Simplified Calorimetric Studies of Various Types DEXTER B. PA'ITISON, JOHN G. MILLER, and WALTER W. LUCASSE University of Pennsylvania, Philadelphia, Pennsylvania
T -
HE IMPORTANCE of thermodynamics in physical chemstry is found not only in such direct applications as thermochemistry but also in the fact that a large proportion of the subject can he presented as a unified picture by means of the laws of thermodynamics. However, as studied in the laboratory, the thermodynamic basis of the phase rule and the laws of vapor pressure are apt to he obscured; the interrelationships of the colligative properties are normally subordinated to the actual measurements; and the determination of the activities, free energy, and heat content changes by electromotive force methods are usually emphasized less than the relative magnitudes of the potentials developed by various types of cells. Some difference in approach to the subject in classroom and in laboratory is perhaps broadening and is, without doubt, often justifiable in view of the limitations of time, available apparatus, and accuracy of experimentation. Nevertheless, with the importance of thermodynamics, i t is unfortunate that there are so few simple experiments designed to make the various thermodynamic quantities measurable and real to the student. Even in thermochemistry, although most laboratory texts contain one or more experiments measuring heats of reaction in aqueous solutions, the number of such studies is small and their variety rather limited. In the present paper, a series of calorimetric experiments are given which are thought to be suitable for undergraduates. Together with studies of heats of solution and dilution, these include an oxidation-reduction reaction, organic reactions, reactions in which a gas is evolved or a precipitate results, and, finally, ones in which a complex ion or an nndissociated molecule is formed. In addition to variety, the objective in developing these experiments has been to use simple apparatus of moderate accuracy and, in so far as possible, reagents which can be readily obtained in a pure state and from which solutions of known concentrations can he prepared without elaborate standardization. THE GENERAL EXPERIMENTAL PROCEDURE
breakage. Titer test thermometers, reading in tenths of a degree from 15' to 35'C., are sufficiently accurate and of a convenient range. For most of the thermochemical experiments to he discussed, two solutions are prepared of appropriate concentrations known, by standardization if necessary, to about one per cent. In order to establish thermal equilibrium with the surroundings, the solutions should be made up a t least twenty-four hours before use, but in any case, after introducing 200 cc. of each into two separate 250-cc. beakers, they should he allowed to stand protected from air drafts and covered with a watch glass for ten to twenty minutes. During this time, the thermos bottle is washed with room-temperature distilled water and allowed to drain by inverting on a piece of filter paper for five minutes. No attempt should be made to dry the bottle with solvents or by means of a blower since the abnormal cooling would be of more consequence than the few drops of water clinging to the walls. When the bottle has drained, the stopper carrying the thermometer is introduced and the temperature of the empty bottle obtained after allowing ample time for thermal equilibrium to be achieved. After the two solutions have come nearly to room temperature, the temperature of each is estimated to the nearest hundredth of a degree, using a magnifying lens, and recorded on alternate minutes over a period of ten minutes. To avoid errors in calibration, it is essential that the same thermometer, which with care may he used to stir the solutions, be used to determine the temperatures of both solutions, drying quickly between each transfer. It is advisable to keep the solutions covered with a watch glass as much of the time as possible, and to delay taking temperature readings until the two solutions have the same temperature within half a degree, although this latter precaution does not seem to be necessary to obtain results of moderate accuracy. At the eleventh minute, the measured amounts of the two solutions are poured into the thermos bottle and thoroughly mixed by inverting the bottle several times. Starting with the twelfth minute, the temperature of the mixture is read each minute until the twentieth minute or for a longer period of time if the reaction is not instantaneous.
