Topics in..
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These articles, most of which are to be contributed by gwpt authors, are intended to serve the readms of this JOURNAL by calling attention to new developments in the theory, design, m. mailability of chemical laboratory instrumentation, m by presenting useful insights and mplamtions of topics that are of practical imporlanee lo Uose who use, or teach the use of, modern instmmenlationand instrumental techniques.
XXXIII. Recent Developments in Calorimetry Part One-introductory Survey of Calorimetry RANDOLPH C. WILHOIT, Thermodynamics Research Center, Department o f Chemistry, Texos A 8 M University, College Station, Texas 7 7 8 4 3 SCOPE AND PURPOSE OF CALORIMETRIC INVESTIGATION Calorimeters are used to measure the change in internal energy or enthalpy which occurs when a system changes from an initial state to a find state. Such data are required for many thermodynamic and thermochemical calculations. Calorimeters are also suitable for mdytical tools. They can be used, qualitatively, to detect thepresenceof exothermic or endothermic processes, and quantitatively, to determine the extent to which processes occur. They can be applied to the study of the equilibrium properties of matter as well as to the study of rates of change of such properties in nonequilibrium states. Careful calorimetric studies of phase changes in condensed systems have produced some of the most accurate data. available on the equilibrium temperature for these changes, as well as quantitative estimates of the purity of the samples. Calorimeters have been used in the study of properties of matter for well over a century and modern edlorimetric instrumentation and techniques are the result of s. long evolution and extensive refinement. In spite of this long history, calorimetry is still an active area of research which utilizes many of the most sophisticated of modern instruments. Many major laboratories throughout the wurld are devoted partly, or completely, to calorimetric resemch, and the demand for these data far exceeds the supply. Because of the wide range of systems, phenomena, and conditions of interest to thermochemists, the choice of standard ready-made calorimeters is limited to s. relatively few specific areas. Although several valuable new calorimeters have appeaed on the market within the past few years, the thermochemist, more often than not, still finds it
necessary to modify existing instruments or to construct them entirely to his spec%-
general and to describe recent developments, especially in manufactured instruments, in a. few areas of calorimetlic research. The literature on calorimetry is very extensive. More detailed i n f o r m tion can be found in several monographs (1-7), which should be consulted for references to the origind literature. In 1946, a t the urging of Dr. Hugh H. Huffman, a group of scientists interested in experimental calorimetry organized a series of informal meetings to discuss common problems. These meetings have continued on an annual basis under the sponsorship of the Calorimetry Conference and have grown to include some 150 to 200 participants, who present fifty or more repork each year on current research in calorimetry. These meetings have had great iduence in impruving the standards of celorimetrio techniques and of reporting data in publications. Similar national conferences have been organized in the Soviet Union, England, and Japan. International conferences on calorimetry are conducted bi-annually by the Subcommittee on Thermadynsmics and Thermochemistry of the Internrational Union of Pure and Applied Chemistry. The design and operetion of a calorimeter is simple in principle and much useful data can be generated with very simple equipment. IIowever, precision measurements, compatible with the best modem practice, require exacting technique and meticulous attention to detail. Figure 1 shows, in a schematic way, the basic parts of a typical oalorimeter. The calorimeter contains the system under study, one or more thermometers, and perhaps, an elec-
h unlivc TPXILII, Dr. Randolph C Wilhoit 1.er.civcr1his fc,rrnnl rtll~cationa Tritiity University (San Antonio), th University of Kansas, andNorthwester University, where he received the Ph.C working with Professor Malcolm Dnlr He spent a year's postdoctoral a Indiana Universit.y, then joined th faculty of T e x s Technological College which he left in favor of New 1Iexic' Highlands University. Shire 1964 h has been Associate Professor of Chem istry and Assistant Director of th Thermodynamics Research Center a Texas A & 41 University. His re search interests we centered arounm calorimet,ry, with part,iedar emphasi on the thermochemist,ry and thermc dynamic properties of organic con pounds, and applications of thermc dynamics to biochemistry. He is member of the ACS, AAAS, Sigma X and the Calorimetry Conference. trical heater and devices for mixing or stirring. The calorimeter is surrounded by the jacket, which also contains one or more thermometers and usudly some provision for controlling its temperature. Heat may he transferred between the calorimeter and the jacket by conduction through solid materials conneoting them hy conduction and convection through any gas which may be present, and by thermal radiation. Work energy may also be transferred to the calorimeter by mechanioal motion used in stirring or mixing, by compression or expansion against an external pressure, or by an electric c u m n t used to operate a heater. Following the
(Continued on page 4S72)
Volume 4 4 , Number 7, July 1967
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A571
Chemical Instrumentation
of energy meaartred ranges from around 100 kcal for the stndy of explosives to around 10 kcal for heats of combustion and down to microcalories for certain studies. The time scale varies from fractions of a second to hours, or even days. I n addition to the study of the familiar kinds of uhsse chanees and chemical reactions. gases, energies which accompany the relnxalion of strains h, solids, energies of nuclear transformations, heat generated by living organisms ranging from bacteria to man, and the energy present in eleelromagnetic or ionizing radiation.
