580
J. TAYLOR, C. R. L. HALL, AND H. THOMAS
THE THERMOCHEMISTRY OF PROPELLEKT EXPLOSIVES J. TAYLOR, C. R . L. HALL,
AND
H. THOMAS
Research Department, Imperial Chemical Industries, Limited, Explosives Division, Stevenston, A yrshire, Scotland Received March 87,1946 Revised copy received October 9 , 194s
The normal method of determining the heat of combustion of an organic substance is, of course, to burn it with gaseous oxygen in a suitable calorimetric bomb. In the case of certain explosive substances, such as cordite and propellent powders, for example, in which exothermic reaction can be brought about without supplying any free oxygen, it is the usual practice to explode them in special calorimetric bombs capable of withstanding high pressures, and to measure directly the heat produced by the explo,sion. At the same time the total gas volume and the permanent-gas volume produced by the explosion can be ascertained. The heat produced per gram of explosive is termed “the calorific value.” The final products of decomposition thus derived theoretically will not, in general, coincide with those obtained in practice, but they may be transformed into the practical products by a simple water-gas reaction involving a negligible heat change. The heat evolution or absorption as calculated in the above arbitrary manner will consequently be the same as that in the practical case. QUA’ASTITATIVE TRE.iTYEiiT FOR A1CY CO~IPOUND
Consider the case of any compound C,H,O,S,, which is the type usually dealt with in propellants. Let F be the molecular heat of formation in calories at constant volume and 33°C. The compound may be explosive or non-explosive, but it is assumed that it can be made to react in the calorimetric bomb as a component of an explosive mixture, the final gaseous products being the water-gas constituents and nitrogen, as already described. The heat liberation mill be independent of the mechanism of decomposition of the compound and explosive, and will depend solely on &e final state. Moreover, if the water is considered in the liquid state, as it is in the calorimetric bomb, the heat liberation will be independent of the actual relative concentrations of hydrogen, water, carbon monoxide, and carbon dioxide xithin the limits of accuracy set by the heat liberation in the ivater-gas reaction. On this basis the hypothetical decomposition of the compound C,H,O,K;, may now be discussed. The initial decomposition may he regarded purely hypothet,ically as
C,H,O-Xa
---f
pC
+
H2
+
a
O2
+ 22 V-
-F
The carbon, hydrogen, and oxygen vi11 intercombine with one another or with the molecules of the decomposed explosive or with the water-gas constituents. There are a number of n-ays in which combination may take place, as follows:
THERMOCHEMISTRY OF PROPELLENT EXF’LOSIVES
(3)
c + OZ + coz c + $02-+ co c + coz -+ 2 c o
(4)
C
(1) (2)
581
+ HzO -+ GO + Hz Hz + COz HzO + GO Hz + -+ HzO GO + io2 co*
(5)
-+
(6)
$02
(7)
-+
It is always possible, however, to transform the products of the final results of intercombination into the products of any other intercombination by a simple water-gas reaction, so that according t o the established theorem it is only necessary to consider one mode of decomposition in order to derive a quantitative expression for the molecular calorific value (water liquid) of the compound. Any of the above reactions .ivould serve for the present purposes, but the carbon dioxide and nater reactions may be chosen, namely: pC
+ pOa = pCOz + 94,029~
(20)
and (T
- 2p)H2 + f ( ~- 2p)02
=
(T
- 2p)H20
+
(T -
2~)67,343
(21)
Combining equations 19, 20, and 21, the following equation is obtained: The thermochemical constants of propellants are widely used for ballistic calculations and control of manufacture, and it is of importance to be able to calculate them for any composition and to predict the effect of any change of constituent. The present paper describes a simple method for calculating the calorific values for propellants. This method has been in extensive use for fifteen years in the Research Department of Imperial Chemical Industries Ltd., Explosives Division, and has proved to be both convenient and accurate in use. Whilst the method was primarily developed for use with propellent explosives, it has wider applications to any assembly in which the products are hydrogen, water, carbon dioxide, carbon monoxide, and nitrogen, and provides an alternative method to the normal one for determining approximately the heats of combustion or formation of organic compounds including non-explosive compounds. THCRMOCHEMlCAL COXSIDERATIOSS
Modern propellants largely consist of colloidal mixtures of nitroglycerin and nitrocotton, mith the addition of various organic compounds aq stabilizers and coolers. Such propellants contain insufficient oxygen in their constitution t o oxidizc
582
J. TAYLOR, C. R. L. HALL, AND H. THOMAS
fully the carbon and hydrogen, and it is established that the reactions occurring in their gaseous products are governed primarily by the water-gas reaction : COz
+ Hz = CO + Hz0
A small amount of methane is produced by a secondary action during cooling and this must be corrected for. In addition, certain explosives can deposit carbon during explosion and this must be carefully watched in any experimental work. Thus, the gaseous products can be regarded as consisting almost uniquely of carbon monoxide, carbon dioxide, hydrogen, water, and nitrogen, the relative concentrations of the first four gases being determined by the water-gas equilibrium constant corresponding to the “freezing-out” temperature. In the ensuing thermochemical considerations for such a gaseous assembly the following thermal equations are utilized, the heats of reaction being expressed in calories at 25°C. and constant pressure as given by Rossini (5, 6).