The apparatus and general experimental method employed in the various heat studies have proved satisfactory for undergraduate use over the last several years. Vacuum or "thennos" bottles are readily obTHE GENERAL METHOD OF CALCULATION tainable and the pint size is convenient in view of the moderate amount of material required. They offer Regardless of the path pursued between the initial advantage over the Dewar tube in being self-support- and final states, AH, the "heat content change," has a ing and, with ordinary care, show remarkably low single definite value depending only upon the two
states. The path can, therefore, be restricted to one which will allow a ready calculation of the value. When no work, other than that against the constant pressure of the atmosphere, is done in the process, A H is the heat absorbed. Since calorimetric measurements a t constant atmospheric pressure are very convenient, the quantity AH has found widespread use and its properties make its value useful in interpreting the nature of various processes and in evaluating other quantities which are related by thermodyuamic laws. The most useful values of A H are those for processes taking place not only a t constant atmospheric pressure but also a t constant temperature. If a reaction were to be carried out isothermally, the reaction system would have to be surrounded by a thermostating bath which would absorb or evolve heat, as the case might be, thus maintaining the system a t constant temperature. A device for such a direct measurement, if it is to yield the amount of heat, is di5mlt to construct and to manipulate, so that the calorimeter is more commonly an adiabatic one, the heat change being determined by the rise or fall in temperature of the reacting system. However, on the basis of the first law of thermodynamics, concerning the nature of A H , the path of the process can be broken into several paths, one oi which is the desired isotherm. If the reaction is carried out adiabatically, the heat evolved will not escape hut will raise the temperature of the system. The rise in temperature allows a calculation of the amount of heat that would be given off if the reaction were carried out isothermally a t either the higher temperature reached when the solutions have reacted or a t the lower one a t which they were mixed. The following figure and discussion will prove this:
INITSTAT=
solutions e and b at temperature TI
solution ab at temperature T2
solutions a and b at temoerature T.
solution ab at temoerature T,
FINAL STATE
,
While the adiabatic measurement would appear to proceed along some such path as E, the progress of the reaction from the initial to the final state may be interpreted as following the paths A and B or C and D. Thus, if the original solutions were allowed to react isothermally a t T I and the resulting solution heated to T,, the same result would be observed. The adiabatic process might he visualized as tak'mg place in two initantaneous steps, the reaction along-A immediately followed bv use of the heat evolved to raise the temperature of the solution along B to Tz. Similarly, in following the paths C and D, the heat required to raise the solutions a and b to the temperature T zis instantly restored to the system by the heat evolvea in the isothermal reaction a t the higher temperature. Actually, all of these paths and others are followed
by different parts of the system due to the nature of the mixing method, hut it is an advantage of the First Law of Thermodynamics that allows such a path construction with the assurance that A H for path E will be the same as the sum of that for A and B and foi C and D. If the process is truly adiabatic, the beat absorbed along B will be equal to that evolved along A and that absorbed along C will be equal to that evolved along D. In symbols, AHA = - AHs AHD = -AHc
and AHB =
0
These equations form the basis for the calculation of the value of A H for the reaction as if it were carried out isothermally at two diierent temperatures. The lower of these, the mixing temperature, can be fixed a t any desired point, showing an advantageous freedom in the adiabatic methods whichmight not a t first be suspected. The temperature rise due to the reaction is calmlated by plotting the temperature of the solutions a and b and that of the solution ab as ordinates against the time in minutes. The extrapolated curves should intersect the mixing time ordinate to give the temperature increase necessary for the calculation-this temperature increase, by virtue of the extrapolation, being the temperature change which would have been realized for an instantaneous reaction in the absence of radiation and thermometer lag. The amount of heat given out a t the lower temperature corresponds to the amount of heat required to raise the temperature of the solution ab, the thermos bottle, the stopper, and the thermometer by the amount Tz - TI. The heat required for the solution can be calculated from its volume, density, and speafic heat together with the temperature rise. The beat required for the calorimeter (bottle, stopper, and thermometer) is calculated from the temperature rise, Tz - T I , and the water equivalent of the calorimeter (i. e., the number of gram calories required to raise the temperature of the calorimeter one decree). ,. which for the calorimeter used in most of the experiments reported was found to be 13.2. Calcnlation of the amount of heat given out a t the upper temperature requires, in addition to the temperature rise and the water equivalent of the calorimeter, the volume, density, and specific heat of each of the solutions a and b. Introducing the volumes of solution indicated above, the equations for the calmlation of the heat given out by the reaction a t the lower and higher temperatures take the following
-
form.
m ma,.t;.,Jrr. i.,"y--.C..-LJ
Qp,
=
QT% =
.
- TJ (400) (d.d(c.d (T* - T ~ (200) ) (d.)(c.) ( T P- Td (200)(da)(cs)
(T,
+ ( T I - Td(c.)
++(Tn - TJ
(6.)