TYPES OF CALORIMETERS
Figure 1.
Schematic diagram of a calorimebr.
usud practice in thermodynamics in which the calorimeter plus its contents is regarded as the system, a calorimetric esperiment can be described in terms of the heat and work transferred to or fmm the calorimeter and the change* in the vsriables of state of the calorimeter and its cantents when they change from an initial to s final state. According to the first l a s of thermodynamics, y
+ w = E, - Ei = A E ,
(1)
where the subscript, t, designa~es the calorimeter plus its contents. If the volume of the cdolorimeter is constant, no pressure-volume work is done and w , in eqn. (I), represents other types of work. If the pl.essure is kept constant, then, g
+ w'
= H, - H , = AH,
(2)
where w' is work other than pressure-volume work. The objective of a calorimetric experiment is to measure the heat absorbed, q, and the work done, to or w', as aecurntely as possible and to relate them to changes in internal energy or enthxlpy of the contents of the cdorimeter. Sioce the mensurement of the heat exchange, g, usually presents the most difficult part of the experiment, calorimeters are uwally designed to keep the heat exchange ns smsll as possible. However, the hent exchange is deliberately made large in sonlo types of experiments, and the evaluation of AEt or AH,, then depends upon an armrate measurement of q. Calorimetric studies are nor made on a large variety of systemsunder s a-ide range of conditions. Systems include the gas, liquid, and solid states, either ss single phases or as two or more phases. Nearly all types and classes of chemical compounds are included. Temperatures range from wound 1 to over 1500°B, and pressures range from the micron region to several hundred atmospheres. The quantity
A572 / Journal of Chemical Education
Although the wide range of systems nod conditions stltdied in cdolorimeters requires a. great variety of fipecifie instruments and techniques, certain features common tn nearly $1 calorimeters have evolved into a few specific types. These features are found in a great mnny combinations in speoific calorimeters. Static calorimeters operate between definite equilibrium (or metastable) initial and final states a t constant, or nearly constant, temperat,nres. Dynamic ealorimeters are run with a continuous change in temperature, so that the contentq never attain a state of t,rne equilibrium. Dynamic calorimeters are usually of smsll s i ~ e so that the temperature can be maintained uniform throughout the calorimeter. In flovr calorimeters a constsrnt flow of material, usually liqnid or gas, is maintained into and out of the calorimeter, nsunlly operated in a steady st,ate condition. Cxlorimebers in which a constant flow of material is introduced. with the oroduets of the calorimeters. With respect tn t.he interaction hetween the calorimeter and t,he jaeket, three types can be recognized. I n calorimeters having isofhemal or adialmlic jackets, the heat exchange, p, is kept small compared with the total change of energy of the calorimeter and its contents. In eonrluctia calarimeters, however, the heat exchange is approximately equal tu the change in energy of the eslorimetm and contenb. The temperatnre of an isothermal jacket is kept constant during the measurement, while the temperature of an adiabatic jacket is adjusted to match that of the calorimeter st all times. Both adiabstie and isothermal jaokets have been used for many years. The principal advantage of adiabatic control is that, ideally, there is no heat exchange between jacket and cdorimeter, and thus the temperature of the cdlorimeter is very nearly constant in the initial and final states. This is verv imoortant in some investigations where the system reqtdres an appreciable time to reach equilibrium, and, in itself, may be sufficient to deaide in favor of the adiabatic jacket. Besides, it is much easier to measure accurately a constant temperature than a changing one. On the other hand, it is more difficult to construct an adiabatic than an isothermal jacket. Provision must be made for raoid and uniform heating and cooling. control of the temperature is very tedious and demanding if done
mannally, or requires complex instrumentation if done automatically. I n spite of the advantages of adiabatic calorimetry, many workers prefer an isothermal jacket for certain types of highly accurate measurements. The use of an isothermal jacket requires that the heat exchanged between calorimeter and jacket be carefully evaluated. IIowever, i t is seldom possible to attain ideal temperature e o n t ~ din an adiabatic jacket, and i t is f r e qoently necessary to calculate a correction for heat exchange for the adiabatic jacket also. The principal sonrce of error in the calaulation of the heat transier is the lack nf uniformity of temperature on the surfaces of the cslorimeter and the jacket. Since the temperature of an isothermal jacket is more likely to be uniform than that of an adiabatic jacket, it is preferable in this respect. Thns, even thongh the heat exchange may be larger far an isothermal jaeket, the error in calculating the heat exchange may he less. I n many instances the choice hetween an isothermal or an adiabatic jacket of the same overall accuracy is a matLer of personal preference. The adiahstie jaeket is more difficult to construct and to operate unless elaborate automatic controls m e installed. The isothermal jacket requires more thorough