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Rejoinder to: “On the thermodynamic consistency test of ternary vapor-liquid equilibrium data”
Chemical Engineering Science, 1969, Vol. 24, p. 1641.
Pergamon Press.
Printed in Great Britain.
Rejoinder to: “On the thermodynamic consistency test of ternary vapor-liquid equilibrium data” (Received 1April 1969) Dear Sirs, Further to the letter by Lu and Chang[l], may it be pointed out that the method proposed[2] for testing thermodynamic consistency of ternary vapor-liquid equilibrium data is intended to be specifically used whenever such data are obtained by the technique which consists in keeping x~/ (xg+xc) = K (a const.), and varying xA. The method of obtaining experimental data using this technique was indicated in my earlier communication [2]. The development of the method results from imposing the restriction xr,/(,+,+xc) = K upon Eq. (6) of Li and Lu[5], and following this by a few mathematical manipulations. It could also be remarked that: (1) Equation (3) of Tao [3] is identical to Eq. (4) of Herington[4]. This can be shown, by neglecting the quantities A and B in Eq. (3), and carrying out the differentiation with respect to xc instead of x1. (2) Equations (4) of Tao[3] is identical to Eq. (6) of Herington[4]. This can be shown by carrying out the integration from 0 to 1I( 1 + x) , where x = x~/x~ (3) Equation (6) of Li and Lu[5] is identical to Eq. (6) of Herington[4]. This can be shown by eliminating dx,, instead of dx,, from Eo. (5) of Li and Lu and by placing the integration limits a and 6 as respectively equal to 0 and 1( 1 + x) . (4) Eauations (3) and (4) of Tao131 are identical to Van Ness[6]Eqs. (11 jand (13j, respectively. (5) Neglecting the quantities A and B in Eq. (3), Eqs. (3) and (4) of Tao[3] become identical to Eqs. (3) and (5) of Li
and Lu [5]. This can be shown by differentiation of Eq. (3) of [5] with respect to X,. In summary: The relations developed by the various authors [3, 5, 61 are all developments following Herington [4] and a statement to this effect was made in my communication [2] instead of listing out all the references. Some of the equations used at the start of the derivations in the different papers are identical. However, on that score, it cannot be stated that the approach employed by one author duplicates that of the other. Each paper has a definite message to convey. Equation (4) of Tao[3] becomes identical to Eq. (10) of my communication[2], by imposing the restriction xs/ (x~ + xc) = K and neglecting the quantities A and B. In my communication[2], it was indicated that the volume of mixing term AVdP/RT was neglected in the development since this introduces only a small error at low pressure conditions. If, however, the equations are to be made exact, that term should be included. It is usual practice to neglect the heat of mixing term for isobaric data and the volume of mixing term for isothermal data at low pressures. The effects of these factors are small and within the probable experimental errors. Department of Chemical Engineering College of Engineering Andhra University, Waltuir, S. India
REFERENCES [l] LU B. C. Y. and SHINN-DER CHANG, Chem. Engng Sci. 1969 24 1405. [21SUBBARAO B. V. Chem. Engng Sci. 1968 23 188. 131 TAO L. C., Ind. Engng Chem. 1964 56 No. 2,36. [41 HERINGTON E. F. G.,J. appl. Chem. 1952 2 14. [5] LI J. C. M. and LU B. C. Y., Can. J. them. Engng 1959 37 117. 161 VAN NESS., Chem. Engng Sci. 1959 10225.
1641
B. V. SUBBARAO
Pergamon Press.
Printed in Great Britain.
Rejoinder to: “On the thermodynamic consistency test of ternary vapor-liquid equilibrium data” (Received 1April 1969) Dear Sirs, Further to the letter by Lu and Chang[l], may it be pointed out that the method proposed[2] for testing thermodynamic consistency of ternary vapor-liquid equilibrium data is intended to be specifically used whenever such data are obtained by the technique which consists in keeping x~/ (xg+xc) = K (a const.), and varying xA. The method of obtaining experimental data using this technique was indicated in my earlier communication [2]. The development of the method results from imposing the restriction xr,/(,+,+xc) = K upon Eq. (6) of Li and Lu[5], and following this by a few mathematical manipulations. It could also be remarked that: (1) Equation (3) of Tao [3] is identical to Eq. (4) of Herington[4]. This can be shown, by neglecting the quantities A and B in Eq. (3), and carrying out the differentiation with respect to xc instead of x1. (2) Equations (4) of Tao[3] is identical to Eq. (6) of Herington[4]. This can be shown by carrying out the integration from 0 to 1I( 1 + x) , where x = x~/x~ (3) Equation (6) of Li and Lu[5] is identical to Eq. (6) of Herington[4]. This can be shown by eliminating dx,, instead of dx,, from Eo. (5) of Li and Lu and by placing the integration limits a and 6 as respectively equal to 0 and 1( 1 + x) . (4) Eauations (3) and (4) of Tao131 are identical to Van Ness[6]Eqs. (11 jand (13j, respectively. (5) Neglecting the quantities A and B in Eq. (3), Eqs. (3) and (4) of Tao[3] become identical to Eqs. (3) and (5) of Li
and Lu [5]. This can be shown by differentiation of Eq. (3) of [5] with respect to X,. In summary: The relations developed by the various authors [3, 5, 61 are all developments following Herington [4] and a statement to this effect was made in my communication [2] instead of listing out all the references. Some of the equations used at the start of the derivations in the different papers are identical. However, on that score, it cannot be stated that the approach employed by one author duplicates that of the other. Each paper has a definite message to convey. Equation (4) of Tao[3] becomes identical to Eq. (10) of my communication[2], by imposing the restriction xs/ (x~ + xc) = K and neglecting the quantities A and B. In my communication[2], it was indicated that the volume of mixing term AVdP/RT was neglected in the development since this introduces only a small error at low pressure conditions. If, however, the equations are to be made exact, that term should be included. It is usual practice to neglect the heat of mixing term for isobaric data and the volume of mixing term for isothermal data at low pressures. The effects of these factors are small and within the probable experimental errors. Department of Chemical Engineering College of Engineering Andhra University, Waltuir, S. India
REFERENCES [l] LU B. C. Y. and SHINN-DER CHANG, Chem. Engng Sci. 1969 24 1405. [21SUBBARAO B. V. Chem. Engng Sci. 1968 23 188. 131 TAO L. C., Ind. Engng Chem. 1964 56 No. 2,36. [41 HERINGTON E. F. G.,J. appl. Chem. 1952 2 14. [5] LI J. C. M. and LU B. C. Y., Can. J. them. Engng 1959 37 117. 161 VAN NESS., Chem. Engng Sci. 1959 10225.
1641
B. V. SUBBARAO