,he,,
TI is the temperature of the solution ab extrapolated to the eleventh minute
T. is the temperature of the solution a extrapolated to the eleventh minute
Tb is the temperature of the solution b extrapolated to the eleventh minute TIis ' 1 2 (Ta Td d is the denstty (d. is the density of the solution a, etc.) c is the specific heat of the designated solution 6, is the calorimeter equivalent
+
It is obvious that for accurate calculations, the densities and specific heats of the solutions a t the proper concentrations must be known, and whenever these figures have been readily available, the experimental results given below have been calculated with their use. In dilute aqueous solutions, however, the heat of the reaction can often be calculated within one or two per cent error by assuming that the product of the density and specific heat of each solution is equal to unity. This was sometimes resorted to in the present work, in which case the distinction between the heat of reaction a t the two temperatures disappears, and the equation for calculation simplifies to:
Q
=
(T* - T d (400)
+ (T2 - TJ(c.)
From Q, the molar heat of reaction, AH, is easily calculated : A H - --Q mols ab
EXPERIMENTAL WORK
Details of a wide variety of thermochemical experiments are given below together with indication of the accuracy which may be expected under the conditions. All of the experimental results are the average of three or more determinations unless otherwise stated and, in general, the average deviation is about 0.2 cal. per mol. Modifications of the general experimental procedure and method of calculation are indicated wherever they may not be entirely obvious. The experiments are grouped according to the general type of reaction studied.
Heats of Reaction in which a GUSis Ewolwed The Decomposition of Hydrogen Peroxide. About 50 cc. of commercial three per cent hydrogen peroxide is thoroughly mixed with about 450 cc. of water, and 400 cc. i f the solution introduced into the thermos bottle. The bottle is equipped with a two-hole rubber stopper; one hole contains the thermometer and the other a short glass tube connected to a rubber hose which extends under the open end of an inverted 500-cc. graduated cylinder, completely filled with water, securely clamped, and standing in a water bath. The temperature of the hydrogen peroxide is estimated to O.Ol°C. a t two-minute intervals for ten minutes; then exactly on the eleventh minute 2 g. of finely powdered manganese dioxide are added. The flask is immediately stoppered and the oxygen gas, which is rapidly evolved, collected in the cylinder. The evolution is complete after about twei~tymore minutes, during which time readings of both the volume of the evolved oxygen and the temperature of the solution are taken a t two-minute intervals. The results can be plotted on graph paper and a typical experimental curve is shown in Figure 1.
In the calculation of the molar heat of reaction, A H , the number of mols of hydrogen peroxide used may be calculated from the volume of oxygen evolved, by means of the perfect gas law. If adequate time is allowed, the temperature of the gas may be taken as that of the room; otherwise, the temperature of the water may give a more nearly correct value. The pressure may be calculated from the barometric reading by correcting for the diierence in the height of the water within the graduated cylinder and in the bath, as well as for the vapor pressure of the water. The experimental value, -23.2, agrees well with that calculated from the heats of formation given in the literature; according to which AHis -22.8 cal. per mol (3). In order to check the procedure, the concentration of the hydrogen was determined by adding potassium iodide and acid, and titrating the liberated iodine with standardized sodium thiosulfate to the starch endpoint. Calculation of A H on this basis led to the value -23.1 cal. per mol, justifying the experimentally simple collecting of the gas as a means of measuring the amount of reactant involved. Incidentally, this physical approach is not only quicker than the usual analytical determination, but also serves to remind the students that, in industrial and other work, special methods are frequently employed rather than the standard techniques. The Reaction of Calcium Carbide with Hydrochloric Acid. The heat of reaction of calcium carbide with hydrochloric acid is readily measured. About 400 cc. of approximately fifth normal hydrochloric acid, prepared by diluting 12 cc. of concentrated acid to 500 cc., are introduced directly into the thermos bottle, fitted
