for illustrations and details of many types of calorimeters. Development of Physical Laws from Thermal Data
The usefulness of calorimetric data in the formulation of physical laws and theories is undoubtedly determined by two factors among others: the accuracy of the data and the state of development of the related laws and theories a t the time of making the measurement. As a general rnle we could say-and this undoubtedly applies to other fields of science as well-that where the theories are vague and inadequate, any data even of only moderate accuracy becomes an assistance in clarifying the picture, and a law may be established, even in the absence of a theory. As the precision of the data improves, the demands upon law and upon the theory become more stringent. On the other hand, additional data are of little use unless they are of sufficient accuracy to confirm law or theory in places where these are subject to uncertainty or to point out weaknesses and gaps. It is interesting to look a t two early situations in calorimetry in which laws were presented on the basis of data of limited accuracy and amount, and to see how differently these two situations turned out in subsequent development. Law of Hess. At the time of publication of his thermochemical investigations, Hess (36) enunciated three laws-one of which has become the very cornerstone of thermochemistry and is now accepted as an essentially absolute law. This law, according to which we would now say that the enthalpy change in a reaction is constant whether the reaction is carried out directly or stepwise, mas developed by Hess early in his thermochemical work and used consistently by him throughout his work. The experimental measurements upon which Hess based hi formulation of the law consisted of dilution of sulfuric and other acids and neutralization of the acids in various degrees of dilution by bases. The heats evolved in the dilution and neutralization were measured separately, and the sums were compared for the various degrees of dilution. A few of hi observations are shown in Table 1. The range of the sums in any series is about 1yO, Later work on the conservation of energy by Joule (Zl),Mayer (46), and Kirchhoff (47) gave a sound basis for this law in the theory of thermodynamics, and there has since then been little i n c l i t i o n to search for failures or limitations of the law. Rather, it is taken as one of the indispensable work-saving devices of thermoVolume 41, Number 6, June 1964
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justified in assuming a t the very least that the data were not sufficiently precise to show that the atomic heat capacities differed. They made the more optimistic assumption that the agreement was sufficiently good for the statement of a law-that the heat capacities are the same. Contrary to the reception accorded t o the law of Hess, the proposed law of Petit and Dulong, despite its simplicity and widespread use, was always subject to some uncertainty and was ultimately shown to be quite invalid, as were analogous laws for compounds proposed by Neumann ( 5 4 and by Kopp (55). Even from the beginning, deviations were noted. Elements of low atomic weights (Be, B, C, and Si) had very low specific heats compared with those required by the proposed law. Specific heats did unmistakably vary with temperature, and did not have the same temperature coefficients. Thus if the law were strictly true a t one temperature it could not be true a t another. Many elements are capable of existing in several crystal modifications which differ from one another in their specific heats.
-
Table 3. Data Leading to the Law of Petit ond Dulong. "The Atoms of All the Elements Have Exactly the Same Capacity for Heat"
chemistry to calculate the heat of a reaction for which no feasible method of measurement can be found, and to check values for a given heat of formation as determined by different processes. For its general interest in revealing the degree of exactness with which one can expect recent experimental measurements to adhere to this law, the data in Table 2 are shown for the heat of combustion of ethylene as determined by a direct measurement (equation (4)) and as determined from a series of other measurements leading to an indirect determination (equation (4')). The two values differ by less than 0.2 kcal mole-'. This example was selected more or less a t random, and probably is typical of reactions involving C, H, and 0. Table 1. Some Data Leading to the Low of Hess (Numerous Other Supporting Data a r e Given b y Hess.) Heat Evolved on Dilution ond Neutralization of Sulfuric Acid b y Solutions of Bases
Heat,developed by Ammonm Water
Acid
Mean
Heat developed by KOH Water
Acid HeO.SOa (H*O)S.SO~ (H*O)a.SOa (H,O)e,SOs
597.2 527.1 483.4 443.4
77.8 116.7 155. 6
547 .Q
597.2 604.9 600.1 601 .Os Mean 601.0"
a Note that in the table as reproduced by Ostwald (Klassiker No. 9), there are errors in the sum and mean. These do not affect the validity of the conclusion.
Table 2. Data to Demonstrate Current Precision Attainable in the Summation of Chemical Reactions
Reaction
Average of two values, see (50). 'Converted from international joules using the factor 4.18331 int. joule = 1 cel. The indicated "uncertainties" in the tables are those given by the original authors, and are not necessarily strictly comparable.
Law of Petit and Dulong. "The atoms of all the elements have exactly the same capacity for heat." This law, proposed in 1819 (SO),was based on measurements on thirteen elements, mostly metals. Thevalues cited are shown in Table 3. With a maxunuin range of about 4'%, the product of specific heat and atomic weight is nearly constant. Because of uncertainties in both the specific heat measurements and the atomic weights of the elements, the authors were certainly 304 / Journal o f Chemical Education
Specific heat
Total
Atomic weight Atomic weight X specific heat ( 0 = 1)
Bismuth Lesd Gold Platinum Tin Silver Zinc Tellurium Copper Nickel Iron Cobalt Snlf1,r .-. .