data logging and a more complex calc~dittionprocedure. The isothermal jacket is to be preferred for those calorimeters which change temperature rapidly. I n the eondudim calorimeter, all or uearly all of the hent evolved or absorbed in the calorimeter is conducted to or from the jacket. The measurement of AEt or AH~dependsentinlyon the oalculc~tionof the heat exchange. This depends on a knowledee of the temoeratmes of the j:,cLvt :end rnlorirwk I n t :,I1 t i n w durin): tln. i t ? t . i l ~ ~ w w n 31.d l 1111 the k ~ . ~ ~ l v of dye the 1111: d ht.:>t tm11.fer 3 - :I f a t w t i ~id~ ~ these temperatures. The best accuracy which can be attained with a conduction calorimeter is less than that which can be attained with isothermal or adiabatic jxoket calorimeters. Conduction calorimeters mav be of the static tvne.. in which < a - r the juvket i. kept at a am.tant temprnitmrr 1111.1 1l1e in$tis,la d 1111:,I t m ~ p ~ r x t u w s d i l ~ Wr I O I I I I I P I ~ L I~IYtht S:IIIW a, IIIP jsvkta~Lcnqwrawn,, or tlwy ma!. be uf tloc 11yn:mic t)qw, i n which c:,ae tllc d i t l c m w ~ In,tuvrn thy tenmvnt i t c i c r f the lnckrt and calorimeter is kkpt constant so that the rate of heat transfer iu also constant. An adiabatic jacket calorimeter can be easily converted to s. dynamic conduction c a b rimeter. Adiabatic calorimeters which ulilize a stirrer a n frequently run with the jacket temperature slightly below the calorimeter temperature in order to remove the hent generated by the stirring. This can be called ~seudo-adiabaticcontrol. The labyrinth flow calorimeter ia a type of conduction calorimeter which is located in a series of coaxial tuhes so that any heat which is evolved or absorbed is transmitted to or from water which is circulated through the tubes. The rate of evolution or ahsorption of heat can he odculnted from the rate of flow of water and the difference between the temperature of the water a t the inlet and the outlet.
.
(Cmlinued m page A574)
calibratiw~~onslbnlof 18.91 calories per ersm nf mercurv. Acetic acid., nauhthalene, attd phenol are other substances applicable lo this type of calorimeter. Phase-chauge calorimeters based on a Another variation, which takes many liquid-vapor equilibrium h w e also been specific forms, is the twin or differential used. Evolution uf heat generates addicalorimeter. I n this modification two tional vapor, which can be withdrawn fmm matched calorimeters are placed in either the calorimeter and condensed to deterthe same or in different jackets. They are mine the amount. This principle hsa been operated simult,aneously, with a standard used to study reaclions which take place in system in one calorimeter and the system hoiling soluticnm ol ammonia m d of carbon being studied in the other. The two calatetrachloride. The solvent serves as the rimeters are kept a t the same temperatore auxiliary material in these cases. by supplying electrical energy to one of Drop calorimeiel.~are designed to meathem. Their use rests on the assumption sure the change ilr enthwlpy which results that, if the two calorimeters are a t the when t,he temperature of the sample is same temperature, there is no heat transfer changed by a relatively large amount. between them and that the rate of heat exThe initial temperatwe of the sample, change between each calorimeter and the which may be either above or below the jacket is the same. If this assumption is initial temperature of the calorimeter, is valid, the electrical energy is equal to the established in a suitable environment bedifference between the energy change for fore it is placed in the calorimeter. The the standard system and the energy change sample is then quickly dropped into the for the system being studied. Thus, calorimeter and the final temperature of neither the temperatures of the calorimthe calorimeter and sample determined eters or the heat, exchange need he known. after they have reached equilibrium. The The advantage is obvious. If this condition is not met exactly s. small correct,ion calorimeter may consist of a black of highly conducting metal, such as copper or silver, can be applied. I n some designs the two or a, container uf liquid, such as water. calorimeters are separate and insulated from each other, while in others they are From a knowledge of the heat capacity of the calorimeter, the initial temperatures of thermally connected. Twin edlorimeters the sample and the calorimeter, and the may he either static or dynamic, and they find temperature of calorimeter plus may have either adiabatic or isothermal jackets, or be of the conduction type. sample, the change in the enthdpy of the Twin calorimeters have the greatest adsample may he ciilculated. The sample is often placed in a. protecting capsule. If vantage when the system being sbndied is this is done, the heat evolved hy the very similar to the reference system used capsule must he subtracted from the total. for comparison, for example, a pure solvent A series of such measurements, with the and a dilute solution. A phaspehange calorimeter contains a. sample a t different initial temperatures, relrttively large quantity of an auxiliary will serve to determine heat capacities, substance in good thermal contact with the heats of transition, and heate of fusion. system under study. The auxiliary suhThe calorimeter may have either an stance is in the form of two phases in equiadiabatic or an isothermal jacket. librium a t constant