+ 115,600 + 10,520 C + S COz + 94,030 (graphite) 2CO + 02 S 2C02 + 135,280 CH, + 17,889 C + 2H2 2H2
+
0 2 2HzO(g) HtO(g) S HlO(1iq.)
(1)
0 2
$
(graphite)
+
2C 0 (graphite) Hence :
2
2CO
+ 52,780
+ COz S HzO(g) + CO - 9,840 CO + 3Hz S CHI + HzO(g) + 49,299 Hz
(4) (5) Ref: (4) (6)
(7) (8)
Consider now the gaseous products of a propellant fired in a calorimetric bomb. The experimental result obtained will be a calorific value (water liquid) corresponding to certain gaseous products. If the relative concentrations of the gaseous products are imagined as being altered, then the change must $eke place according to the water-gas equilibrium but, as in the case considered the final state of the water is liquid, the equation governing the heat change will be, from equations 7 and 2: Hz
+ COz
HzO(liq.)
+ CO + 680
a t constant pressure. In a calorimetric-bomb system, however, the reaction occurs at constant volume, and for such conditions the water-gas equation becomes: HZ
+ Cot
$ HlO(1iq.)
+ CO + 84
THERMOCHEMISTRY OF PROPELLENT EXPLOSIVES
583
The heat exchange in the water-gas reaction depends on the latent heat of vaporization of the water, and it is obviously possible by choosing a suitable temperature to make the heat liberation zero. Actually, a t 33°C. in constantvolume conditions, there is no heat evolved or absorbed in the water-gas reaction, when the water formed is considered in the liquid phase. It may be concluded, therefore, that the calorific value of a propellant a t constant volume and at 33"C., with the water produced in the liquid state, is quite accurately independent of the composition of the resultant gaseous products. It is obviously advantageous to use 33°C. as a datum temperature for calculations. It is also advantageous to make all the calculations under the constant-volume conditions which apply to the calorimetric bomb. Consequently the thermal data given by Rossini have been suitably corrected to apply to constant-volume conditions at 33OC., the equations now reading as follows: 2Hz
+
0 2
HlO(g)
e 2HzO(g) + 115,036
+ 9,825 + + + +
HzO(1iq.)