.-
a Note that a numerical error in calculation of this quantity causes the table to show fortuitously good agreement.
On the basis of his own and other low temperature heat capacity measurements, Tilden (1905) (56) mas able to give as his presidential address to the Chemical Society an analysis and refutation of the law of Petit and Dulong. I n particular, the nonvalidity of the law was shown strikingly by Dewar (1904) (56) in measurements below the boiling point of liquid air, which showed that the heat capacity of diamond is less than 1% of that predicted by the law. Even though ultimately shown to be invalid, and more in the nature of a limiting law, the proposal had been a great scientific advance in the following sense: it had provided a working criterion with which to compare measurements, and a stimulus for inlproving calorimetric measurements to ascertain whether the calorimetry, the atomic weights, or the law was in error, and therefore the cause of the discrepancies that were observed from time to time. Furthermorc, the proposal was sufficiently valid that a theoretical justification, still today acceptable in the limit, could be proposed for it by Boltzmann (1871) (58); and it is still used today in rule-of-thumb estimates of heat capacities at room temperature or higher.
At a point marked approximately by the work of Dewar, the proposed law of Petit and Dulong had reached the end of its usefulness in the development of an understanding of the properties of matter. It may he of interest, however, to examine briefly the later ramifications of research stimulated by it. Shortly after the work of Dewar, Einstein (1905) (59) proposed his theory to account for the decrease of specific heat a t low temperatures on the basis of absorption of energy in quanta. This was one of the earliest successes of the quantum theqry and undoubtedly had a significant effect in its acceptance. Within a few years Einstein's treatment was improved by Debye (1912) (60) and by Born and von KbrmAn (1912, 1913) (61). The principle of the theory remains essentially unchanged; the refinements, which are continuing to the present day (6.8), consist principally of attempts to define more explicitly the energy absorption spectrum of the crystal, which Einstein assumed to he monochromatic. More complex spectra in which the actual structure of the crystal became involved were proposed by later workers. I n recent years, much attention has been devoted to analysis of deviations from simple Debye or combined Dehye-Einstein functions for various substances. These deviations may be due to anisotropy or imperfections of crystals, phase changes, rotational and other configurational changes of molecules in a lattice, ferromagnetic and paramagnetic effects, the behavior of snperfluids, and other sources of anomalous heat capacity-temperature functions. Other extremely important consequences of the discovery of the diminution of heat capacity a t low temperatures mere the development by Nernst of his famous Heat Theorem-the theory of the decline of entropy to zero a t the absolute zero of temperature, and the development of the third law of thermodynamics. For some years an area of interest very intensively pursued was the verification of the validity of the third law of thermodynamics and the calculation of absolute values of entropy. Much interest has been attached to explanations of nonzero entropy a t the absolute zero of temperature. In the foregoing we have seen some stages in the developn~entof a theory based on calorimetric measurements initially near room temperature and of very modest accuracy. As it turned out, the ensuing development of the theory for some years resulted more from the extension of the temperature range of the experiments than from improved precision. However, a t the point where the theory became sound enough to explain the variation of heat capacity with temperature, and when the reasons for the differences between the elements and compounds became evident, the demands for increasing accuracy and range became much more pronounced. New measurements meeting these demands have made clear the fact that the heat capacity is a complicated function, of which the accurate prediction will involve detailed knowledge of the energies of interactions and the possible arrangements and motions of the atoms in the crystal. Conversely, accurate determinations of heat capacity have lead to a possibility of gaining information about these features. As a result, there has been a continuing drive to achieve ever greater accuracy in heat capacity measurements.
The Present State a n d Potential o f Calorimetry
We shall not attempt further to outlime here advances in chemistry or physics sparked by measurements of heat quantities. The interested reader may find additional information, particularly in thermochen~istry, in reviews by Mnir (6S), Rossini (64), Parks (66), and Skinner (66). However, a few comments on the application of calorimetry in gathering useful data are appropriate. I n this connection, we should like to quote Lewis and Randall, Pitzer and Brewer, on the influence of theoretical thermodynamics (67): "Here [in the application of thermodynamics to physics and especially to chemistry] the methods of thermodynamics have brought quantitative precision in place of the old vague theories of chemical affinity, and thus chemistry has made the greatest advance toward the status of an exact science since the early chemists Lavoisier, Richter, and Dalton laid the foundations of stoichiometry." The useful data of thermodynamics are in large measure the data provided by calorimetry. Here we may refer to the suggestion made by Rossini (1936) (64) that "the aim of thermochemistry is to provide the experimental data for compiling a table of values from which may be calculated the heat of every possible chemical reaction." Without distorting the intent of Rossini this data can he construed to include measnrements of heat capacities and of enthalpies associated with phase changes, as well as heats of reaction processes. The aim is far from realized. Several notable attempts have been made to systematize the data which have been obtained so far experimentally and to prepare the results in the form of tables in much the manner that Rossini proposed. These have included tables of data on hydrocarbons (68), inorganic compounds (69),metals and alloys (YO), and others. No systematic attempt has been made to compile data on the organic compounds as a whole; but the principal lack is that data on the chemical compounds of all classes are far from complete. The fillimg in of such a table of properties is enough to occupy thermochemists for many years to come, unless adequate correlating schemes are devised for prediction of the properties. Table 4.
