152
WARDN. HUBBARD, DONALD W. SCOTT AND GUYWADDINGTON
was equivalent t o corrections of 0.40,0.31,0.27 and 0.25 kcal. mole-‘, respectively, t o AUco for the four compounds. For purposes of calculation of the uncertainty interval, an uncertainty of *l cal. per combusti on experiment was assigned to the correction. Summary.-Experience with the rotating-bomb method for the combustion calorimetry of organic sulfur compounds shows that it is an improvement over the Huffman-Ellis method in several respects. (a) The aqueous solution in the final state is essentially homogeneous. (b) Analytically determined amounts of hydrogen ion in the final solution that are closer to the theoretical amounts suggest that the chemistry of the bomb process is more
1‘01. 58
nearly in accord with the assumptions made as to its over-all nature. (c) The greater dilution of the final solution in the rotating-bomb method decreases the possibility of error from the formation of a complex of sulfuric acid with an oxide of nitrogen. (d) The oxides of nitrogen in the final gaseous phase are reduced to insignificant amounts in the rotating-bomb method. Acknowledgment.-The authors wish to express their gratitude to Dr. Stig Sunner of t.he University of Lund, Sweden, for supplying the sample of thiankhrene, for making his data available to this Laboratory prior to publication, and for cooperating in many other ways.
REDUCTION TO STANDARD STATES (AT 2 5 O ) OF BOMB CBLORIMETRIC DATA FOR COMPOUNDS OF CARBON, HYDROGEN, OXYGEN AND SULFUR’ BY WARDN. HUBBARD, DONALD W. SCOTTAND GUYWADDINGTON Contribution No. 58 from the Thermodynamics Laboratory, Petroleum Experiment Stution, Bureau of Mines, Bartlesville, Okln. Received June %, 10.53
The Washburn corrections, i. e., corrections for the reduction of bomb calorimetric data to standard states! are extended to apply to compounds that contain sulfur in addition to carbon, hydrogen and:xygen. A critical selection is made of the values of the numerical constants that are required for these correctionR at 25 . The correction8 are presented in a form which is (a) general enough to cover a wide range of experimental conditions, (b) readily adaptable to revision whenever better values of any of the numerical constants become available and (c) suitable for extenfiion to include compounds of carbon, hydrogen, oxygen and elements other than sulfur.
In 1933, in a paper entitled “Standard States for Bomb Calorimetry,” Washburn2emphasized that the energy evolved when the combustion of a substance takes place in a bomb calorimeter may differ significantly from the decrease in internal energy for the combustion reaction under standard conditions. He treated in detail the corrections that must be applied to bomb calorimetric data in order that investigators may obtain values of the standard change of internal energy. Washburn’s treatment (a), applied to the Combustion of compounds that contain only carbon, hydrogen and oxygen and (b), referred these combustion reactions to a temperature of 20’. In high-precision combustion calorimetry, it has become standard practice to apply the corrections proposed by Washburn. They are usually referred to as the “Washburn corrections” or collectively as the “Washburn reduction.’’ Several developments have occurred in the field of combustion Calorimetry since publication of Washburn’s paper two decades ago. First, great improvements have been made in techniques for determining heats of combustion of compounds that contain elements other than carbon, hydrogen and oxygen (in particular, sulfur and the halogens). For these classes of compounds, to which Washburn’s treatment does not apply, data are being obtained, or are likely to be obtained in the near fu(1) This investigation was part of American Petroleum Institute Research Project 48A on “The Production, Isolation and Purification of Sulfur Compounds and Measurement of their Properties,” which the Bureau of Mines conducts a t Bartlesville, Okla., and Laramie, WYO. ( 2 ) E.
W. Washburn,
Bur. llandarda J . Reerarnh, $ 0 , 525 (1883).
ture, that must be reduced to standard states if full advantage is to be taken of their accuracy. Second, there is an increasing tendency to conduct combustion calorimetry at temperatures near 25” or at least to refer the combustion reactions to that temperature. Third, more accurate experimental values have become available for a number of the quantities that enter into the Washbum corrections. This paper is intended to meet some of the needs that have arisen as a result of these developments. The original stimulus for the work reported herein was the necessity of applying Washburn corrections to bomb calorimetric data that are being obtained in this Laboratory for organic sulfur compounds. Therefore, the primary purpose was extension of the Washburn corrections to include organic sulfur compounds. However, a more general result was obtained, namely, a revision of the Washburn corrections that applies to 25” and takes advantage of the more accurate experimental data that have become available since 1933. Although the treatment as presented is limited to compounds that contain only sulfur in addition to carbon, hydrogen and oxygen, the method and many of the individual details are more general in nature. This treatment can therefore serve as the basis for future extensions of the Washburn corrections to other classes of organic compounds, for instance halogen compounds, whenever the need for such extensions arises. General Considerations Theory.-The Washhurn corrections, as presented hsra, apply to the combustion of a sub-
Feb., 1954
REDUCTION OF BO^ CALORIMETRIC DATATO STANDARD STATE
153
stance whose general formula is C.HbO,Sd. It is nitrogen and water vapor and (e) a liquid phase understood that some of the subscripts in this consisting of water saturated with dissolved oxygen formula may be zero. For example, for a pure and nitrogen. The next process consists of bringhydrocarbon, c and d are both zero. The calori- ing these initial contents of the bomb from their metric determination of the heat of combustion equilibrium state at 25" to their equilibrium state of this substance takes place as follows. The sub- at the initial temperature, ti, of the actual bomb stance, oxygen (in excess), nitrogen and water are process. The next process is the actual bomb procintroduced into a combustion bomb. (The ni- ess, in which the actual initial contents of the bomb trogen may be merely an impurity in the oxygen, or are converted t o the actual final contents of the it may be introduced deliberately to catalyze the bomb, and the temperature increases from ti to tr, oxidation of sulfur t o the +6 oxidation state.) The the final temperature of the actual bomb process. substance is caused to react with the oxygen t o pro- Two phases result, namely, (a) a gaseous phase duce carbon dioxide, water and sulfuric acid. Side consisting of oxygen, carbon dioxide, nitrogen and reactions that produce nitric and nitrous acids may water vapor and (b) a liquid phase consisting of an occur simultaneously. After the reactioa is com- aqueous solution of sulfuric, nitric and nitrous acids plete, the bomb contains carbon dioxide, water, saturated with dissolved oxygen, carbon dioxide sulfuric acid, the oxygen not consumed in the rear- and nitrogen. The next process consists of bringtion, nitrogen, and possibly nitric and nitroiis acids. ing these final contents of the bomb from their The process just described takes place in a bomb equilibrium state at the temperature, tr, to their calorimeter. The increase in temperature of the equilibrium state a t 25". I n the final process, the calorimeter is measured, and, by suitable calibra- nitric and nitrous acids are decomposed into tiitrotion of the calorimeter, this increase in tempera- gen, oxygen and water; all of the oxygen, carbon ture is related to the heat liberated by the process. dioxide and nitrogen are removed from the bomb, The heat liberated is equal to the decrease in inter- separated from each other and brought individunal energy of the contents of the bomb when they are ally to their standard states a t 25"; all of the water converted from the particular state in which they and sulfuric acid is removed from the bomb as an exist before the combustion reaction to thepartirular aqueous sulfuric acid solution under 1atm. pressure; state in which they exist after the combustion rear- and this solution is adjusted to the designated contion, Le., the change in internal energy for the artual centration by the isothermal addition or removal of bomb process. In practice, by applying appropriate liquid water in its standard state a t 25". The net calorimetric corrections, this is reduced to the change in this series of