+ * + + +
C 0 2 COa 94,029 (graphite) 2CO 02 2C02 134,688 C 2H2 e C& 17,331 (graphite) 2C Oz e 2CO 53,370 (graphite) so that, from these equations:
+ COz HiO(g) + CO - 9,825 + 3Hz e CHI + HnO(g) + 48,164
Hz CO
(9) (10)
(11)
(14)
(15) (16)
THERMOCHEMISTRY OF A MIXTURE OF PROPELLANTS
The deduction which we have just made above may be stated in another form, as follows: The calorific value a t constant volume and 33°C. (water liquid) of a propellent explosive is unaffected by any reaction which may be brought about among the gaseous molecules according to the water-gas reaction. This theorem enables some important deductions about the calorific value of mixtures to be made. If a composite propellant comprising a parts of composition A of calorific value Q A (water liquid), b parts of composition B of calorific value QB, and so on, is made, then the final calorific value of the composite powder is given by ~ Q =
or with obvious notation
Q
+ A
+
~ Q B
CQC
a+b+c+
+
*
*
+ mQ,
... + m
(17)
584
J. TAYLOR, C. R. L. H.4LL, \SDH. THOMAS
The calorific value (water liquid) of a propellant is thus an additive property of the calorific values of its components. Equation 18 introduces a great simplification and enables the Calorific vdue (xater liquidj of many t,ypes of propellants and mixtures to be determined from a few knoir-n values. I t might be thought that only mixtures of esplosives could be treated in this manner, but this is not so, for the treatment can he applied to a misture of a propellent explosive with non-explosive organic substances provided, a? \iill be sho\\-n, suitable negative calorific values are adopted for the non-explosive constituents. Any constituent of the propellant may lie considered as tlecomposing and reacting ivith the gaseous products in any manner ivhatevcr provitled thP final products are hydrogen, Tvater, carbon dioxide, carbon monositlc. rind nitrogen. This decomposition will be characterized by an evolution or nliso~ytionof hcat which maybe calculated, if the heat of formation of thc siilwtnnrc ill qiie>tion is known.
C D H q 0 , X 8+ $ 0 2
+
(T
- 2p)ET&
'rhc gaseous products given in equation 22 may hr ronhkierrrl to untlcrg~ia water-gas reaction without evoliition or a h r p t i o i i of heat. until the actual cnmoosition corresponding to the practical c a w is achicvcd The molecular calorific value (water liquid) of the compound at cwnstarit 1-olumc and 33°C. is therefore given by the expression: yFT =
-40,GTp
+ (iT,343i. - F
(23)
Finally, the calorific constant h for the substancr may lv defined as the heat evolved or absorbed on decomposition in calories per 0.01 p. of rhe siibntance at const,ant volume and 33°C. (water liqiiid) as follo\vs: h
--!!Ep-
100 X gram-molecular weight
It should be noted t,hat the molecular calorific value, qii. may assume positive or negative values according as heat is evolved or atisorbed on decomposition and reaction of the compound. For the purposes of calculating the calorific valuer of propellants then, the calorific constant h as defined b y equation 24 may be used in conjunction with a simple extension of equation 18. It follo~vs directly that t,he calorific value (water liquid) in calories per gram of a propellent esplosivp is given Iiy the expression: Q = Z (hs) (per cent S)
(25)
\\.here h b , the calorific constant of each of the constituents, mag he determined erperimentally or calculated in a simple manner. In the calculations based on the heat+ of formation a': published in the litera-
585
THERMOCHEMISTRY OF PROPELLEXT EXPLOSIVES
ture, it is assumed that the compound is contained in the propellant in its normal physical state. The experimentally determined values of the calorific value are obtained at a mean temperature of 17°C. Two methods are available for relating the theoretically calculated value of qH to the experimentally observed va!ue. Firstly, the experimentally observed value of y H at 17°C. may be corrected to apply to 33°C. This calculation requires a knowledge of the specific heat of the compound and of the gaseous products. Alternatively, the molecular calorific value, q H , may be calculated at 17OC. Thus, proceeding as in equations 19, 20, 21, and 22, with the corresponding heats of reaction at 17"C.,then the following equation is obtained:
C,H,O,N,
-+
pC01
+ ( r - 2p)Hz0 H2
+
+
Ss - 4 0 , 9 8 7 ~ 67,509~- F (26)
The gaseous products given in equation 2G may be transformed into the actual gaseous products by the water-gas reaction. At 17°C. and constant volume, with the water considered as liquid, the water-gas reaction becomes: Hz
+ CO, = HzO(1iq.) + CO + 169
(27)
For one particular compound there are two extreme cases which must be considered; firstly, one in which the products consist of water and carbon monoxide, and secondly, one in which the products consist of hydrogen and carbon dioxide. It follows therefore that the maximum scatter in the calorific value of a propellant at 17OC. due to the water-gas reaction is (p
+ 2*)169 cal.
The mean of
;(
these two molecular calorific values is therefore correct to within f-p
3
+-
169.
For the generalized case of the compound C,H,O,N. this mean molecular calorific value is given by
q~
=
- 40,5152,
+ 85 + 67,440~- F
(28)
and for any particular experimental observation a t 17°C.