with a two-hole rubber stopper with the thermometer observed, however, and the obviously simple experiin one hole and the other serving as a vent. After ment gives an interestingly large value of the molal taking the temperatures for a period of about ten min- heat content change. Utes, a 1.5-g. lump of comniercial calcium carbide, weighed to the nearest milligram, is introduced. It is Heats of Reaction in Which an Undissociated Molecule advisable to have the carbide well wra~pedin filter ora ComplexIm.is Formed paper both to delay the initial reaction and to keep i t The Readion of Mercuric Nitrate w'th Sodium Chlofrom direct contact with drops of water a t the mouth ride. The general experimental procedure is suitable of the bottle where the seal may be weakest and subject to measure the heat of reaction of mercuric nitrate to breakage with a sudden local evolution of heat. with sodium chloride to form mercuric chloride. MerThe bottle should be stoppered immediately and tem- curic nitrate is very deliquescent so that an excess perature readings taken a t two-minute intervals for should be weighed out. Solutions of appropriate conthe next twenty minutes. The gas evolution stops after centrations are made by dissolving 25 g. of mercuric about five minutes and it is well to mix the contents of nitrate in 250 cc. of solution containing 10 cc. of conthe bottle a t that time, placing a finger over the open centrated nitric acid and by dissolving exactly 7.305 g. hole. of nure sodium chloride in enourh water to make 250 As before, it is necessary to determine the tempera- cc. of solution. The experimental value for the heat tures a t the time of mixing, by extrapolation, in order of reaction under these conditions is -12.7 cal. per to obtain as nearly as possible the value of change which mol and the literature values (3, 5, 7) vary from-11.2 would have been observed if the reaction had been to -12.7 with -12.4 cal. per mol the most probable instantaneous. In the absence of other information, value. it is necessary, also, to assume that the pieces of calcium This experiment requires no standardizations and is, carbide, which should be carefully selected to be as therefore, very convenient for student use. free as possible of adhering oxide and other impuriThe Reaction of CopfierSulfate u d h Excess Ammonia. ties, are 100 per cent pure. This assumption was To measure the heat of reaction of copper sulfate with probably incorrect for the samples used since the ex- excess ammonia to form the deep blue complex ion, perimental value of the heat of the reaction, -58.7 the general experimental procedure is used. A satiscal. per mol, is markedly lower than the literature value, factory temperature rise is obtained upon mixmg 200 -60.8 cal. per rnol (3), a difference which can scarcely cc. of 0.2 molar copper sulfate with an equal volume of be attributed to the excess acid. a 1.2 molar solution of ammonia. A typical graph for It is not feasible to determine the purity of the com- this reaction is shown in Figure 2. The average ex~ o u n dand the extent of the reaction by the amount perimental value a t about 25'C., using 0.960 and of the gas evolved since acetylene is fairly soluble in 1.030 as the specific heat and density, respectively, of water. The chief experimental ditficulty is the evolu- the copper sulfate solution and 1.000 and 0.991 as the tion of about 500 cc. of acetylene, a malodorous and corresponding figures ior ammonia, was - 19.3 cal. per highly inflammable gas. Proper precautions can be mol. The concentrations suggested would indicate reaction with six molecules of anmonia; however, the heat of reaction varies with the excess of ammonia used and for exact work the ammonia solution should be standardized. Literature values (4) for dilute aqueous solutions a t 10°C. are as follows: CuSOl + 5NHs = CuSOc5NHr; AH = -19.5 cal. CuSO. 6NHa = CUSO~~NHJ; AH = -20.0 cal. CUSOI+ 8NH8 = CuSOc8NH8; AH = -20.7 cal.
-
+
Advantages of this experiment are the inexpensiveness of the reagents and the fact that no standardizations are necessary, unless i t is desired to distinguish between the possible reactions. Since standardization is not essential, less time is required than for the conventional measurement of the heat of neutralization of an acid and a base, and the experiment can be used advantageously to fill out a laboratory period only partly needed for other thermochemical work.