processes is just the idealized change in internal energy for the isothermal bomb combustion reaction. The sum of the changes in internal energy for all the processes is therefore the process. The quantity which an investigator wishes to energy of the idealized combustion reaction, AU,". obtain from bomb calorimetric data is not the The actual bomb process and the processes immechange in internal energy for the isothermal bomb diately preceding and following it constitute the process, but the change in internal energy for an isothermal bomb process, for which the change in idealized combustion reaction. This is defined as internal energy is obtained calorimetrically. The the reaction, isothermally at a given temperature changes in internal energy for the other two proc(25" in the present treatment), of unit quantity of esses are the Washburn corrections, the addition of substance in its standard state with an equivalent which to the experimentally determined change in amount of pure oxygen gas and the necessary internal energy for the isotherinal bomb process amount of pure liquid water, both of which are jn gives the desired quantity, AU,". The calculation their standard states, to produce the stoichiometric of the Washhurn corrections then consists of the amounts of pure carbon dioxide and an aqueous sul- calculation of the changes in internal energy for furic acid solution of a designated concentration, these other imaginary processes. Standard States.-The standard states are deboth of which are in their standard states. The fined in a manner consistent with current thermoequation of the reaction is dynamic usage. The definitions are: (a) for CaHbOoSd(S or I ) f (U f b / 4 - C/2 f 3 d / 2 ) 0 r ( g ) f oxygen, nitrogen and carbon dioxide, the pure (nd - b / 2 + d)HzO(l) = substances in the ideal gas state a t 1 atm. pressure, aCOz(g) d(HzSO4.nHtO) (1) (b) for the substance, the material in a thermodynamically defined state (solid or liquid) under a The change in internal energy associated with this pressure of 1 atm., (e) for water, the pure liquid process is called the "energy of the idealized corn- under a pressure of 1 atm. and (d) for the aqueous bustion reaction" and is designated AU,". The idealized combustion reaction is conven- sulfuric acid solution, the liquid a t a defined coniently regarded as occurring in a series of processes, centration (which is selected to be approximately one of which is the actual bomb process and the re- that obtained in the actual combustion experiment) mainder of which are imaginary. The first process under a pressure of 1 atm. Manner of Presentation.-The way in which the starts with the substance, oxygen (in excess), nitrogen and water, all in their standard states at 25". treatment is presented in this paper was determined These are placed in the combustion bomb, and by several considerations. One was that all of the equilibrium is established at 25", except that the corrections that must be applied to the original substance is not allowed t o mix with the other ma- calorimetric data should be included. Some of terials. Three phases result, nawely, (a) pure suh- these corrections are calorimetric, some are thermostance, (b) a gaseous phase consisting of oxygen, chemical end only the rent are those ueudly
+
154
WARD
N. H U B B A R D , DOXALD W.
regarded as the Washburn corrections. However, these different kinds of corrections are not all strictly independent, and there may be ambiguity about the classification of certain of the corrections and uncertainty about the order in which they are to be applied. These difficulties are removed if all of the corrections are included in one consistent treatment. A second consideration was that the treatment should be as complete and rigorous as it is practical to make it. This consideration led to the inclusion of terms that are negligible for the experimental conditions and attainable precision that the authors consider usual in combustion calorimetry. However, these terms are included so that an investigator who uses different experimental conditions, or who obtains increased precision may determine the magnitude of these terms and decide whether or not they are negligible for his purpose. A third consideration was that all of the terms should be kept separate and not combined into a single complex expression, as was done by Washburn. Keeping the terms separate has several advantages: (a) The individual terms are more easily examined t o determine whether they are significant or negligible. (b) When a more reliable experimental value for a quantity which enters the treatment becomes available, the term or terms that contain this quantity may be conveniently revised without disturbing the rest of the treatment. (c) Many of the terms of this treatment will apply, either unchanged or with slight modifications, to extensions of the Washburn corrections to other classes of organic compounds. The transfer of these terms to other extensions of the Washburn corrections will ’ be simpler if they are kept separate.. A fourth consideration was that the treatment should be presented in a way that is adaptable for use by other investigators. The rather long calculations involved in applying all of the corrections to the original calorimetric data are conveniently carried out on a computation form. The presentation is therefore given as the items which make up such a computation form, interspersed with explanatory text. These items, 100 in number, consist of the input data (experimental values, molecular weights, physical constants, auxiliary energy quantities, etc.) and the quantities that the investigator must calculate from them to obtain the desired quantity, AU,”, which is item 100. The items are so ordered that the calculation of a particular one depends only on the numerical values obtained for prior items and are so designed that the numerical operations are conveniently performed with a desk calculator. Items 1-67, which relate to the description of the initial and final states of the isothermal bomb process, items 68-80, which relate to energy factors and calorimetric data, and items 81-100, which relate to the changes in internal energy, are treated in the next three sections. As an illustration of the use of the method, and as a means of illustrating the magnitude of the various terms, a numerical example of the calculations is given. This numerical example is selected from a series of experiments carried out in this Laboratory to determine the heat of combustion of 3-methylthiophene.
1‘01. 58
S C O T T AND G U Y W A D D I N G T O N
Initial and Final States Substance.-The substance is defined as all of the material that undergoes combustion, and consists of the compound whose heat of combustion is being determined and any other combustible materials added for any purpose, e.g., the auxiliary material and the fuse. The first 18 items of the computation sheet list the formula (chemical or empirical), mass m, molecular weight &I, number of moles n, density p , and volume v, of each of the materials that comprise the substance. Primes are used t o distinguish different materials. In the numerical example, the compound is 3-niethylthiophene, the auxiliary material is a hydrocarbon oil the empirical formula of which is CHI.s91,and the fuse is filter paper the empirical formula of which is CH1.68600.843. Starred item numbers denote input data, and unstarred item numbers denote calculated quantities. (I*) (2*) (3*) (4) (5*) (6) (7*) (8*)
(9*)
(IO) (11*) (12) (13*) (14*) (15*) (16) (17*) (18)
Formula of cpd., C,’H~’O,’SJ’ m‘, mass of cpd. M‘, mol. wt. of cpd. n’ = m‘/M’ p’, density of cpd.
CB“S 0.85715 g. 98.164 g. mole-‘ 0.00873182 mole 1.02 g. ml.-l 0.0008 I. D’ = m’/1000p’ Formula of auxiliary material, Co”Hb”Oe”SdC CHi.sei m‘, mass of auxiliary material 0.05354 g. W’, mol. wt. of auxiliary material 13.916 g. mole-1 0.0038474 mole n” = m”/M” p“, density of auxiliary material 0.87 g. mL-* 2)” = m”/1000pf’ 0.0001 1. Formula of fuse, C a “ ’ H ~ “ ‘ O ~ ” ’ S ~ ” ’ CHI.6aaOo.843 m”’, mass of fuse 0.00410 g. M“‘, mol. wt. of fuse 27.197 g. mole-l n”‘ = m”‘/M”’ 0.0001508 mole p”’, density of fuse 1.5 g. mI.-l D”‘ = m”’/lOOOp”’ 0.0000 1.
I n the numerical example, c’, c”, d” and d”’ are zero. Items 19-25 list the subscripts, a, b, c and d, of the empirical formula C,HbO,S,j, and the mass, m(sub.), molecular weight, M(sub.), and the number of moles, %(sub.), of the total substance that undergoes combustion. The subscripts a, b, c and d are defined so that n(sub.) is always unity.
+ + + +
+ + + +
(19) (20) (21) (22) (23) (24)
a = n‘a‘ n”a” n”‘a“‘ 6 = n’b’ n”b” n”’6”’ c = n‘c’ n”c” n”’~’’’ d = n’d’ n“d” n”’d”‘ m(sub.) = m‘ nit’ m“‘ M(sub.) = 12.010a 1.0086
(25)
n(sub.) = m(sub.)/M(sub.)