By means of this equation the experimental value of the calorific value is related to the theoretical value, so that the heat of formation of the compound may be calculated. The calorific effect of any substance added to a propellant may be readily calculated by means of equation 25. Thus consider a propellent powder h of calorific value (constant volume, water liquid) Q1and let Q2be the corresponding
586
J. TAYLOR, C. R. L. HALL, I N D H. THOMAS
calorific value of an intimate mixture of (100 - p ) per rent of A and p per cent of a substance B. Then from equation 25: Q2 =
Q1
+ ph
If the heat of formation of the substance is knon n, then by mcanb of equations 28 and 24 the value of h may be calculated. Conversely, the heat of formation of the substance may be calculated from the experimentally determined h value. It is to be observed however, that the heat of formation of the substance as generally reported in the literature refers to the ordinary state, and this may not correspond exactly to the value of the heat of formation for the substance when incorporated in the propellent powder, since its physical condition may be different. In the calorimetry of propellent ponders, it is preferable therefore to use values for h which have been experimentally determined from finished propellent powders. The values actually observed for various substances will no\\ be considered. The calorific values of the propellent powders I\ ere experimentally determined in a specially designed calorimetric bomb. The calorimetric bomb and its accessories together with the experimental technique employed are described elsewhere (8). Nitroglycerin I t is of fundamental importance in the piesent work that the calorific effect of nitroglycerin contained in propellent powders should be carefully determined. The calorific values of a large number of propellants consisting of nitroglycerin, nitrocellulose, and ethyl centralite or mineral jelly were therefore determined experimentally in the calorimetric bomb. It mould appear from a careful analysis of the results so obtained that the calorific effect of nitroglycerin varies slightly with the physical condition of the nitroglycerin in the propellant, and that it is highest and of almost uniform value in well-gelatinized powders. In actual practice propellants are almost all of the type characterized by the stable high nitroglycerin calorific constant. The effect, however, is important, since a value for the calorific constant h for nitroglycerin must be selected for use in the thermochemical calculations. From consideration of the experimental results the figure of 17.55 cal. for 0.01 g. (at 17'C.) has been selected for the calorific constant of nitroglycerin as describing its behavior in normal propellants and in matured propellants whether of the solvent or the non-solvent type. It has been established (8) that nitroglycerin alone decomposes as follows in the calorimetric bomb: CaHSN309 = 3C02
+ 2+H20 +1$
Sz
+
a 0 2
THERllOCHEMISTRY OF PROPELLEST EXPLOGI VES
587
and the heat evolved at constant volume is 366.6 kg.-cal. per mole (mater liquid). Further, the liberated oxygen will be available to oxidize carbon monoxide to carbon dioxide or hydrogen to water as follows:
+ 302 = COz + 67,340 HZ+ ioz = HzO(liq.) + (37,509 CO
Thus the mean quantity of heat, liberated by the available oxygen is 33.712 cal. It follows therefore that the theoretical calorific effect of nitroglycerin in propellants is 400.3 kg.-cal. per mole, or 17.63 cal. per 0.01 g. (at 17OC.). The agreement between the theoretical and experimental values for the calorific constant, of nitroglycerin is very satisfactory. Sitlocellulose The experimentally determined calorific values and gas volumes have been reported in a recent communication (8). I t is reasonable t o suppose a formula of C6HloObor CeH,02(0H)3for cellulose, and nitrocellulose may then be considered as being formed by replacing the OH groups by S O 3 groups. The general formula for a nitrocellulose is then CBHi02(3 - z)OH
+ Zso3
where 5 lies between the extreme values of 0 and 3. Let p be the per cent by weight of nitrogen in the nitrocellulose considered; then it may be shown that the gram-atoms of carbon, hydrogen, oxygen, and nit'rogen per kilogram of nitrocellulose are :
c = 37.024 - 1 . 1 8 9 1 ~
-
H = 61.698 - 2.69597 5, = 30.849 4-0.43675~
3
= 0.714291,
and consequently the gas volume per gram of nitrocellulose of p per cent nitrogen is : T* = 1520.3 - 48.8371, The p per cent nitrogen is, of course, the true nitrogen content of the nitrocellulose and if the analytical nitrogen figures observed are systematically different from these, then there will be a systematic error in the calculations of the gas volume. The results show excellent agreement between the gas volumes as measured directly and as calculated from this equation. For the nitrocelluloses of higher nitrogen content (13.16 per cent and 13.24 per cent) the measured gas volumes are greater than those calculated from the nitrometer nitrogen figure. This slight discrepancy may be due t o nitrometer nitrogen determination or to a slight inaccuracy in the methane determinations.