~.-TEYPERATURI+TIME CURVES POR THIL REACFIGURE TION OP COPPER SDLPATE WITH EXCESS AMUONIA
Heat of an Oxidation-ReductionReactimt The Readion of Potassium Brumate with Hydrobromic Acid. The reaction between potassium bromate and hydrobromic acid with excess hydrochloric acid present
proceeds fairly slowly, and under the conditions used was complete in about fifteen minutes. Neither solution requires standardization but the cost of the reageuts is an adverse factor and disposing of the bromine water formed is inconvenient. One solution is made by dissolving 2.0875 g. of potassium bromate in enough water to make 250 cc. of solution, and the other by dissolving 7.438 g. of potassium bromide and 16 cc. of concentrated hydrochloric acid to produce 250 cc. of solution. With the 0.05 molar potassium bromate and the 0.25 molar hydrobromic acid thus made, the heat of reaction is measured accordiug to the general experimental method. The average value obtained, -49.7 cal. per mol, is somewhat lower than the values given in the literature, -51.2 and -53.1 cal. per mol
(2,3,5). Heats of Readwn i n Which a Precipitate i s Formed The Reaction of Magnesium Sulfate and of Aluminum Sulfate with Sodium Hydroxide. The reactions of magnesium sulfate and aluminum sulfate with sodium hydroxide are very interesting because the two reactions are very similar but have widely different heats of reaction. The value for the heat of reaction of magnesium sulfate in dilute aqueous solution was found to he +0.2 cal. per mol and the corresponding value for aluminum sulfate, -31.9 cal. per mol. These experimental values agree reasonably with those in the literature (3, 5). Half-normal solutions of base were used in both cases and 0.25 molar and 0.0833 molar solutions of magnesium sulfate and aluminum sulfate, respectively. Both of these salts can be obtained readily of sufficient purity for use without standardization. The specific heats and densities, respectively, of the solutions are 0.963 and 1.029 for magnesium sulfate, 0.975 and 1.028 for aluminum sulfate and 0.989 and 1.006 for sodium hydroxide.
Heats of Organic Reactions The Reaction of Acetic Anhydride with Sodium H y droxide. The heat of reaction of acetic anhydride with sodium hydroxide was measured using a slight modification of the general experimental method. After introducing 400 cc. of approximately 0.3 N base into the thermos bottle and observing the temperature for ten minutes, about 4 g. of acetic anhydride, weighed accurately to the nearest milligram, were introduced. Following the addition of the anhydride, the temperature became constant after about eight minutes. The experimental value for the heat of the reaction, -38.5 cal. per mol, which is the average of only two results, is in poor agreement with the calculated literature value, -43.7 cal. per mol (1, 5, 6). However, the literature values ( I ) , on which the calculation was based, are old and if a one per cent error had been made in the measurement of the heat of combustion, this would account for the discrepancy. The Reaction of Hydroxylamine with Acetone. The reaction between hydroxylamine and acetone to form acetone oxime has H fairly large heat of reaction and,
L 0
FIGURE~.-TEMPERATWRE-TIME CURVESFOR THE REACTION OR HYDROXYLAMINE' WITX ACETONE therefore, can be studied readily using the present method and apparatus. After introducing 8.780 g. of hydroxylamine hydrochloride and 125 cc. of normal sodium hydroxide into a 250-cc. volumetric flask, the solution is diluted with water, up to the graduation, to produce a half-normal solution of hydroxylamine. Because the solution decomposes slowly, it should be prepared immediately before use. For the other solution, 6 cc. of acetone should he thoroughly mixed with 244 cc. of water. The regular experimental procedure is used to measure the heat content change. The reaction is fairly slow; a typical graph is given in Figure 3 which, furthermore, shows that the temperatures of the reactants are markedly different because of the addition of the base to the hydroxylamine hydrochloride. This cannot be avoided readily since the solutions must be used soon after they are prepared in this case, and the success of the experiment demonstrates that it is not necessary to have these reactant temperatures nearly identical, especially if only one A H value is sought in the experiment. The average experimental value obtained under these conditions was -13.8 cal. per mol. No value for the heat of the reaction was found in the literature. The reaction was studied, however, under several d i e r e n t conditions. Hydroxylamine hydrochloride is quite stable in aqueous solutions but free hydroxylamine decomposes slowly. A 0.975 N solution apparently decreased in concentration to 0.953 after standing for two hours and to 0.870 N by the end of two days. The actual decrease in concentration is somewhat uncertain since hydroxylamine can decompose in several ways, to form basi~im~urities:
+ NH* + 3 8 0 4NHaOH = N 2 0 + 2NH8 + 3 8 0
3NHzOH = Nz