+
+
+
+
0.0476573 0.0599206 0.0001271 0.00873 18 0.91479 g. 16.000~ 32.066d 0.91479 g. mole-’ 1.00000 mole
+
02,N2 and HzO in the Initial State.-Items 2636 deal with the amounts of Oz,N2 and HzO in the bomb, and the distribution of these compounds between the gaseous and liquid phases, in the initial state of the isothermal bomb process. Except for stoichiometry, the Nz is treated as though it were 02. This approximation is justified because (a) Nz and Oz have similar physical properties, (b) the mole fraction of Nz in the bomb gases is small (less than 0.03 in current practice) and (c) the errors from treating N2 as 0 2 in the initial state are nearly compensated by similar errors from so
Fel)., 1954
REDUCTION O F BOMB CALORIMETRIC D A T A
treating it in the final state, since Nz is present in nearly the same amount and condition in both states. In the equations to follow, superscripts i and f are used to designate the initial and final states, respectively, of the isothermd bomb process. (Subscripts i and f are reserved to designate the initial and final states of the actual bomb process.) The material to which a symbol applies and the state of that material are given parenthetically after the symbol. The abbreviations used include the chemical formulas of single compounds and the following other .abbreviations: sub., total substance; gas., gaseous mixture of 0 2 , Nz and H20vapor (and COz in the final state) ; soln., aqueous solution of HzS04, HNOs and "0%; vap., vapor; liq., liquid; diss., dissolved; and tot., total. The next three items list the volume of the bomb, v (bomb), the volume of HzOadded to the bomb, vi(HzOtot.), and the initial pressure at 25", $(gas.). The volume of the bomb is defined as the internal volume, exclusive of the volume occupied by the crucible, electrodes and other non-combustible accessories. In the numerical example, 10.03 ml. of water is introduced into the bomb, the volume of which is 347.1 ml., and the bomb, which contains air at atmospheric pressure, is charged to a total pressure of 30.00 atm. (at 25'). (26*) v(bomb) (27*) ~ ' ( H z 0tot.) (28*) Pi(gas.)
0.3471 1. 0.01003 1. 30.00 atm.
The density at 25", 997 g. 1.-l, and molecular weight, 18.016 g. molew1,of HzO are used to calculate the mass and number of moles of total HzO in the bomb. (29) (30)
m'(Hz0 tot.) = 997vi(Hz0 tot.) ni(HzO tot.) = rni(Hz0 tot.)/18.016
10.00 g. 0.5551 mole
155
TO S T A N D A R D S T A T E
air4 have been superseded by more recently determined data.5 The value of a selected here 0.000105 g. 1.-' atm.-l, is based on the smoothed data of Deaton and FrostSbfor air at 400 lb. in.-2 gage (28.1 atm. absolute). The number of moles, ni(HzO vap.), of water in the gaseous phase is calculated from the equation (32)
+
ni(HzO vap.) = [0.02304 0.000105P~(gas.)]~~(gas.)/18.016
0.000489 mole
The number of moles, ni(H20 liq.), of liquid water is obtained by difference. The equation of state at 25", Pv = n(24.465) (1 - O.O006lP), fits the PvT data of 02 exactly for P = 30 atm. and to a sufficiently good approximation over the range P = 20 to P = 40 atm. This equation applies to the gaseous phase, since NZis treated as though it were Oz and the concentration of HzOvapor is too small toaffect the P v T behavior significantly. It is used to calculate the number of moles, %'(gas.), of the gaseous mixture. (34)
ni(gas.) = Pi(gas.)vi(gas.)/(24.465 [l - 0.00061Pi(gas.)]} 0.4199 mole
The solubility of Oz in aqueous HzS04 solutioiis at 25" will be discussed in the next subsection. The limiting value for pure H20, 0.0000228 mole per mole of HzO per atm. O2 partial pressure, is used to calculate the number of moles of 0 2 Nz dissolved in the liquid H20. Nz)diss.] = (35) ni[(Oz
+
+
0.0000228ni(H20 liq.) [Pi(gas.) - 0.031 0.000379 mole
The quantity, 0.03, in item 35 is the approximate partial pressure of HzO vapor (in atm.) in the gaseous mixture. The total number of moles of O2 Nz is calculated next.
+
The volume occupied by the gaseous phase is obtained by subtracting the volume of liquid HzO (36) ni[(Oz Nz) tot.] = and of substance from the volume of the bomb. ni(gaa.) - ni(H20 vap.) ni[(O2 Nz)diss.] The volume of liquid HzO differs from vi(H2Otot.) 0.4198 mole only by the amount vaporized into the gaseous 02,COZ,Nz, HzO, HzS04,HNOI and HNOzin phase, an amount which is insignificant in this cal- the Final State.-Items 37-67 deal with the comculation. pounds present in the bomb in the final state of the isothermal bomb process, and the distribution of (31) oi(gas.) = v(bomb) vi(Hz0 tot.) - V' - V" - v"' 0.3362 I. these between the gaseous and aqueous phases. The substance has reacted with Oz according to the The concentration of saturated HzO vapor in net equation gases at various pressures, Cw, may be represented CaHaOcSa ( a b/4 - c/2 3d/2)02 = by the equation given by Washburn [eq. 105 of ref. aCOz (b/2 - d)HzO dHzSOc 21, CW = Co +*crP. The term, Co, which is the concentration of saturated HzO vapor in the ab- Side reactions may have occurred according to the sence of other gases, is 0.02304 g. 1.-' at 25°.3 P net equations '/zN2 '/do2 1/2H20 = HNOs is the pressure of other gas, which, for the pressure range of interest here, does not differ significantly and 1/zN2 8/402 l/zHzO = HN02 from the total pressure. The constant a is determined by the nature of the gas phase. Unfortu- The extent of these side reactions is determined exnately experimental data are still unavailable for perimentally by chemical analysis of the final bomb the evaluation of a for 0 2 , and it is necessary to as(4) (a) E. P. Bartlett, J . Am. Chem. SOC.,49, 65 (1927); (b) F. sume, as Washburn did, that a is the same for O2as Polliteer and E. Strebel, 2. physik. Chem., 110, 768 (1924). (6) ( 8 ) A. W. Saddington and N. W. Krase, J. Am. Chsm. Soc., 66, for N2 or air. However, the data used by Washburn for the concentration of HzO vapor in Nz and 353 (1934); (b) W.M.Deaton and E,M. Frost,Jr., Am. Gar A ~ s o c . .
+
+
+ +
++
+ +
(3) N. S. Osborne, H. F. Stimson and D. C . Ginninga, J. Reaearoh N a f l . Bur. Standards, 23, 261 (1938).
+
+
+
+
Pi-00. Natural Gas $sot., 143 (1941). (6) J. A. Beattie and 0. C. Bridgeman, Proc. Am. Acad. A r b ScL, 63, 229 (1928).
AND GUYWADDIXGTOK WARDN. HUBBARD, DONALD W. SCOTT
156
Yol. 58
solution.' In the numerical example, it was found that 0.00069 mole of HNOI and 0.000005 mole of HNOz were formed.
The volume of the gaseous mixture is obtained by difference.
0.00069 mole 0.000005 mole
The number of moles of C02 produced in the combustion is calculated from stoichiometry.
(37*) n'(HN03) (38*) n'(HN02)
The number of moles of H2S04 produced in the combustion is calculated by stoichiometry (39)
n'(H~S04)= &(sub.)
0.008732 mole
The number of moles of HzO in the liquid phase is given rigorously by n'(Hz0 tot.)
+l/znf(HNO,) (b/2 - d)n(sub.) - 1/2nf(HNOt) - nf(H20 vap.)
However, the final term (which is small compared to the first two terms) is not known a t this stage of calculation. If the HzSO4solution in the final state is relatively dilute, the number of moles of HzO vapor are not greatly different in the initial and final states, and it is a satisfactory approximation to substitute n i ( H 2 O vap.) for nf(H20vap.). The validity of this approximation may be verified after item 67 is calculated. (40)
+
nf(HaOliq.) = ni(H20tot.) (b/2 - d)n(sub.) 1/2nf(HN03) l/anf(HNOz) - ni(Hz0 vap.) 0.5755 mole
-
(49)
(50)
+
Density data for HzS04and HNOs solutions individually* may be represented, for the concentration ranges of interest here, by p = 0.9970 0.0066 wt. % (HzS04) and p = 0.9970 0.0054 wt. % (HNOa) g. m1,-1. In the calculation of the density and volume of the aqueous solution, two approxiinmations are made: (a) that HzS04 and "03 crease the density of H 2 0 additively according to weight per cent., and (b) that the small amount of The HNOz may be treated as though it were "0,. second approximation will be made repeatedly throughout this subsection.