588
J. TAYLOR, C. R .
12.
HALL, AND H.THOMAS
The relation Ixtween the finally corrected calorific value and the nitrogen content of the nitrocelluloseis linear, and this fact may be used as a very stringent test of the theory. Since the relation between the calorific value and the nitrogen content is linear, the intercept of the graph on the axis of ordinates (calorific values) must represent the calorific effect of n nitrocellulose of zero nitrogen content, i e., cellulose. The heat of combustion of cellulose at constant pressure and 18°C. is 4181 cal. per gram (3). From this value, and by equations 23 and 24, the calculated calorific constant per gram of cellulose is 834.8 cal. at 18OC In order to ohtain the linear relation betlleen the calorific value and the nitrogen content, one more point must be considered. It is convenient to consider the extreme point : namely, the nitrocellulose containing 13.24 per cent nitrogen and of calorific value of 1060 cal. per gram. The linear relation is then given by: Q18oc
= 1 4 3 . 5 ~- 834.8
(33)
Tihere Q1pc is the calorific value (constant volume, nater liquid) of pure dry gelatinized nitrocellulose of p per cent nitrogen. The very satisfactory fit of the experimental values shom that there is little doubt of the substantial accuracy of the theory. If M is the gram-molecular might of the nitrocellulose, then from equation 26 :
9. = M
P -40,515 -
M
r F + 42.5 4 + G7,440 -M M M
(34)
BH/M is the calorific value (water liquid) of 1 gram of the substance at constant volume, usually denoted by &, while p / M and q / M are the number of gramatoms of carbon and hydrogen in 1 gram of the substance. F / M is the heat of formation per gram at a constant pressure of 1 atm. and 18'C. If the general formula for nitrocellulose is taken to be CsH,O2(3 - z)(OH) r N 0 8 ,as before, then the values of p / M etc. can be expressed in terms of P , the percentage of nitrogen in the nitrocellulose, by the following equations:
+
- 0.0011891P
2
= 0.037024
4 M
= 0.061698 - 0.0026959P
M
- -- 0.030849 fll
+ 0.00043675P
On substituting these values of p/.M etc. in cquation 34 n e obtain:
&,
= 583
F + 77.GP - M
(35)
Thus, knowing the calorific value of the nitrocellulose and the percentage of nitrogen which it contains, equation 35 may be used to calculate the heat of
THERMOCHEMISTRY O F PROPELLENT EXPLOSIVES
589
formation per gram of the nitrocellulose at constant pressure. I t is considered that this is a superior method to determining the heat of formation from the heat of combustion of the nitrocellulose in excess of oxygen, since the heat of combustion is about four times the heat of formation, while the calorific value is generally less than twice the heat of formation. The method has also the advantage of eliminating the uncertainty caused by the formation of oxides of nitrogen when the burning takes place in excess of oxygen. It has been shown that the experimentally determined calorific values of the dry gelatinized nitrocelluloses may be expressed by a linear equation (33). On eliminating &, between equations 33 and 35, the following expression is obtained for the heat of formation of dry gelatinized nitrocellulose
F = M
1417.8
- 65”
cal. per gram
(36)
at a constant pressure of 1 atm. and 17°C. The heats of formation a t constant pressure of the various nitrocelluloses examined as calculated from this equation are set out in table 1 . TABLE 1 Heats of formation of nitrocellulose PEPCENIAGE BY WElGEI OF NITROGEN I N TEE PITTROCELLULOSE
pcr
i
HEAT OF FORMATION OF NITROCELLULOSE AT CONSTANT PRESSURE ALMI 18’c.
ccrlt
CL%l./P.
