NBS REFERENCE PUBLICATIONS NBSIR 86-3054 THE THERMODYNAMIC PROPERTIES OF NITROGEN TETROXIDE A111D2 Sb4bbD NAri INST OF STANDARDS & TECH R.I.C. All 102564660 D/The thermodynamic prop OCIOO U56 N0.86-3054 1906 VI 9 C.1 NBS-P Hooert u. McCarty Hans-Ulrich Steurer C.M. Daily National Bureau of Standards U.S. Department of Commerce Boulder, Colorado 80303 July 1986 -QC 100 . U56 86-3054 1986 NBS RESEARCH INFORMATION CENTER NBSIR 86-3054 THE THERMODYNAMIC PROPERTIES OF NITROGEN TETROXIDE Robert D. McCarty Hans-Ulrich Steurer C.M. Daily Thermophysics Division Center for Chemical Engineering National Engineering Laboratory National Bureau of Standards Boulder, Colorado 80303 July 1986 Sponsored by NASA John F. Kennedy Space Center, Florida 32899 (Final Report on NASA Contract CC-26848B) U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director Contents Page 1 . Introduction 1 2. Literature Search 1 3. N 2OH Dissociation 1 i). Vapor Pressure 2 5. Saturation Densities 2 6 . Conversion of P-p-T Data 3 7 . Equation of State for the Pure Components 7 8 . Mathematical Model of the Equation of State 9 9. Derived Thermodynamic Properties 11 10. Discussion 11 1 1 . Conclusions 11 12. Acknowledgments 11 13 . References 12 Appendix A 18 Appendix B 31 Appendix C 78 List of Tables Table 1. Coefficients for eq (3) 2 Table 2. Coefficients for eq ( 6 ) 3 Table 3. Coefficients for eq (Ml) 10 Table 4. Critical Point Constraints 10 Table A1 . Comparison of Experimental and Calculated Densities Used in Fitting eq (41 ) 19 Table A2. Comparison of Calculated Vapor Pressures and Input Data to eq (3) 28 Table A3. Comparison of Input and Calculated Saturated Liquid and Vapor Densities From eq ( 6 ) 29 Table B1 . Isobaric Tables of N2 O 4 Properties Calculated With Equations From This Work (SI Units) 32 Table B2. Isobaric Tables of N 2 O 4 Properties Calculated With Equations From This Work (Engineering Units) 55 Table Cl. Computer Program Listings 79 List of Figures Figure 1 . p-T Plot of Input Data 4 i i i ) Nomenclature a extent of reaction, eq (1) 8 extent of reaction, eq (2) 6 binary interaction coefficient f fugacity p density Y nonlinear coefficient in eq (Ml A arbitrary component, also B, C and D a amount of arbitrary component, also b, < and d P pressure p partial pressure _ R gas constant 0.00831 M3M MPa*dm3-mol 1 »K' 1 T temperature Z volume compressibility factor x mole fraction X reduced variables Superscript o ideal gas at 0.101325 MPa (1 atm) Subscripts o saturation 3 triple point c critical point L liquid R ideal gas v vapor x mixture i,j component iv The Thermodynamic Properties of Nitrogen Tetroxide Robert D. McCarty, Hans-Ulrich Steurer and C. M. Daily Thermophysics Division Center for Chemical Engineering National Bureau of Standards Boulder, Colorado 80303 A mathematical model of the equation of state of nitrogen tetroxide is presented. Isobaric tables of P-p-T and composition for temperatures from the triple point (261.95 K) to 600 K with pressures to 40 MPa are also given. The mathematical model of the equation of state is a 32 term modified Benedict-Webb-Rubin equation. A method of calculating chemical equilibrium for the system is also presented. Key words: chemical equilibrium; composition; density; equation of state; nitrogen tetroxide; pressure; temperature. 1 . Introduction of nitrogen tetroxide, hereafter referred to as N O are of The thermodynamic properties 2 4 , interest in at least two major areas. The fluid is widely used as an oxidizer for small rockets and as an agent in heat transfer problems. A search of the world's literature revealed a substantial experimental data base but few correlations of those data, and the correlations that do exist either cover only portions of the P-p-T surface or involve ideal gas assumptions which, for a wide range of pressures and temperatures, result in substantial inaccuracies. The National Bureau of Standards, under contract with NASA Kennedy Space Center, undertook a study to produce a correlation of the thermodynamic properties of N 2 O 4 based on the existing experimental data. The following is the final report on that study. 