temperature. The Figure 2 illustrat,e? a drop calorimeter calorimeter is placed in a jacket a t the manufactured by the Dynatech Corp., same temperature, and thus i t is both Cambridge, Mass. They offer a series of adiabatic and isothermal. The heat such calorimeters which consist of either a evolved or absorbed by the system results copper block or a, water bath. These are ins. change, not of temperature, but of the desiened to onerate in the ranee of -160" relative amounts of the two phases present. are furnish& withvarito I & I ~ " c . The change in enthalpy of the system is ous accessories such as furnaces, refrigeradeternhrd I,? ,ovawring thn :!ntuunt of tom, and temperature indicators, rephu* vhttngr. The mcm f:>mdi:wex~tn~plc corders, and controllers. Accuracies in of thk 1YDr of c?lorimeicr i- the Hunsrn ice the mesrurement of specific heat are in the calorirn&r. The system is placed in a range of 3-5'%,, depending on t,he model chamber which is surrounded by a mantle of ice, which, in turn, is surrounded by liquid water. The calorimeter is completely filled with the ice and liquid water. A change in the relative amounts of liquid and solid produces a change in volume which is detected by means of a cspillary tube filled with mercury connected from the calorimeter to the outside. The quantity of mercury may be determined v o l i ~ metrically or gravimetrically. Careful measurements have shown that 1 g of mercury corresponds to 64.64 calories of heat. I n the presence of the icewater system, the measurement is restricted to O T ; however, other substances may he used to establish a solid-liquid equilibrium a t other temperatures. Substances used for this purpose should he stable, ohtainable in a state of high purity, and should attain a reproducible solid-liquid equilibFigure 2. Drop Calorimeter (Courtesy of rium readily. Diphenyl ether is a suitable Dyootech Corp.1 material; it melts a t 26.91"C and gives a
Chemical Instrumentation
-
-
.
he^
~ n the d initid temperature of the samplc. The Thermu-Physics Corp., Csmbridgc, Xasn., markets a similar drop calorimeter consisting of a furnace designed for trmperatures up to 1600°C and a Bunsen ice enlorimeter to receive the sample. The ehange in quantity of mercury in the ~ y s tem is determined by weighing. .4emracies of 1% or better in the measurement of heat delivered to the calorimeter are specified. They also will furnish optional equipment which permits initial cooling of the sample down to liquid nitrogen temperatums, and also permits keeping the sample in s. vacuum or in s n inert atmosphere. The availability of high-tempel.%t u x drop calorimeters in ready-made form seems to be n rather recent development,.
AREAS OF CALORIMETRIC INVESTIGATION Calorimet,ric research can he c l a d i r d into several well recognized areas according tn tho kind of measurement or s)-stem being studied. Each such area. is identified by certaiu common problems and objectives. Low-tmpcralxre aslarimetry nsually refers to ihe measurement of heat eapaeiiy, heats of phase transitions, and derived properties in condensed systems below room temperature. The objective is frequently to obtain the absolute entropy a t room temperatme through use of the third law of thermodynamics. Such data also play an important role in theories of the sdid state. An excellent review of lowtemperature calorimetry has been written by Edgar Westrum (8). I n the early years the lower limit for these measuremenla was us~tallyabout 77.3S0K, the boiling puint of liquid nitrogen. However, ahsolute entropy based on meaaurement,s to this temperature are unreliable, and measnremenls down to around 20.7i°K, the boilingpoini of hydrogen, or to4.2I0K, the boiling point of helium, have benme rout,ine for third law studies. Calorimetric studies a t a few tenths of a degree on tho Kelvin scale have been made by using ihe techuique of adiabatic dernngnetisation. Modern low-temperatwe calorimeters are nearly always of the static type with an isothermal, or, more frequently, an adiabatic jacket. Low-lempemture calorimetry has become 1111 ndvanced and highly developed a1.i. The equipment is custom built and requi1.e~R. number of years to develop. The Rdfl.ian Cryogenics Inc., Rahway, N. J., can sopply a number of special purpose cryostats, among which i~ one designed for w e with low-temperature calorimeters. The Linde Co., New York, and Cryogenic Engineering Co., Denver, supply storage Dewars and equipment for handling crwgenic fluids s , ~ as h liquid hydrogen and helium. Low-temperature calorimeters are also highly automated. The one in use a t the Bureau of Mines Thermochemistry Laboratory in Bartlesville, Okla., is an outstanding example. Accuracies of one part per thousand in the measurement of heat capacities in the range from 20' to 300°K are now considered routine, and some pnhlished data approach accuracies of one part in five thousand. The limiting factor in (Catinued on pug? 457fi)
Chemical Instrumentation many such measurements is in the irregularities inherent in the definition of the temperature scales in this range. Measurements above room temperature fall in the omvince of hioh temmrature cal-