12.10 12.65 13.16 13.24
621.6 585.4 551 .B 546.6
Graphite By calculation from equations 24 and 29 the h value for pure graphite is -33.76 i- 0.07 cal. The graphite used in propellants is of a good commercial quality, and may contain up to 10 per cent mineral matter. The experimental value of h for graphite should therefore he numerically less than -33.76 but greater than -30.38 cal. .4n intimate mixture of 95 per cent of a propellant (which consisted of 50 per cent of nitroglycerin and 50 per cent of guncotton) and 5 per cent graphite was prepared, and its calorific value determined in the calorimetric bomb. The calorific value of the propellant itself was also determined experimentally, and yielded the result 1385.5 cal. per gram (constant volume, water liquid). The calorific value of the mixture was 1148, so that, using equation 32: 1148 = 0.95 X 1385.5
+ 5h
whence h = -33.64 cal. The agreement between the theoretical and experimental values is therefore satisfactory.
590
J. TAYLOR, C. R . L. HALL, AWD H. THOM.4S
Diiiitrotoluene
-Anintimate mixture of 95 per cent of the propellent, poivder of the last example and 5 per cent of dinitrotoluene was prepared, and its calorific value determined in the calorimetric bomb. The resulting experimental value for the constant h was 1.30 cal. By means of equation 14 the heat of formation of dinitrotoluene at constant pressure is determined as 8.8 kg.-cal. per mole; consequently the heat of combustion of dinitrotoluene to carbon dioxide, water (liq.), and nitrogen at constant pressure and 20°C. is 853.8 kg.-cal. per mole. Garner and Abernethy (2) report a direct experimental value of 852.8 kg.-cal. per mole for this heat of combustion. A direct experimental value of 856.5 kg.-eal. per mole has also been reported (7). The agreement between the values is reasonably satisfactory. In our calculations a specific heat of 0.3 cal. per gram per "C. has been assumed for dinitrotoluene ; only negligible errors are introduced by this assumption. Dibutyl phthalate The calorific constant, h, of this compound was found by calorimetric invcstigation of a propellant containing 2 per cent of dibutyl phthalate. A value of -20.2 cal. was thus determined. Consequently, the calculated heat of formation a t constant pressure and 17OC. of dibutyl phthalate is 1820 kg.-cal. per mole, and the heat of combustion to carbon dioxide, ivater (liq.), and nitrogen is 2070 kg.-cal. per mole. The corresponding heats of combustion reported in the literature are 2058 kg.-cal. per mole (1) and 2160 kg.-cal. per mole (7). It may be considered therefore that the value obtained in the present u-ork is fairly close to the true heat of combustion of dibutyl phthalatr. Methyl centralite The effect of methyl centralite on the calorific value of propellent powders was investigated in the usual manner, and the value of -23.8 cal. found for the calorific constant, h. A direct determination of the heat of combustion of methyl centralite \\-as carried out in our own laboratories and resu1t)ecl in the value of 1948.5 kg.-cal. per mole. The heat of combustion calculated from the calorific constant, h, is 1930 kg.-cal. per mole at 17'C. and constant pressure. The results are therefore in reasonable agreement. Ethyl centralite
h similar investigation on ethyl centralite resulted in a value of -24.4 cal. for the calorific constant, h. This corresponds to a heat of combustion of 2253 kg.-cal. per mole a t 17OC. and constant pressure. The corresponding value of the heat of combustion of ethyl centralite derived by direct experiment was 2264.6 kg.-cal. per mole. The experimental values of the calorific constant, h, for some of the compounds used in propellent explosives are set out in table 2. Thus, consider a propellent explosive of '(dry" composition: nitrocellulose
59 1
THERMOCHEMISTRY O F PROPELLEKT EXPLOSIVES
(13.08 per cent nitrogen), 65 per cent; nitroglycerin, 30 per cent; mineral jelly, 5 per cent. The volatile matter is 0.37 per cent and the “ash” 0.16 per cent. $ssume (as is justified by experience) that the volatiles are half water and half acetone; then the reduced composition is: nitrocellulose, 64.66 per cent; nitroglycerin, 29.84 per cent; mineral jelly, 4.97 per cent; moisture, 0.19 per cent; acetone, 0.18 per cent; ash, 0.16 per cent, and by direct application of the present theory and the given experimental h values the calorific value of this composition is given by:
a,
=
=
+
10.45 X 64.66 17.60 X 29.84 - 34.60 X 4.97 1027.5 cal. per gram
-
19.80 X 0.18
The experimentally observed calorific value of this composition corrected for methane formation is 1027 cal./g. at 17”C., in agreement with the calculated values. TABLE 2 Values of h for some compounds used in propellent ezplosives lhINCAIIOPIESPEP0.01 G.ATl7‘C.