Combustion of Aluminum in Oxygen
Investigetars
A120s: - AHI"*,, (keal/mole)
Msh (1957) (77) Sehneider and Gattow (1954) (76) Holley and Huber (1951) (76) Oketani and Maebashi (1950) (74) Snyder and Seltz (1945) (75) Roth and Muller (1929) (72) Moose and Parr (1924) (71) " See note e under Table 2.
Whereas the accuracy of determinations of the heats of combustion and hence heats of formation of organic compounds was very good by 1930, the same could not be said for the heats of formation of many inorganic compounds. A major improvement has been made since then in the latter area. As an illustration, Table 4 shows the measurements made on the combustion of aluminum in oxygen in the last forty years. The heat of combustion, which is the heat of formation of aluVolume 41, Number 6, June 1964
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n~inumoxide, has shown a pronounced shift to more negative values, probably reflecting better control of the completeness of combustion. There is remarkably good agreement between the more recent measurements made in the United States. It has long been recognized by many, but perhaps not often clearly stated, that the energy state of a body is among its most fundamentally important attributes. A key piece of evidence of an ultimate understanding of the nature of matter and its interactions will be found in the ability to predict the interaction energies between particles, and between aggregates of particles of varying degrees of complexity. Among the chemical snbstances, except for the very simplest systems, the outstanding way to determine these energies is by calorimetry. One might suppose that the present massive concentration of scientific effort upon the subatomic particles and their interactions is clear evidence that particles of atomic size and larger are well understood. Now if we take as a criterion of adequate understanding of the theory of atomic and molecular interactions the ability to predict or calculate the energy of the interaction with as much accuracy as it can be measured, then we find that there is by no means adequate understanding nor is it close to attainment. Only for a very limited number of substances and classes of substances do the theories and the mathematical resources for implementing them provide answers of accuracy the same as or greater t h m can be achieved by experiment. To illustrate this point, Table 5 gives a classif~cationof substances by complexity of structure, and a suggestion as to the current state of the relative merits of theoretical calculation as compared to experimental measurements in two areas amenable to calorimetry: differences in total hinding energies of atoms and differences in enthalpy corresponding to changes in temperature.
differences in binding energy. In these cases another experimental method-spectroscopy -can he used when circumstances are favorable. I n the case of ideal gases, heat capacities, as mentioned earlier, can he calculated better than they can be measured. I n real gases, also, calorimetry is not the best way to determine nonhonded interactions, which are better determined by P-V-T measurements (but see Rossini and Frandsen (78) for an example in which the nonbonded interactions were determined calorimetrically, in good agreement with P-V-T data). Aside from these instances, however, the great mass of information about binding energies in diatomic molecular gases, polyatomic molecular gases, liauids, , and solids has been obtained by direct calorimetry. Because calorimetric measurements have most frequently involved suhstances in a state of diatomic or more complex molecules, the energies determined generally do not relate to the atomic species as such, and therefore most calorimetric measurements referred to immediately above apply to differences in binding energy rather than to total hinding energy. The link between total binding energy and the calorimetrically determined quantities is most often, though not always, provided by noncalorimetric experiments, such as measurements of spectroscopic dissociation, vaporization, or other processes leading to the free atoms. Table 6. Accuracy of Some Published Estimates of Heats of Formation of Fluoridesa
Error of estimate (kcal m o k L ) +57 +82 +46 +23 -17 +14 +21
Table 5. Relative Accuracies of Experimental and Theoretical Determinations of Heats of Formation and Enthalpies 1963
-16
+8 +90 +66 -39 +I6 +5 +22
H*TI - HOT,
Class of substance Monatomic gas Dixtnmir nnrl
Pa8 Liquid Solid
AHf' (from gaseous atoms)
( = J;C~"~T)
HItl&rv >
Theory > experiment Theorv" >
For
ex-
For all othera experiperimentb> theory Experiment > theory Experiment > theory Experiment > theory Experiment > theory
;Aaauming molecular geometry and force constants are known.
Speetmseapie dissociation energy in same cases is superior to ealorimetrie measurement.
Here we see the rather strikmg fact that, thus far, despite the perfection of the quantum mechanics, its successes in accurate calculation of hinding energies of molecules are limited to the very simplest system-the hydrogen molecule, and a few moleculeions containing only nuclei and one or two electrons. I n some diatomic and polyatomic species, calorimetry is not the best experimental way to determine the hinding energy, or 306
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+9
-38 +12
Average error 1 3 0 kc$ mole-' Average bias +I7 'Estimates and measured values are selected f n m a review by Armstro~gand Krieger (79). See note c under Tsble 2.
As a further illustration of the relative inability of a chemist to predict the results of a calorimetric measurement, there are shown in Table 6 a series of heats of formation estimated for substances for which no experimental measurement existed at the time of estimation, together with an experimentally determined value determined later. The average error of 30 kcal mole-' gives a measure of the lack of success achieved, and shows that for a certain class of substances very large errors may he made. With a situation like this it is certain that calorimetric measurements will be needed for many years to come.