+
(44) (45)
+
+ 0.0066+wt. % (HzS04) +
pf(so1n.) = 0.9970 0.0054 wt. SX
("03
vf(so1n.) = mf(soln.)/lOOOpf(soln.)
1.626 N
f(
(48)
nf(HnOliq.)/nf(H2S04)
H(NO2)
+
-0.5 0.0
0.5 1.0 1.5 (51)
K(C0z) X 104
356.5 340.5 326.9 314.5 304.5
N (HaSOc) N ("01
'/z
"0s)
-+
2.0 2.5 3.0 3.5 4.0
K(COd X 104
297.0 290.8 285.0 279.2 274.2
0.0303 mole I.-'
K(C0a)
atm.-I
In the computation of the number of moles of C 0 2 dissolved in the aqueous phase, it is necessary t o take account of (a) the fugacity of the CO2 gas in the presence of the 0 2 gas and (b) the total pressure on the aqueous phase. It is convenient to treat the COZ and 0 2 as ideal gases and then use a fictitioiis solubility constant, K * ( C 0 2 ) , that includes corrections for fugacity and total pres~ure.'~ The fictitious solubility constant is obtained by multiplication of the actual solubility constant by a factor, D ( C 0 2 ) . Values of D ( C 0 2 )are tabulated below as a function of the mole fraction of COZ, z(C02), and the final pressure, Pf(gas.). At this stage of the computation, only approximate estimates of z(C02)and Pf(gas.) are required; the estimated values may be checked after accurate values have been calculated in items 63 and 65.
1.049 g. ml.-l 0.01074 1.
N(H2S04)= 2nf(HzS04)/vf(soln.) N(HNO8 "02) = [nf( HN03) 3. n HNO2)]/~ f(s o h )
+
0.017657 mole
"02)
The normality of H2S04and of the combined nitrogen acids, and the molar ratio of H20 t o HzS04 are calculated in the next three items. (46) (47)
n'(COz tot.) = an(sub.)
N (HzSOd N HNOi
'/a
+
The weight per cent. of H2S04and of the combined nitrogen acids are calculated next. (42) wt. % (HzS04)= 9808nf(HzS0,)/mf(soln.) 7.60%
0.3364 1.
+
mf(soln.) = 18.016nf(Hz0 li ,) 98.1nf(HzS04) 63nf(HNOs) 47nl"oz) 11.27 g.
+
- vf(so1n.)
The solubility of C 0 2 in aqueous H2S04solution is read from a smooth curve through a large scale plot of the data of Markham and Kobe,g Kobe and Williams,'o Geffcken" and Sunner.12 The table of smoothed values given below will permit investigators to plot this solubility curve for their own use. The data of Geffcken show that HN03, on a normality basis, increases the solubility of C02in aqueous solutions approximately half as much as H2S04 decreases it. The independent variable is therefore selected t o be N(H2AO.J - 1/2N(HN03 " 0 2 ) . An extrapolation to negative values of this variable is included to cover cases in which nitrogen acids are present and Hi304 is not. The solubility con, defined as the number of moles of stant, K ( C 0 2 )is COZ dissolved in 1 1. of solution at unit fugacity of CO2 gas.
The mass of solution is obtained by summing the masses of the constituents. (41)
vf(gas.) = v(bomb)
0.065 N 65.91
(7) The corrections for iron wire discussed by Washburn are omitted from this treatment, a8 the iron wire method of firing has been superseded b y better methods that do not require these apecial corrections. (8) "International Critical Tables," Vol. 111, McQraw-Mill Book CO.,I I W ~ N,E WYnrk, N. X,, 1828. p p ~58-69
Z(CW
20
Pf(gas.), atm. 30'
40
0.0
0.914 .goo .887
0.873 .854 .836
0.834 .810 ,787
0.1 0.2 ~~
(9) A. E. Markham and K. A. Kobe, J . Am. Chem. Soc., 68, 1165 (1941). (10) K.A. Kobe and J. 8 Williams, Ind. Eng. Chem., Anal. Ed., 7. 37 (1935). (11) G. Geffcken, 2.physik. Chem., 49, 257 (1904). (12) 8. gunner, Dissertation, "Studies in Combustion Calorimetry Applied t o Organo-Sulfur Compounds," Carl Bloms Boktryckeri. Lund, Sweden, 1949. (13) The equation of state of item 65 was used in the computation of the fugaaity of Cos gaa in the presence of Or gas. A value of 33 ml. for the partial molal volume of COz in aqueous solution wag used in the cnmpiitatim of the effect of tatel DrenrIure.
REDUCTION OF BOMB CALORIMETRIC DATATO STANDARD STATE
Feb., 1954
The number of moles of gaseous mixture is calculated next. As in item 40, ni(HzO vap.) is used as an approximation for nf(HzOvap.).
In the numerical example, the estimated values are 0.12 for z(C02) and 28 atm. for Pf(gas.). (52) (53)
D(C0z)
0.859
K*(COz) = 1)(C02)K(C02)
(62) 0.0260 mole I.-'
ntm.-l
(54)
nf(COzdiss.) = 24.465K*(COz)vf(soln.)/vf(gas.) nf(COztot.) 1 24.465K*(COz)vf(soln.)/v'(gas.) 0.000949 mole
(63)
+ = + -7/4nf(HNOa) + -b / 45/4nf(HNOil - c/2 + 3d/2)n(sub.) , .
-,
, .
-.
(64)
0.3429 mole
The solubility of O2in aqueous H2S04 solution is read from a large scale plot of the data of Geffcken." Smoothed values are given below. As HNOa 12.60 11.81 11.26 10.77 10.31
WOd
(57) wt.
2.5 3.0 3.5 4.0
9.85 9.39 8.95 8.61
0.00106 mole I.-'
z(COz) = nf(COz gas)/nf(gas.)
0.1198
pf(gas.) = 0.00061[ 1 4-3.21~(Coz)[l
+ 1.33~(cO2)]} 0.00088 atrn.-l 1
+
P'(gas') = [0.040875vf(gas.)/nf(gas.)] pf(gas.) 27.66 atm.
+
atm.-l
%
wt %, (HnSOr)
+ HNOd,
0
2
4
6
8
10
12
14
16
18
1.0000
0.9905 ,9878 .(3852 ,9525
0.9812 ,9785 ,0759 ,9732
0.9720 .9693 ,9662
0.9618 .9591 .9565 ,9535
0.9522 .9495 .9469 ,9442
0.9416 ,9389 .9363 .9m
0.92Y0 ,9203 .02:37 .(3210
0.9147 .9120 .go94
0.8983 .8956 ,8930
,9067
,8003
.9973 ,9947 *. nmn
.~FZO
0.9til
g
decreases the solubility of O2approximately half as much as HzS04,on a normality basis, the independent variable is selected to be N(H2S04) '/&(HN03 HNOJ. The solubility constant, K(Oz), is defined as the iiumber of moles of 0 2 dissolved in 1 1. of solution per atm. O2partial pressure. The solubility of O2 N2in the aqueous solution is handled hi much the same way as that of COZ. However, as the solubility of O2 N2 is much smaller, it is uiinecessary to use fugacity instead of pressure or to consider the effect of pressure on the aqueous phase. The values of D(O2) tabulated below merely correct for the deviation of the partial pressure of 0 2 Nz from that calculated from the ideal gas law.