countered and the hardware are quite different. According to the Stefan-Bolteman law, the rste of radiation of thermal energyfrom a surface is proportional to the fourth power of the absolute temperature. As a consequence the control of radiative hest transfer, especially above a, few hundred degrees Celsius, is the overriding problem in high-temperature calorimetry. The measurement of temperature and the location of suitable construction materials present other difficulties. Static cdlorimeters with adiabatic jackets, differentid dynamic calorimeters, and drop oalarimeters are useful up to temperatures of around 1000°C. So far, only drop calorimeters have been found to be practicable much above this temperature. When using drop calorimeters for measurements in the higher temperature range, the ssmple must be transferred to the calorimeter very quickly to prevent undue loss of heat by radiation. Elaborate meohmisms have been devised for this purpose. The initid temperature of the calorimeter in these measurements is usually around room temperature. However, sometimes when it is desirable to avoid transitions which may take place in the sample a t lower temperatures, the calorimeter also may be kept at an elevated temperature. The heats of formation of most organic compounds, inorganic oxides, and a few other inorganic compounds are derived from measurements of the heats of combustion in oxygen. For compounds in the liquid or solid state, these measurements are made with a. bomb calorimeter in which the sample is burned in an atmosphere of oxygen at a. pressure of 15-40 atms. Gaseous compounds are burned in a flame calorimeter a t atmospheric pressure. Heats of combustion have been measured for about 90 years, and the technique has become highly developed and standardized. Some laboratories routinely obtain data accurate to one part in ten tho,,sand, and occasioally, to one part in twenty thousand. These accuracies are needed since he& of formation are ubt i n e d as relatively small differenres between the heats of combustion and the heats of formation of the products of combustion. The major limitation lies not in the measurement of temperat,ure or energy but in the preparation of samples of sufficient purity, in the determination of the quantity of materid burned, and in the identification and application of corrections for the numerous side reactions. In addition to the highly precise measnrements of the heat of combustion of pore compounds, many measurements of lower accuracy are made to determine the heat value of fuels. Several manufacturers supply combustion calorimeters. These will be described in Part 111 of this review.
(Cmtinued on page A578)
A576 / Journol o f Chemical Education
Chemical Instrumentation The standard combustion calorimeter consists of a bomb, capable of withstanding high internal pressure, of about 300 ml capacity which is placed in s, bucket eontaining around 2 liters of water. One to three grams of sample are burned, produeing s. temperature rise of one or two degrees. Isothermal jackets are usually used although adiabatic jackets are becoming more popular. Aneroid enlorimeters consist of the bomb only, or bomb imbedded in a. block of metd. These also have been applied to high precision measurements in recent years, enpecially where only a. limited quantity of sample can be obtained. Organic compounds which contain only the elements carbon, hydrogen, oxygen, or nitrogen can he satisfactorily burned in s. stationary bomb. However, compounds which cont.ain sulfur or halogens must be burned in a rotating bomb to obtsin reliable values. The rotation is needed to mix the liquid products of combustion so that they are homogeneous. Combustions in other oxidizing atmospheres may also be studied in a. calorimeter. Some organic and inorganic compounds can he burned in chlorine or fluorine. Fluorine bomb calorimetry has been a valuable new development for the study of many refractory inorganic materials which will not burn in oxygen. Some reactive metals can be burned in nitrogen. The heat capacities of gases are usually measured in s uapo~flmu calorimeter. The gas is passed through the calorimeter a t a
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constsnt rate. I t first flaws around a thermometer placed near the inlet, then over a carefully designed electricd heater. and finally past mother thermometer near the exit. Thermocouples or resistance thermometers are usually employed. The heat capacity of the gas can be cslcrhted from its mass flaw rate, the electrical power dissipated by the heater, and the tempemlures a t the inlet and exit. Corrections mast be applied for the hent exchmge between the calorimeter and t,he jacket, t.he transfer of heat from the heater to the thermometers by radiat,ion, the JouleThompson effect, and the departure from a steady state condit,ion. The s ~ ~ c e c a of s this method depends upon having a cantrolled, stable flow of vapor. This can often be secamplished by vaporizing t,he liquid form of the compound in a boiler. The liquid is kept at. the boiling temperature by surrounding the boiler with the refluxing vapor of the same material. Yaporization is accomplished by means of a n eleet,rie heater immersed in the liquid. The flaw of vapor is proportional to the heating rate and may he ealeulsted from n. knowledge of the heat. of vaporization. Or, by measuring the flow rate independently, the heat of vaporization may be cslculated. Thus it isvery common to combine the vapor flow calorimeter with the measurement of heat of vaporization. Thc rate of generation of vapor can be found by condensing the vapor and messuring the amount collected in a given time. The measurement of heat of vaporiaat,ion and vapor heat capacity may be carried out in separate experiments, or they may be