heat of solution of anhydrous sodium acetate is 3.86 cal. and that of the trihydrate, -4.85 cal. (3). In order to obtain a convenient temperature rise, 16.40 Furthermore, hydroxylamine can react with any oxygen g. of the anhydrous salt and 13.60 g. of the trihydrated present to form acidic impurities. sodium acetate are used, each with 400 cc. of water. The decrease in concentration was determined ,by The specific heats and densities, respectively, of the allowing 10-cc. samples of hydroxylamine hydrochlo- two solutions a t these concentrations are 0.967 and ride to stand with a slight excess of base and with dis1.019 for the first and 0.985 and 1.008for the second. tilled water. After a proper time interval, hydroThese easily conducted experiments on heats of chloric acid or sodium hydroxide was added until the solution, like certain of the other studies, can be used bromphenol blue end point was reached. Then excess with profit to fill a laboratory period primarily devoted acetone was added and the hydroxylamine gradually to a more elaborate thermochemical measurement. reacted to form acetone oxime and free hydrochloric acid. The liberated acid was titrated to the brom- Heats ofDilution phenol blue end point with standard alkali. The final The Heat of Dilution of Ethyl Alcohol by Water. The end point is permanent but since the reaction is fairly slow, titration extends over a period of ten or fifteen heat content change of the exothermic dilution of 95.6 minutes. The color change is from yellow to blue with per cent (by weight) ethyl alcohol by several different no acetone oxime present and is very sharp; in the proportions of water can readily be measured. The presence of the oxime, however, the final end point is volumes chosen for the dilution, which may be estiyellow-red which can best be seen under strong illumi- mated with sufficient accuracy by means of graduates, nation with a white background, and the color change is are as follows: rather gradual. This method can be used to standard(1) 10 y of 95;6 pef cent alcohol, 400 cc. of water ize acetone solutions using an excess of hydroxylamine (2) 20 " " 400 " hydrochloride solution which has previously been made neutral to bromphenol blue. The reaction between acetone and hydroxylamine is reversible: In the first four cases, the specified volume of room0 N-OH temperature distilled water is placed in the previously II II rinsed and drained thermos bottle and the specified CHI-C-CH1 f NHIOH CH3-C-CHs &O volume of 95.6 per cent alcohol in a clean dry conUnder the conditions used, the reaction is probably tainer of suitable size. The temperatures of the water almost quantitatively complete. With 122 per cent and alcohol are read and recorded on alternate minutes of the theoretical amount of acetone, the measured for a period of ten minutes. On the eleventh minute heat value was -13.8 cal. per mol; and with 282 per the alcohol is poured into the water and the solution cent of the theoretical acetone, -14.2 cal. per mol. thoroughly mixed by inverting the bottle several Measurements in acid solutions with either hydrochloric times. Starting with the twelfth minute, the temor acetic as the free acid gave much lower results. perature in the bottle is read each minute until the Also, when sodium acetate was added to hydroxylamine twentieth. hydrochloride the reaction of the hydroxylamine with In the last two cases, and in any others if the room acetone in the presence of the resultant sodium ace- temperature is too low to permit the above procedure, tate, sodium chloride, and acetic acid was very rapid, the following modification is made. The temperabut the measured value of A H was only -6.6 cal. per ture of the empty thermos bottle is taken after it has mol. Each of the above results is the average of only been rinsed and allowed to drain. In the meantime, two experiments. the specified volumes of alcohol and water are measured into two separate beakers and the temperatures Heats of Solution recorded on alternate minutes for a ten-minute period. The Heats of Solution of Anhydrous and Hydrated On the eleventh minute, the two liquids are thoroughly Sodium Acetate. In many laboratory manuals, experi- mixed in the thermos bottle and thereafter the temments are given to measure the heats of solution of a peratures recorded every minute until the twentieth pair of salts, frequently anhydrous and decahydrated minute is reached. The manner of calculation is similar to the general sodium sulfate. These salts are rather unsatisfactory, anhydrous sodium sulfate having only a small heat of method, using differences in temperature found by solution and commercial Glauber's salt being of in- means of temperature-time graphs. In order that the definite composition because of the ease with which it various parts of the experiment shall be comparable, loses water of hydration. Anhydrous and trihydrated the heats of dilution in each case should be determined sodium acetate present neither of these difficultiesand a t the same temperature. This would suggest that have appreciable heats of solution of opposite sign. the mixing temperature in each part be the same and The salts are inexpensive and can be obtained com- would necessitate a knowledge of the density and spemercially in a satisfactory state of purity. The molal cific heat of each final solution. Since the amounts used
+
may vary somewhat from those suggested and the necessary values for the individual liquids are readily available, i t is more convenient to make the calculation a t the higher temperature. Although the basic temperature may then vary somewhat from one part of the experiment to another, the experimental error in the value of A H is doubtlessly sufficient to render this diierence unimportant. For each concentration, the heat change a t the higher temperature can be calculated by means of the following equation, in which the significance of the symbols is quite obvious:
purposes, inorganic reactions which have a measurably slow rate of reaction are particularly fruitful, in order to impress the student with the fact that not all inorganic reactions are instantaneous. Because many students who take laboratory work in physical chemistry are primarily interested in organic chemistry, it probably would be more interesting and stimulating to some to measure the heats of a number of organic reactions. Ex~erimentsof hoth types .. are included in this study.