+
+
+
+
+
x(C0d
20
0.0 .I .2
0.988 .989 .9'30
(58)
WOr)
(591
K * ( ~ z=) U(Ot)K(Oz)
(61)
+ n*(HzO vap.) 0.3898 mole
The ratio, g, of the vapor pressure of water over to that the solution of HzS04 and HN03 "0.2 over pure HzO is obtained by interpolation from a large scale plot. Such a plot may be constructed from the values of g in the following table, which is based on data from a number of sources.14
(liN01
0.0 0.4 0.8 1.2 (68)
4-nf(COt gas)
The pressure of the final gaseous mixture is calculated from the equation of state. (65)
0.0 0.5 1.0 1.5 2.0
+
Washburn gives an equation for p in the equation of state, Pv = nRT(1 - p P ) , for 02-COZ mixtures as a function of x(COz) [eq. 28 of ref. 21. The equation applies strictly a t Z O O , but may be used at 25" without significant loss of accuracy.
+ Nzin the final state
The number of moles of O2 is calculated next. ~ ' [ ( O Z Nz) tot.] ~ ' [ ( O Z Nz) tot.] - ( U
%'(gas.) = ~ ' [ ( O Z Nz) gasl
Item 63 lists the mole fraction of COz in the gaseous mixture, z(COz).
+
(56)
157
Pf(gas.),atrn. 30
0.982 . Y885 .985
40
0.976 .978 .980
0.985 0.00104 mole 1.-1 atm.-'
++Nz) gasl = Np) tot.] - nf[(Oi + Nz) diss.]
nf[(02
/bf[(O$
0.3426 mole
The value of Wiebe and Gaddylbforthe concentration of saturated water vapor in COz at 25 atm. and 25" leads to a value of 0.00048 g. 1.- l atrn.-' for a in the equation, CW = Co aP. The value of a previouslyselectedforOzis0.000105g. l.-latm.-l. Assuming that a for Oz-COz mixtures varies linearly with the mole fraction of COZ,one may write Cw = 0.02304 + [0.000105 0.00037~(COz)]Pg. I.-' This relationship is used to calculate the number of moles of HzO vapor in the gaseous phase.
+
+
(67) nf(HzO vap.) = g( 0.02304 [0.000105
+
+ 0.0003S~(CO~)]P'(gas.)}v~(gas.) 18.016
0.000488 mole
Energy Factors and Calorimetric Data The description of the initial and final states of the isothermal bomb process is complete with item 67. Before the calculation of the actual corrections, it is convenient to tabulate values of certain quantities which are unique for the particular experiment or the particular substance and therefore cannot be expressed in a general form. These quantities are tabulated in items 68-80. (14) (a) C. H. Grcenewalt, I n d . Env. Chem., 17, 522 (1925); (b) E. M. Collins, THISJOURNAL, 37, 1191, (1933); (c) 8.Shankman and A. R . Gordon, J . A m . Chem. Soc., 61, 2370 (1934); (d) ref. 8. Vol. 111, p. 304. (15) R . Wiebe and V. L. Gaddy. J . Am. Chem. Soc., 63, 475 (1941).
158
WARDN. HUBBARD, DONALD W. SCOTT AND GUYWADDINGTON
The first of these are values of (bU/bP)Tfor the materials which constitute the substance. As discussed by Washburn (ref. 2, pp. 542-543), it is a satisfactory approximation to take (bU/bP), equal to -T(bv/bT),. In the numerical example, the ) ~1.013 X lo+, 8.50 X lo-' values of ( b ~ / b Tare and ca. lo+ 1. g.-l deg.-' for 3-methylthiophene, the auxiliary oil, and the fuse, respectively.
Vol. 68
The next two items list the energy of the idealized combustion reaction, AUco, for the auxiliary material and for the fuse. These quantities must have been determined in previous series of experiments. (72*) AU,"(auxiliary material) (73*) AU,"(fuse)
-152850 cal. mole-' - 106710 cal. mole-'
The next three items deal with the energy equivalent of the calorimetric system. This is conveniently divided into two parts, one the energy equivalent of the whole system minus the contents of the bomb, Cen. (calor.),17which is the same in the initial and final states, and the other the energy equivThe value of ( b U / d P ) , for the final solution is alent of the contents of the bomb, CeB.(cont.), also required. It is read from a large scale plot of which is different in the initial and final states. this quantit.y as a function of wt. yo (HzS04).Such The value of CeR. (calor.) must have been detera plot may be made from the following table, which mined experimentally, either by electrical calibrais based on density data for H2S04solutions*and the tion or by combustion of a standard substance such approximateequalityof ( d U / b P ) ,and - l " ( b ~ / d T ) ~as . benzoic acid. (68*) ( ~ U / ~ P )=T '-7221(dV/dT)p' -0.00731 cal. g.-l atm.-l ( d u / d P ) ~ "= -i221(dv/dT)p" -0.00614 cal. g. -I atm. - l ( d u / d P ) ~ " ' = -7221( dv/dT)p"' -0.007 cal. g. --I atm.
(i4*)
Ceff.(calor. )
3909.44 cal. deg.-l
The values of Ceff.(co1lt.) are obtained by sum0 - 186 10 -281 ming the heat capacity of all the contents of the 2 -213 12 -292 bomb. The gaseous phase may be considered to be 4 -235 14 -302 a t constant volume, as the change in volume from 6 -254 16 -312 thermal expansion of the bomb and of the con8 -269 18 -321 densed phases and from vaporization of H,O is neg(69) (dU/dP)T'lsoln.) -0.00266 cal. g.-] atm.-l ligible. Similarly the condensed phases may be Values are also required for the change in internal considered to be at constant pressure, as the change of pressure with temperature is too small to be energy for diluting (or concentrating) the HN03 HNOz t o a concentration of 0.1 N and the H2S04t o significant. The effective heat capacity of the twoan even concentration close t o that obtained in the phase system, liquid HzO or aqueous solution plus actual experiment. In the numerical example, the HzO vapor, may be represented by two terms, even concentration is selected to be HzS04.70Hz0. one proportional to the total mass, and the second The quantity, A U d i l n . ("03 HNOz), is read di- a "vaporization correction" proportional to the rectly from a plot, and the quantity, A U d i l n . (HzSO~), amount of H20 vapor at 25".18 Thus for the initial is obtained as the difference between AHo of forma- state tion of HzS04a t the even concentration and that at C,tt.(HpO tot.) = Arni(H20 tot.) + Bni(H20vap.) the concentration of the final solution. The required values of AHoffor HzS04 are read from a large scale and for the final state plot of that quantity as a function of n(HzO)/ C,rf.(soln. HzO vap.) = A [rnf(soln.) 18nf(Hz0vap.)] Bnf(HzO vap.) n(H2S04). Numerical values from which the two plots may be constructed are given below. These The following values of A as a function of the conare based on data from the tables of selected values. centration of the solution are based on heat capacwt. 7 0 A L'diln. ("08 ity data for HzS0419 and HN0320solutions. As (HNOa + + "02); n(HaO) AHor(H2SOS, "03, on a wt. % basis, lowers the heat, capacn(HzSO4) cal. mole-1 HNOd cal. moleity about 1.6 times as much as HzS04,the inde0.0 102 25 -211190 pendent variable is selected t o be wt. % (HzS04) .1 46 30 -211280 1.6 wt. % ("03 "02). .2 31 40 -21 1380
+
+
+
+
.3 .4 .5 .B .8
+ + + 21 + 13 + + -
7 2 6 12 23 29
1.0 1.5 2.0 2.5 - 34 - 37 3.0 3.5 - 39 (70) AUdi~n.("o~ "02) (71) AUdilm(HzSO4)
+
+
+
50 60
io
80 90
100 115 130 150
-21 1440 -211475 -211506 -211534 -211562 -21 1590 -21 1629 -211665 -211711
+14 cal. mole-' -12 cal. mole-'
(16) "Selected Values of Chemical Thermodynamic Properties," Series 1. Tables 14-7 and 18-6, Natl. Bur. Standards Circular 500 Washington, D. C., 1952.