determinod ~imult,aneouslyby collecting the vapor after it has passed through the How calorimeter. These measurements, of course, may also he conducted over a. range of temperature and pressure. A largevariety of calorimeters have been used for meamring heats of solution, heats of mixing of liquids, and heats of reactions in solution. These measurements all have the common characteristic of studying the effect of mixing two samples, either both liquid, a solid and e. liqt~id,or occasionslly a gas and a liqnid. Thus, there must he some provisinn for keeping the two samples eeoamte ontil the nraoer t,ime and then far these calorimeters either contain a motor driven stirrer, or the whole cdolorimeter is rocked back and forth or rotated. Calorimetric studies can be carried out, not only on aqueous and nonaqueous solulions in the vicinity of roam temperature, but a h an solutions a t low temperature, such as those in liquid ammonia, and solutions a t high temperature, such as in molten salts or liquid metal systems. The hest effect which secompmies the vaporisation or condensation of the volatile components of the solution must always be considered as an important source of error in solution calorimctrv. I n fact, the vals, tility of the materials being mixed i d u ences to s. large extent the design of the calorimeter. Highly volatile msterials must be mixed in a calorimeter which is completely filled b a t t before and after
(Continued m page A580)
Chemical Instrumentation nixing so t.hnt there is no vapor space a t any time. Although a vapor space can be tolerated when mixing components whose vapor pressure is less than around 50-100 torr, the vapor space should be kept small in careful work, and the calorimeter should be nearly vapor tight to prevent appreeiable loss of vapor. Reaotions which prcdirce a gas are always troublesome since the gas tends to carry sway mme vapor. Most solution calorimeters are of the
in recent years. A simple calorimeter suitable for measurements of low or intermediate accuraoy on relatively nonvolatile system may be constructed from a.Dewar flmk fitted with a cover, a thermometer, a. stirrer, and a. pipet. Measurements of high accuracy are conducted in elaborate calorimeters with isothermal or adiabatic jackets. They may be of the single or of the twin type. Thermometric titration calorimetem are easy to build and generate a large amount of data in a short time. They are particularly advantageous when studying complex reactions which involve several intermediate steps. Reactia ealonmeiq, includes the study of many chemical reactions other than combustion. To he suitable for calorimetric study, a chemical reaction should proceed quantitatively a t a convenient rate to produce products of definite and r e producible composition. This includes many reactions which occur in liquid solution. Heats of hydrogenation, helogensi tion, and hydrohalogenation of unsaturated organic compounds in liquid and gas phases have been measured in Bow calorimeters. A fairly extensive literature exists on heats of polymerization. ,1Zievocalorimetry includes the study of systems in which the total temperature change, the total amount of heat produced, or the rate of production of beat is small. Solution calorimeters often operate in this range. Heats of dilution or of mixing of nonpolar liquids often require the measurement of very small temperature changes. Calorimeters which can detect temperature changes of 10P deg C have been canstruoted by using multijunction t,hermccouples, and ones which can detect changes of 1 0 F deg C or a little less by using thermistors. The fitudies of some biochemical reactions or of the heat produced by radioactive isotopes are examples of situations where the available quantity of material may be limited. Calorimeters which can measure fractions of a millicalorie have been designed far these applications. Although the total amount of heat generated by a slow reaction may be large, a microcalorimeter may be required to detect it. The measurement of the heat produced by the setting of cement or by the germination of seeds are examples. A major problem in microcalorimetry is the identification and removd of sources of
mixing devices, from adsorption, and from temperature gradients in the environment
(Continued on page A582)
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lournol of Chemical Education
Chemical instrumentation nre very troublesome. Twin calorimeters have been used effectively to reduce these sources of inberferenee. Electrical noise always sets a lower limit of sensitivity when using thermocouples or &stance bhermometers t o detect changes in temperatwe. The commercially available micruoalorimetew are of the conduction t,ype. They will be described i l l P a r l 111 of this review. The following outline identifies, in a gew era1 way, the types of oxlorimebars which have been used for various kinds of messurements. It does not include all combinations or certain calorimeters designed for apecific purposes.
Speciflc Heats and Heats of Transition in Condensed Phases I m o Tcmperalure: St,atic calo~%neters wit,h either adiabatic or isothermal jackets. High Temperature: (a) %tie calorimeters with an adiabatic jacket: (b) Drop ealorimetem with the receiver having either s n isothermal or an adiabatic jacket, or a phase-change calorimeter; (c) Dynamic twin conduction calorimeters.