SUBSTAXCE
Nitrocellulose (13.1 per cent nitrogen). . . . . . . . . . . . . . . . . . . . . . . . . Sitroglycerin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I Mineral jelly... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................., ~
~
$10.48 +17.60
-34.60 -19.80
C.4LCULATIOK O F THE GAS VOLUME GIVEN BY A POWDER
Since the gaseous products of propellent powders, when corrected for the small quantities of methane formed, contain only carbon dioxide, carbon monoxide, water (vapor), hydrogen, and nitrogen, no alteration in the volume of the gases can take place due to interaction of the constituent gases, since any such change must he finally in the nature of a water-gas reaction,-namely,
CO2
+
H2
= GO
+ HzO
and this reaction involves no increase or diminution of volume. It is evident, therefore, that the total gas volume in molecules per gram of the propellent powder as derived experimentally (corrected for any methane formation) does correspond exactly with the number of molecules. It follows that the total gas volume, cc. per gram of powder at N.T.P. (corrected for any methane Eormed) is given by the expression T’,
c,
=
22.4(c
+ +n+ iz]
(37)
here H, 3 are the gram-atoms of carbon, hydrogen, and nitrogen contained in 1 kg. of the powder. Furthermore, the gas volume is an additive property of the gram-atoms of carbon, hydrogen, and nitrogen contained in the constituents of the poi\ der,
592
J . TAYLOH, C. R . L. HALL, AND H. THObiAS
and as a consequenceequation 37 may be expressed more simply in terms of the percentages of nitroglycerin, nitrocotton, etc. in the composition, as follows: Ti, = Z(Vs)(per cent S)/100 where Vs is the gas volume constant characteristic of the substance S. The calculation of the constant V Sfor mos’t compounds is direct and simple. The constant V S has been designated the “gas volume constant” of the compound, and deiines the gas volume in cubic centimeters given by 0.01 g. of the compound when contained as a constituent of a propellent explosive. SUMMhRY
A method has been developed for calcblating the calorific values and gas volumes of modern propellent explosives. It has been established that, when such propellants are fired in a calorimetric bomb, the explosion products consist almost uniquely of carbon dioxide, carbon monoxide, hydrogen, water (liquid), and nitrogen. The final equilibrium is therefore determined by the well-known water-gas reaction, and the present thermochemical considerations are applicable to any such gaseous assembly. It has been shown t’hatxith the water considered in the liquid phase, and under constant-volume conditions, then the heat exchange in the water-gas reaction is very small, and in fact, at 33OC. is zero. This fact forms the basis of the present work, and by its application a calorific constant may be defined for the organic compounds used in propellants. Further, the calorific value of a mixture of such compounds may be expressed by a simple additive law of these calorific constants and the composition. The method has proved both convenient and accurate in use, while it may also be employed as an alternative method for determining approximately the heats of combustion and formation of organic compounds. The theoretical and quantitative development of the theory is given. .4pplications of the method to the determinations of the heats of formation and combustion of organic compounds are discussed, ivhile a t,ypical example of its application to normal propellants is also given and detailed consideration has been given to nitrocellulose REFERESCES (1) (2) (3) (4)
(5) (6) (7) (8)
AMBLER, H. R . : J. SOC.Cheni. Ind. 66, 291 (1936). W. E . , AND ABERNETRY, C. I,.: Proc. Roy. S O C . (London) 99, 213 (1921). GARNER, International Critical Tables. PROSES,E. J.: J . Research Natl. Bur. Standards 34,263 (1945). ROSSINI,F. D.: J. Research Natl. Bur. Standards, 22, 407 (1939). ROSSINI,F. D . : J . Research Natl. Bur. Standards, 34, 113 (1915). SCHMIDT, A , : Sprengstoffe 29, 2.59 (1934). TAYLOR, J . , AND HALL,C. R. L.: J . Phys. Colloid Chem. 61, 593 (1947).