+
+
(17) The symbols S and E which have been used in the past to denote the energy equivalent are more commonly used t o denote entropy and energy. T o avoid confusion, a new symbol, Ceff., nieaning the effective heat capacity, is adopted here for the energy equivalent. B y definition, the energy equivalent of a bomb calorimetric systein is the amount of energy that must be added to it, under the conditions o/ the combustion experiment, t o raise its temperature f r o m t to I', divided by (t' - 1 ) . In a combustion exi~eriment,tbe pressure in the bomb changes in going from the initial to the final state, and therefore the elastic strain on the bomb proper and the compression of the crucible and other internal parts also changes. The provision "under,the conditions of the combustion experiment" means that any energy effects associated with these changes in the bomb and internal parts are included in the definition of the energy equivalent. (18) H. J. Hoge, J. Research N a l l . B U T . Standards, 8 6 , 111 (1946). (19) M. Randall and M. D. Taylor, THISJOURNAL, 45, 959 (1941). Note that the values of cp listed in Tables 2 and 3 of ref. I9 are per g. of Ha0 and not per g. of solution. ( 2 0 ) F. D. Rossini, B u r . Standards J. Research, 7 , 47 (1031).
REDUCTION OF BOMB CALORIMETRIC DATATO STANDARD STATE
Feb., 1954
159 23.00239 25.00842’ 0.00631O O
1.6 wt; % (HNOa HNOd
+
A cal. g.-l’deg.-l
0.997 .979 .961 ,945 ,929
0 2 4 6 8
i . 6 wt. % (“0s
“Om)
+
10 12 14 16 18
A , cal. g.-1 deg. - 1
0.914 .898 .883 .869 ,854
The variation of B with the concentration of the solution is not significant, and the value, 550 cal. mole-’ deg. -I, may be used for all concentrations. In the numerical example, the crucible and other parts made of platinum weighed 30.05 g., and the glass ampoule to contain the 3-methylthiophene sample weighed 0.047 g. The applicable heat capacity values are: for 3-methylthiophene, 0.367; for the auxiliary oil, 0.53; and for the fuse, ca. 0.4 cal. deg.-l g.-I. (75)
C,rr.i(cont.) = 5.056ni[(Oz Nz)tot.] 0.997mi(Hz0 tot.) 550d(H~Ovap.) m’cp‘ m”cP” m”’cP’’’ O.O325m(Pt) 0.17m(glass) ., ., . 13.69 cal. deg.-l (76) Ceff,f( cont.) = 5.056nf[(02 N2) tot.] 7.251nf(COztot.) A[mf(soln.) 18nf(Hz0vap.)] 550nf(Hz0 vap.) 0.0325m(Pt) 0.17m(glass) ..... 13.79 cal. deg.-l
+ + ++ + ++ ++ + + + +
+
+
++
The foregoing equations apply strictly a t 25” and a pressure of 30 atm., and approximately a t any temperature near room temperature and any pressure in the usual range of bomb-calorimetric practice. Errors from their use are minimized if the combustion experiment is conducted a t temperatures near 25”, and furthermore, since the expression for Cejy.i(cont.) is somewhat more reliable than that for Ceff.f(cont.),it is advantageous to have the final temperature, tr, close to 25”. The electrical energy supplied to ignite the sample, A U i g n . , is listed next. (77)
AUign.
1.35 cal.
The next three items list the initial and final temperatures of the actual bomb process, ti and t f , and the quantity Atcor., which is the correction that must be applied to the change in temperature of the calorimeter to correct for the heat of stirring and the heat exchanged between the calorimeter and its environment.21 (21) The term, Atcor., is best understood in relation t o the calorimetric experiment. In the calorimetric experiment, the time of experimental observations is divided into three periods. I n the “fore period,” the temperature of the calorimeter, t , is observed as a function of time, T. ( I n this foolnote, Tis used t o denote time and not Kelvin temperature.) At the end of the fore period, T = Ti and t = ti. The “reaction period” begins a t Ti. During the reaction period, the sample is ignited, the rapid increase of temperature is observed, and enough time is allowed to elapse so that the rate of change of temperature is again uniform. The “after period” begins at Tf, a t which time the temperature is [f. I n the after period, the observation of the temperature as a function of time is continued. From the observations in the fore and after periods, the rates of change of temperature a t Ti and Tf, (df/dT)i and (dt/dT)f, are determined, The changes of internal energy equivalent t o the heat of stirring and the heat exchanged between the calorimeter and its environment are designated by AU.tir. and AUex. By definition
A ~ O ,= . [AUm.
+ AUe,.I/[C.ff.(calor.) + Cerr.‘(cont.)]
(1) For the determination of the sinall correction term, Atcor., the dif-
Changes in Internal Energy In this section, the idealized combustion reaction is considered as occurring in a series of steps, and the change of internal energy of each is calculated. The symbol, Alloperation (material), is used to denote the change of internal energy when the indicated operation is performed on the indicated material. The operations are abbreviated as follows: vaporization, vap. ; dilution, dil.; solution, sol. ; mixing, mix.; and decomposition, dec. The symbol AU(materia1)’;1 is used to denote the change in internal energy of the indicated material when the pressure changes from P‘ to P”. When used without a superscript, AU applies either to a mole or to ference in Ceff. (cont.) in the initial and final states is not significant, and Ceff.i(cont.) could have been used in eq. I instead of Ceff.f(cont.). If the rate at which heat of stirring is supplied t o the calorimeter is constant, and if the rate of heat exchange between the calorimeter and environment is proportional to the temperature difference (Newton’s law), then at Ti and Ty
+ (dt/dT)f = z + (dt/dT)i = z
and
a(tenv.
- ti)
(11)
4tenv.
- if)
(111)
The first term on the right is the constant rate of temperature change from stirring, and the second is the rate of temperature change from heat exchange. There are at least three methods in common use for caloulating Atcor. I n the first, the temperature of the environment, ten“., is measured, and z and u are evaluated by simultaneous solution of eq. I1 and 111. The values of z and u are then substituted into the relation
The second method does not require the determinaton of tenv. A “convergence temperature,” to, is defined b y to = d u ten”. Physically, t o is the limiting value the calorimeter temperature would approach after an indefinitely long period of time. Equations 11, 111and IV may be rewritten as
+
(dt/dT)i (dt/dTh
5
a(tc
- ti)
4 t c
- tr)
(V) (VI)
and
The values of 01 and tc are obtained by simultaneous solution of eq. and V I and are then substituted into eq. VII. In the third method, which is the one used in this Laboratory, a “mid-time,” Tm, is defined by the relationship
Separation of the integral of eq. IV into two parts, the addition and subtraction of t i in the first integrand and the addition and subtraction of 1f in the second yields
JJz
+
a(&.
- If
+
ti
- t ) ] dl’
(IX)
B y use of eq. VIII, this may be reduced t o
The value of Tm is obtained from the relationship derivable from eq. VI11
Tm = T f - [ l / ( t r -
ti)]
STT’
( t - ti) d2’
Substitution into eq. X then yields the value of
4LCor,
(XI)
WARDN. HUBBARD, DONALD W. SCOTT AND GUYWADDINGTON
160
a gram of material as convenience dictates. (The units of AU are always evident from the necessity that the equations be dimensionally consistent.) When used with a superscript i or f , AU applies to the actual amount of material involved in the combustion experiment. Step l.-ni(H20 vap.) moles of liquid H20 in its standard state at 25" is decompressed from 1 atm. to its saturation pressure a t 25", P a a t . ( H z O ) , vaporized, and then decompressed in the vapor state to a negligibly small pressure. The change in internal energy is
p.(HzO) + ~ U ~ ~ , . ( H+ ~ OA)U ( H ~ O vap.)]
ni(H20 vap.) { AU(H~Oliq.)]
The two decompression terms are negligibly and only the vaporization term need be considered in the computation form. The data of ref. 3 give AH",,,(H2O) = 10,514 cal. mole-', from which it follows that AU,,,. (H2O) = 9922 cal. mole-l. (81)
AUvap.i( H2O) = 9922ni(H 2 0 vap.)