The mold heat content change a t any dilution on the basis of the alcohol will be equal to -Q divided by the number of mols of alcohol. The number of mols of alcohol in the 95.6 per cent solution can, of course, be found by means of the relationship:
in which M,, is the molecular weight of alcohol. At the same dilution, the amount of water added per mol of alcohol present in the 95.6 per cent solution can be calculated by means of the following equation: 0
Values for water and for 95.6 per cent alcohol suitable for substitution in the above equations are here given over the most commonly used temperature range: Tenb.. ' C
d.,
CU
d,
Ca
In normal times, ethyl alcohol is easily obtainable and inexpensive. A better concentration range can be obtained than with most substances and a graph of the values of - A H as ordinates against the number of mols of water per mol of alcohol in the 95.6 per cent solution is highly significant. A typical student curve is shown in Figure 4. Obviously the form of the curve and particularly the value of the asymptote will be altered slightly by small deviations of the alcohol from exactly 95.6 per cent. It should be noted that if hoth the water and the alcohol were pure, each case would be a study of the heat of solution a t the particular concentration. Since, however, water is already present in the 95.6 per cent alcohol, the experiment and the graph deal with the heat of dilution of an alcoholic solution of this concentration. With the aid of such a plot, numerous points in regard to the several types of heat of dilution and solution can be clarified. DISCUSSION
For calorimetric measurements, it seems well to select a wide variety of different types of reactions in order to emphasize the broad applicability and the basic importance of calorimetry. For pedagogical
,
I
20
40
I
I
60 SO Mols of H10
I 100
1
I
120
140
FIGURE 4.-TEE HEAT O P DILUTION O P 95.6 PBRCENTETHYL ALMHOLBY WATER
Obviously it would not be desirable for every student to conduct all of the experiments outlined, in addition to the usual standard studies of the heat of neutralization and solution. However, a somewhat broader experience by each student accompanied by the knowledge that still other studies -are being conducted by his colleagues is undoubtedly of real value. A few welldiversified experiments in calorimetry, performed during the early part of the course, help to give a more concrete concept of the beat content change and other thermodynamic quantities, making for greater confidence in the reality of less readily measured functions such as the total energy change, the entropy, and the free energy change. Thus a firmer basis is achieved for the more general classroom use of thermodynamics. Students are rarely disturbed by the limited accuracy of these experiments and more often are impressed by the ease with which acceptable approximations can be obtained. It would seem, in any case, that the time needed for rdnement might more profitably, in an introductory course, be devoted to acquiring a more extensive background. In considering the procedure and the calculations involved in catain of the studies outlimed above, some rather obvious and detailed comments have been made. Certain of these have been introduced as precautions hut, in general, they have been points over which students most frequently manifest dfifficulty.
JOURNAL OF
CHEMICAL EDUCATION
LITERATURE CITED
(I1 . . BEILSTEIN."Handbuch der orrankchen Chemie." 4th ed. J. Springer, Berlin,, 1920, Voi. 2, p. 167. Ann. chzm. phys., (61, 7 , 410-26 (1886). (2) BERTHELOT, (3) B ~ c n o w s wAND RosSINI. "Thermochemistry of chemical substances." Reinhold Puhlishinz.Com~auv. . . New York. 1936.
(4) Bouznr. Ann. chim. ehvs.. (71. 29. 305-83 (1903). ( 5 ) "Handbook of chem&t;y add ph$sics," 2 l i t ed.; Chemical Rubber Publishing Company, Cleveland, Ohio, 1936. (6) "International critical tables," McGraw-Hill Publishing Com~auv.New York. 1929. Vol. V. (7) VARET;A&. chim. phyi.. (7),'8, 79-141 (1896)