Specific Heats of Gases and Heats of Vaporization Flow calorimeters (abrmt 50 t w r presminimum).
SWE
Heats of Combustion Gas Flame Calorimeters: Flow calorimeters. Bomb Calorimeters: (a) Static "water bucket" calorimeters with eil.her isalhermal o ~ a d i a b s t i cjack&; ( b ) Static aneroid calorimeters with either isothermal or adiabatic jackets.
Heats of Solution, Dilution, Mixing, and Reactions in Solution ( a ) Dewar flask type wibh either isothermal ur adiabatic jscket;i ( b ) S t a t i c ealwimeter with either adiabatic or isothermal vacuum jacket; ( c ) Twin calarime k r a wit,h adiabatic, isol.hermd, or conduction jaeke1.s; ( d ) Flow calo~imetet.s; ( e ) The~.mometriclitration enlorirnete~~s;(1) I'lme-vhhnge cnlwimeters.
Heats of Hydrogenation, Halogenation, ond Other Catalyzed Reactions (a) Flow ee*lorimeters with isothermal jackets; (h) Flow calorimeters using phase-change principle.
PROCEDURES AND CALCULATIONS Most calo~.imetrieexperiments fall int,o one of two types. These differ not in the design or operation of the calorimeter, b u l io the objectives of the measorement, snrl in {.he treatment of the dstn. The ohjec-
(Continued on page A584)
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Chemical Instrumentation live of 8 Type I experiment is to det,ermino the ent,halpy of the oontenbs of the oalorimeter as a function of temperature. I t s derivative with respect to temperature is the heat capacity. Electricxl energy, r e p resented by w' in eqn. (2), is added to the calorimeter and its temperature changes from Ti t,o TI. For this type of eaperiment eqn. (2) may be expanded as, rl
+ w' = AHo + AH, (Co + CAT, =
- Ti)
(3)
where AH0 and AH, represent ihe chitnp~s i u enl.halw . .. of the calothe1,er nnd i1.s aonlents, respectively, and Conud C. represenl, Ihe corresponding average hrnt capacities
over this temperature interval. Sametimes it is convenient to combine part, or all, of q and/or w' with AHo. If this is done, AHo does not represent the true change in enthnlpy of t,he cxlorimete~;hut is more appropriately called the "energy eqoivalent" of the calorimeter. The purpose of a Type I1 experiment is to determine the value of AH (or AE) for a transinrmation which ocer~rsin t,he con-
chemical reactions. These changes are accompanied by ahrupt changes in the properties of the system. Let AH,(T.) represent the change in enthalpy for the trmfiformalion heirrg st,udied a t the refer-
tion. Then, for a Type I1 experiment, eqn. (2) becomes,
+
W' =
+ Ci(T, - Ti) + + Cd1'1 - T,) (4)
C ~ TI Ti) AHdT-1
An accurate knowledge of the heat capacity of the empty calorimeter, Ce, or of the energy equivalent of the calorimeter, is needed for either a Type I or a Type I1 experiment,. This should he obtained in a separete calibration experiment in which a calorimetric saandard is placed in the calorimeter. Calorimetric standards may he either substances of accurately known and reproducible heat capacity, or system3 which undergo a. transformation of known enthalpy change. Specific standards suit,able for various applications will be discussed in Part 11. The cslihrat,ion may either be a Type I or Type 11 experiment,, but should, if possible, he similar in all respect,^ to the measurement of the Itnknown quant,it,y. By making the calibration experiment similrtr to the measurement, systematic errors in the evaluation of q, w', Ti, and TI will largely cancelout in the calculation of C , or AH,(T,). Frequently a calorimeter which is used for a Type I1 experiment will be calibrated by a Type I experiment where a stmdard of known heat capacity is placed in the calorimeter, or, if the heat capacity of the sample is small oompated to that of the calorimeter, the empty calorimeter alone can he used. The properties oi calorimetric standards moat he hased on,mlibmtion experiments in which eleet,~iealenevgy is added to (.he empty eillorimeler. 11, is difficult t,o remove ~ystematieerrors frrm such measurements, aud t,hey must he P W ried out in specially designed ealorimeLers in standardizing laboratories. Thus all modern calorimetric data are based, eithev directly or indirectly, on calibrations using electrical heating in Type I experiments. The unit of energy used in reporting ca1m.imetric data is either the (absolute) jonle 01. the themochemieal calorie, which is defined as 4.184 (exaclly) joules. Calorimetric standards may also be used to test the overall accuracy of the measurement. For this purpose, it is useful to have more than one standard. One can he used for the calibration and the others for testing. When studying endothermic transformstions in Type I1 experiment?, it may be possible to adjust w' so that little or no change in temperature occurs. This makes the term containing the heat cnpacities, CO,Ci, and Cl, ineqn. (4) small, so that only appraximat,e values are needed. I n a sense, the procedure amounts to conducting the measurement and the electrical calibration simultaneously. A procedwe, similar in principle, can he applied to exothermic transitions also, by removing the heat quantitatively. This is done aotomaticdly in the labyrinth flow and phase-change calorimeters which have already been described. Heat can abo be removed quantitatively in a controlled manner by using the Peltier effect in thermocouples. This is done in the Calvet microcalorimeter to he described in Part 111. The availability of new thermoelectric materials in recent years which have large Peltier effects introduces (he (Continued on page A586)