+
+
+4.85 cal.
Step 2.-(a b/4 - c / 2 3d/2)n(sub.) moles of 0 2 in the ideal gas state at 25" is decompressed from 1 atm. to a negligibly small pressure. Step 3.-The 0 2 gas from step 2 is mixed with n'(H20 vap.) moles of H2O vapor from step 1 and ni[(02 N2) tot.] - (a b / 4 - c/2 3d/2) n(sub.) moles of excess O2 and N2 gas initially at a negligibly small pressure a t 25". Step 4.-"ni(H20 Sq.) moles of liquid HzO and n(sub.) moles of the substance in their respective standard states are placed in the bomb at 25". Steps 2, 3 and 4 do not involve any change in internal energy. Step 5.-The liquid water is compressed to a pressure of Pi(gas.). For the pressure range involved, (bU/bP)r may be assumed to be constant. The change in internal energy is ni(HzOliq.)(bU/ bP)r(H20 liq.) [P'(gas.) - 11. The value of (bU/dP)r(H2Oliq.) is -0.00186 cal. g.-I atm.-' (see table immediately preceding item 69) or -0.0335 cal. mole-I atm.-'.
+
(82)
AUi(HzOlis.)] = -0.0335ni(H20 liq.)[Pi(gas.) - 11
Step 6.-The (83)
+
+
-0.54 cal.
substance is similarly compressed.
AU'(sub.)] picgas*) =
++
+
AU,,I,,.(OZ N2) ni[(02 N2) diss.]. The values N,) for aqueous H2S04 solutions of A U s , l n . ( 0 2 will be discussed under step 15; the limiting value for pure HzOis -3200 cal. mole-'.
(84)
+
+ N2) diss.] -1.21
AUso~nj(02 K2) = -3200ni[(02
cal.
Step 8.--ni(gas.) moles of the mixture of O2 gas, N2 gas and H2O vapor is compressed into the remaining space of the bomb to the pressure, Pi(gas.). If the effect of the small concentration of HzO vapor is neglected and the N2 is treated as though it were 02,the change in internal energy may be represented by AU(02 gas)],P'(gaB.)ni(gas.). The calorimetric data of Rossini and F r a n d ~ e nfor ~~ O2 at 28", when corrected to 25" by use of a temperature ~oefficient~~ of -0.4% deg.-l for (dU/ ~ P ) give T AU(02 gas)]: = -1.574P cal. mole-'. (85)
AU'(gas.)]
=I
-1.574Pi(gas.)ni(gas.) - 19.83 cal.
Step 9.-The bomb is placed in the calorimetric system at 25". This step, for which there is no change in internal energy, brings the system to the initial state of the isothermal bomb process. In the foregoing, it has been assumed that all of the substance is liquid or solid in the initial state, and that it does not interact in any way with the other materials in the bomb. This assumption may not be strictly true for relatively non-volatile materials that are not sealed in ampoules but are exposed directly to the bomb gases. For such materials there are energy effects associated with volatilization of a small amount of the material, with the solution of 02,I 3 2 and H2O in liquids, and with the adsorption of these on solids. The corrections for these effects are difficult to assess in practice. Therefore in precision calorimetry, the experiments must be designed in such a way that these effects are negligibly small. Step 10.-The temperature of the system is changed from 25" to ti. The equivalent change in internal energy is [Cetr.(calor.) Cefi.'(cOnt.)](ti - 25). Step 11.-The actual bomb reaction is caused to occur, and the temperature of the system increases from t, t o tf. The equivalent change in internal energy is the sum of the electrical energy supplied to ignite the sample, the stirring energy, and the energy exchanged between the calorimeter and its environment, A U i g n . AUstir. 4- AUex. = AUign. [C,s.(calor.) Ceixf(cont.)IAtcor. Step 12.-The temperature of the system is changed from tf to 25". This step brings the system to the final state of the isothermal bomb process. The equivalent change in internal energy is [C,ff.(calor.) Ceff.'(cont.)](25 - tt). The change of internal energy for the isothermal bomb process, AUI.B.P.,is the sum of the changes of internal energy for steps 1 0 , l l and 12. I
+
+
If the compound is enclosed in a sealed ampoule which it does not fill, the energy of compression of the compound must be replaced by the energy of compression of the ampoule in item 83. As the latter is difficult to estimate, it is desirable to enclose a volatile compound in a completely filled, thin walled ampoule so that the pressure in the bomb is transmitted to the compound. Such a procedure was followed in the numerical example. Step '7.--.ni[(0N2) 2 diss.] moles of 0 2 and Nz gas from the mixture of step 3 are dissolved in the liquid HzO. The change in internal energy is
VOl. 58
+ + +
+
(22) In tlie numerical exatngle. tlie decompression terms are 0.000016 and 0.0024 o a l .
(23) F. D. Rossini and h.1. Frandsen, Bur. Standards J . Research, 9, 733 (1932). (24) E. W.Washburn. ibid., 9, 521 (1932).
REDUCTION OF BOMB CALORIMETRIC DATATO STANDARD STATE
Feb., 1954
Step 13.-The liquid and gas phases are removed from the bomb and calorimeter at 25" and are confined separately a t a pressure of Pf(gas.). No change of internal energy is associated with this step. Step 14.-The dissolved C 0 2 is allowed to escape from the liquid phase and expand to a negligibly small pressure, and is then brought to its standard state at 25". The change in internal energy is -AUso1n.(C02)nf(COz diss.). For pure HzO as solvent, the "selected value'' for AHsoln.(COJ is -4640 cal. mole-' z 5 ; the corresponding value of AUso1n,(CO2) is -4050 cal. mole-'. The solubility of COz in H2S04solutions has been studied as a function of temperature by Geffcken"(0-1: N ) and Sunner12(0-1.2 N ) . Values of the heat of solution were computed from these solubility data, reduced to 25" by use of the temperature coefficient given by Harned and Davis,26and converted t o values of the change of internal energy. The equation, AU,oln.(CO2) = -4050 240 N(H2SO4) cal. mole-', was selected to represent the values so obtained. This equation is consistent with the %elected value" for pure H2O as solvent, and fits the values for H2SO4 solutions with an average deviation of 110 cal. mole-'.
+
(87)
AUSOID.'(COZ) = [4050 - 240N(H2SO4)]nf(CO2 diss.)
101
-0.10 cal.
Step 19.-The H N 0 3 and "02 are decomposed according to the reactions: HN03(aq. 0.1 N ) = '/JM" '/zN2(g) 6/40~(g)and HNOZ (as. '/2N2(g) 3/402(g). The 0 2 0.1 N ) = '/2H20(1) and Nz are allowed to expand to a negligibly small pressure. The water used to make the solution in step 17 and that formed in the decomposition reactions is brought to its standard state. The values of AU for the reactions are calculated from the "selected values" of the heats of formation of HN03, HN02 and HZOz8to be 14074 and -e600 cal. mole-'.
+
++
+
f9.68 cal.
Step 20.-The gaseous phase containing 0 2 , NS, COz and HzO vapor is expanded to a negligibly small pressure. The change in internal energy is AU(gas.)]> (gas.)nf(gas.). The calorimetric data of Rossini and F r a n d ~ e nfor ~ ~the change in internal energy for the compression of 02-C02 mixtures, when reduced to 25", may be represented by AU] ,'= - 1.57.4(1 (93) AU'(w.)]
+ 1.69.z(C02)[ I + z( CO,)] IP cal. mole-' -
+3.47 cal.