2. Literature Search A computerized search of the world's literature produced 172 titles concerned with N 2 O 4 . On the basis of the titles alone, 98 of the 172 appeared to be of possible use in the study. Copies of 62 of the selected references were eventually obtained. Many of these articles are in Russian, in fact 75 of the original 98 selected are of Soviet origin, and copies of some of the articles were difficult or impossible to obtain. A second selection process based on the actual contents of the obtained articles reduced this number even further and references [1-85] include all of the final selection plus those articles which could not be obtained and therefore remain as a possible source of pertinent information. During the course of the second selection process and subsequent correlation, eleven additional articles pertinent to the study were found. The literature search as described above provided an adequate experimental data base for the correlation of N 2 O 4 properties. 3. N 2 O 4 Dissociation The fluid commonly referred to as N O is not pure N O but is in a 2 4 2 4 , reality mixture of N O NO NO, and O . This condition is a 2 4 , 2 , 2 result of the following reactions taking place: n o ;± 2N0 (1) 2 4 2 2N0 ;±r 2N0 + 0 2 2 The extent of these reactions depends on both pressure and temperature and therefor'- ' equilibrium concentration of the various components changes from state point to state point,. The time it takes for equilibrium to occur when the state conditions are changed will n • 1 £ addressed here, and only equilibrium conditions will be considered. Since the concentration of the various components changes with pressure and temperature, a knowledge of the composition at a given state point is necessary to construct an equation of state. The necessity of composition information complicates any correlation attempt via a mathematical model of the equation of state, and this problem will be discussed in the following sections. P-p-T relations of the saturated liquid and vapor are also necessary for the construction of an equation of state. Thus pressure-temperature as well as density- temperature correlations for the saturated liquid and vapor were developed. 4. Vapor Pressure The chemical reactions described in the previous section have no affect on the dependence of vapor pressure on temperature; therefore, methods previously used [ 86 ] on pure fluids were used to produce a mathematical model of N 2 O 4 vapor pressure as a function of temperature. Analysis of the vapor pressure data found in the literature led to the selection of the data reported by Giauque and Kemp [87] and Schlinger and Sage [ 88 ] to fit the function 2 3 4 1-5 = + + + in P N + N x + N x N^x N N x (1 - X ) (3) 1 2 3 ^ 6 where - = (1 - T /T)/(1 T /T ) (4) X tr tr o and T r = 261.95 K (triple point temperature) T c = 431.372 K (critical point temperature) The temperature is in kelvin and the vapor pressure is in megapascal. The coefficients to eq ( 3 ) are given in Table 1. Table 1 . Coefficients for eq (3) - = n = II x 10 Ni 3.98267618 2 5.680987615 CO 4.725629483 _1 -2 N x n = x 10 n x 10 4 = 1.036003737 10 5 4.376388591 6 = 3.674221706 5. Saturation Densities When formulating a mathematical model of the equation of state of a fluid which is to be a single function for both the liquid and vapor phases, the most difficult task is to get a good representation of the saturation boundary. Toward this end, the saturated liquid and vapor densities were correlated independently as a function of temperature; these functions, together with the vapor pressure equation described above, were used to define the saturation boundary to be used later as input data to the final fit of the global equation of state model. The data selected for the saturated density equations were those of Reamer and Sage [89] for the liquid phase and Mittasch et al. [90] for the vapor phase. The equation for both the liquid and the vapor is p + (p ' p (5) P<r c 3 c> 2 0 ) where (L-5) (L-4 4 9 3 - - 6 y = A. S,n x E .1 X E (1 X ( ) L=2 L=5 and . (T - T )/(T - T ) X 0 tr c Temperature is in kelvin, density is in kg/m3, T c and T tr are defined above by the vapor pressure equation and the least squares coefficients are given in Table 2. Table 2. Coefficients for eq (6) Vapor Phase = a -1 x 10 : Ai -2.2660241266 x 10 5 = .2654673246 = x A 2 = 4.3895751856 x 10 A 6 5.7529269561 10 a = -1 .3003886603 a = -1 .3606674467 x 10 3 7 = 1 A a 0.0 A 4 = .9421 498376 x 10 8 9 = Liquid Phase A -5.2151095219 x 10 1 a = 2.1 307429701 x 10 : 1 6 x 10~ 2 a = -9.621 x 10 A 2 8.3309705469 7 9871 908 a -2.5306505949 a = 2.4246461 727 x 10 3 3 x 1 a = -2.4096196971 An 3.9880390339 10 9 2 x 1 a 5 -3.4384688608 = 550.463 kg/m3 0.772 kg/m3 1518 p c tr Ptr o The triple point densities in Table 2 were obtained by extrapolation of the experimental data and the critical point density is from [ 88 ].