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use as small refrigerators. Equrttions corresponding to (3)or (4) may be written for each calorimeter of a twin odorimeter system. If it is assumed that the heat exchange, p, the heat capacities of the two oalorimeters, and the temperatoras of the two oalorimetars are the same, then the differences in the heat capacities of the two d o r i m e t e n may he readily related to the differences in u' for the t,wo calorimeters for a Type I experiment, or the differences in the AH.(T,) may be related to the difference to' for a Type I1 experiment. I t is convenient to separate the experimental data and their associated uncertainties into two erouos. One erouo eonties give rise to the calorimetric errors. The other group consists of data, describing the quantity of sample, the extent and kind of trensformation which has occurred, the extent of side reactions, and other auxiliary data needed to convert the enthalpy change to s. thermodynamic standard state. Modern cdolorimetry has developed to the point where the uncertainties connected with the second group limit t,he overall accuracy of the measurement. The rate of transfer of heat from the jacket to the calorimeter may be represented as,
calorimeter, opposite to the point corresponding to a;. r is an effective thermal conductivity constant for the transfer of best by radiation snd by conduction and convection through the gas between the mlolarimeter and iaeket. x. 0 : . and 8.. in gmthm is carried out over Lhe surface of t,he ealorirnet,er. Tho terms in the summation of eqn. ( 5 ) represent conduction through solid connections, such as elmtrical wires, stirrer shafts, and supports between calorimeter and jacket. The xi's are the effective thermal conductivity of each such connection, and Oij md&, are the temperatures a t t,he t,wo ends of such links. Far practical esleulntions, eqn. ( 5 ) is rwwly always replami i,y,
whelp tf; aud 8. are appropriate average temperatures of jacket and calorimeter and K an overall average thermal coonduclivity. The mte of change of temperature 111 IIlc c:~lo~.iruelcr, wllcu nu slcetrical en-
(Cu~~liwuod m pivage A5S8)
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Journal of Chemical Education
Chemical Instrumentation evgy is being added and no t,ransformat,ion is hking place inside t,he calorimeter, is
where S represents t,he transfer of energy by stirring, evaporation, or ot,her processes not accounted far by eqn. (6). The quantity K/Ca is s n important characterist,ic of a calorimeter. I t can be esleulated from the rneamrement of dT/dt for two different values of R j - R. by use of eq (7). The constancy of K/Co, or lack of it,, a t a given iemperature is a good indication of the magnitude of the calorimet,rio errors. For cnlorimetem designed for highly rtecurat,e work K/Co should be no larger than around lWa min-I. The total heat exchange which oocurs when the calorimeter changes from an initial temperat,ure, T ia t t,ime ti, to a final temperature, T I a t time 11, is
*
=
KJ;
(Bj - *.)dl
(8)
If the oalorimeter and jacket, temperatures are recorded graphically or digitally throughout the experiment,, the integration in eqn. (8) can he carried out either graphically or by use of a digital computer. Numerous approximations of eqn (8) have been developed for specific types of calorimeters. The general reviews listed previously should be consulted for details of these procedures.
BIBLIOGRAPHY, PART I (1) J. SWRTEVANT, "Cd~lim&l'y,"in A. Weissherger (ed.), "Technique of Organic Chemistry,'' 2nd ed., Vol. I , Wiley-Interscience, New York 1949. (2) H. F. STIMSON, Am. J. Phys., 23, 614 (1955). (3) S. B o o ~ n(ed.), "Precision Measurement and Calibration, Vol. 11,Heat and Mechanios." Nst. Bur. S h derds endh hook 77, US. Govt. Printing Ofice, 1961. (4) F. 1). ROSSINI (ed.), "Experimental Thermochemistry, Vol. I," WileyInterscience, New York, 1956; 1-1.A Skinner, (ed.), Vol. 11, 1962. (5) T. If. BENZINCE~ AND C. KITZINGER, "Microcalarimetry, New Methods and Obieotives!' in C. M. Herrfeld (ed.), "Temperature: its Messurement and Control in Science and Industry," Vol. 111, Part 3; Reinhold, New York, 1963. E. CALVETand H. PEAT, "Recent Progress i n Mieroealorimet,ry," M~emillan,New York, 1963. J. 1'. MrCur.r.or~~:n(cd.), "Experimental 'l'lrel'ml9dytlarni