Step 15.-The dissolved 0 2 and N2 are allowed to escape from the liquid phase and expand to a Step 21.-The 02,Nz, COz and HzO vapor are negligibly small pressure. The change in internal separated from each other, and the C 0 2 is brought energy is -AUsoln.(OZ) nf[(Oz N2)diss.I. For to its standard state. There is no change in interpure H20 as solvent, the "selected valueJJ2' for nal energy in this step. Step 22.-The H 2 0 vapor is compressed to its AHS01,.(O2) is -3800 cal. mole-'; the corresponding value for AUsoln,(O2) is -3200 cal. mole-'. The saturation pressure, Ps,t.(H20), condensed to data of Geffcken'l on the solubility of 0 2 in Hi304 liquid, and further compressed to a find pressure solutions a t 15 and 25" lead to values of AUsoln.(02) of 1 atm. The changes in internal energy are at 20" which may be represented by the equation, ~ ' ( H ~v O~ ~ . ) ( A u ( Hvap.)] ~ o ~ ~ t , ( H z o )AU~o~n.(Oz) = -2770 280 N(HzSO4). The assumption that the difference between 20 and 25" is AUvw.(HzO) A U ( H ~ Ok.)] b B a t . ( I~ n ~ ) independent of the H2S04concentration gives the As in step 1, only the vaporization term is s'lgnififollowing equation for 25": AUso1n.(O2) = -3200 cant. 280 N(H2SO4).
+
+
+
(88)
+
+
AL7~o~,t.f(O~ Nzi = (3200 - 280x( HZSO4) In' [(Oz
+ Nz) diss.+0.76 1 cal.
Step 16.-The liquid phase is decompressed to a final pressure of 1 atm. (89)
AU'(soln.)] >(gas,) = (dU/dP)T'(soIn.)m'(soln.) [l
+
- Pf(gas.)]
$0.80 cal.
Step 17.-l'he HNO, HNOz are removed from the solution and dissolved in the amount of 1120 (in its standard state) required to give a 0.1 N solution. +0.01 cal.
Step 18.-Water (in its standard state) is added to or removed from the solution to bring the concentration of H2S04 to tlic selected w e n concentration. (25) Reference 16, Series 1, Table 23-2.
(26) H. S. Harncd and R. Davis, Jr., J . A m . Chem. Soc.. 66, 2030 (1043).
(27) Rcfcrcnoc 10, Scrics 1 . TaLlc 1-1.
(94)
AU,,,.YH~O) = -9922nf(Hz0 vap.)
-4.84 cal.
In the foregoing series of 22 steps, the calorimeter, the bomb, the Nz, the excess 0 2 and the excess HzO are all returned to their original state. The net change is simply the idealized combustion reaction. The energy of the idealized combustion reaction, for the actual amount of substance involved in the combustion experiment, nAU,"(suh.), is therefore just the sum of the changes in internal energy for all of the steps. (95)
nAU,"(sub.), sum of items 81-94 incl. -7830.13 c d .
The previous item applies to the total substance. Corrections for the auxiliary material and fuse are applied in the next three items to obtain the value for the compound alone. (9G) (87)
(98)
"( auxiliary rnnt.e?id) -588.08 ral. n"'A(J,"(fuse) - 16.09 CRI. n'AUno(compound) = nA u,"(suh.)-n"AUO"( auxiliary material) n"'AU,"~fuse) -7225.96 cal. ?I " A r r ,
(28) Rcforcucc 16, Scrics 1, l'ablcs 18-5, 18-6 and 2a-1.
W. H. SLABAUGH
162
The quantity in item 98 is converted to units of cal. g.-I and kcal. mole-1 in the final two items. (99)
(100)
(compound)
n'AU,"(compound) m' -8430.2 cal. g.-l n'AU,'(compound) 1000n' -827.54 kcal. mole-'
=
AUco(conipound)=
The calibration of bomb calorimeters is usually carried out by the combustion of benzoic acid. The standard samples of benzoic acid issued by the National Bureau of Standards are certified in terms of an energy quantity, AUB. In the notation of this paper, AUB is [AUI.B.P, 4- AUde,.'(HN03 "02) AUdiln.f (HNOa "02) - n"'AUo0(fuse)]. If the conditions of the calibration experiment meet the specifications of the certificate with respect to the O2pressure, the ratio of the mass of sample t o the volume of the bomb, and the ratio of the mass of H20 placed in the bomb to the volume of the bomb, then the certified value of AUB may be used directly to compute Ceff.(calor.). If the conditions differ from those specified in the certificate, it is necessary to compute AU," for the benzoic acid and thenreverse the calculations for the new conditions to obtain CeB.(calor.)from the value of AU,". The extension of the present treatment to make it applicable to compounds of carbon, hydrogen, oxygen and nitrogen will be particularly straightforward. For this class of compounds, Nz is a product of the combustion reaction, and there is more Nz present in the final state than in the initial state. For this situation it will no longer be valid to treat the Nzas though it mere 0 2 . The necessary modification of the present treatment will then be the introduction of the appropriate terms for treating the T\Tz separately from the 02.
+
Comments In the foregoing presentation, the treatment has been given in a very general form. In its application to particular calorimetric experiments, certain simplifications will always be possible. For example, since it is a customary procedure to always charge the bomb to a certain predetermined pressure, Pi(gas.) will be the same for all experiments and can be introduced as a constant in items 28, 32, 34, 82, 83 and 85 of the computation form. It will seldom be necessary to make the complete calculation for all the experiments of a series. If the calculation is made for the two experiments with the most widely differing experimental ronditions, it will be evident which of the energy terms (items 81-94 incl.) change significantly with the experimental conditions and which are essentially the same in all experiments. Then it will only be necessary to calculate for each experiment those energy terms that change significantly from experiment to experiment.
Vol. 58
+
+
-
CATION EXCHANGE PROPERTIES OF BENTONITE'" BY W. H. S L A B A U G H ~ ~ Ueparlinenl of Cheixistru, Kansas State College, Manhuttan, Kansus Received June 16, 1969
Equilibrium c0nstant.s based upon the law of mass action and enthalpy changes during the process of ion exchange of aliphatic amine hydrochlorides with sodium bentonite have been experimentally determined. From these data free energy and edtropy changes have been calculated.
Introduction It has been adequately shown by many workers, including HauserZaand Jordan,2bthat amines react chemically with bentonite to form organo-clay complexes. These complexes are the result of ionexchange processes wherein the attractions between the cationic groups of the amine and the anionic sites on the clay are primarily coulombic. In addition there is a significant amount of van der Waals type adsorption which causes the hydrocarbon chain of the higher amines to become adsorbed onto the surface of the clay lamina. The resultant orientation should manifest itself as a significant entropy change. In this study, a specially prepared sodium ben( I ) (a) Presented a t the 124th National Meeting of the American Chemical Society, Chicago, September, 1953. (b) Department of Chemistry, Oregon State College, Corvallis, Oregon. ( 2 ) (a) E. .4. Hauser in Jerome Alexander, "Colloid Chemistry." Yo]. V I I , Reinhold Publ. Corp., New York, N. Y.,1950, pp. 431-32; U. S. Patents 2,531,427and 2,531,812. (b) John W. Jordan, B. J. Hook and C. R f . Finlayson, THISJOURNAL, 64, 11913 (1950).
tonite was treated with aliphatic, straight chain amines. The enthalpy and the equilibrium constant for these exchanges were measured, and the free energy and entropy changes were calculated from these data. Materials and Experimental Procedure A sample of typical Wyoming bentonite, supplied by the Baroid Sales Division of the National Lead Company, was dispersed in water at 2% solids. After three months of aging at room temperature, the non-clay sediment was separated; the supernatant clay suspension was passed through an Amberlite IR-120 column which had been converted to the sodium form by NaCl treatment,. This bentonite suspension, a t approximately 1% solids, was essentially a sodium bentonite, its original content of exchangeable Ca++and Mgff being reduced to less than 1 meq./100 g . clay. The prepared clay, which was very similar to tjhat prepared by Williams and co-workers,s had a base-exchange capacity of 92 meq./100 g. clay, compared to an original BEC of 82 meq./100 g. clay as determined by the ammonium acetate method. The enthalpy of ion exchange was measured in a microcalorimeter which permitted the addition of the exchanging (3) F. J. Williams, b.1. Nesnayko and D. J. Weintritt, ibid., 57, 6 (1953).
