Table Ill.
Analysis of UFs Product
Impurttzes, ~ P.P.M. _ _ Samplr 3 Sample 7 Sample 2
5 ..
<
after vapor-liquid equilibrium had bern reached i n a bomb bet\veen thc gah phase and a solution for ivhich the rota1 ammonia. total carbon dioxide. and the amount of ammonium nitrate are krio\\-ri by analysis or synthesis. ~1.0utilize such e x p ~ l ~ i m e n t data. al it must be assumed that the equilibrium constants a t infinite dilution are kno\vn. arid that thc activity coefficients for the variour chemical species can be evaluated. After the detrrinination of cxperiinerital data b)- carr,ful equilibria .tudic, and anal).zec to obtain numerical data. Equation> i to 11 elutes are ammonia and carbon dioxide. -4solvent definition of 1 kg. of total solution probably \\-odd yield correlations \vhich could be extended more readily into yet higher solute concentrations but \vould make the necessary manipulations of computation much more cumbersome. Exclusion of arnmoniuni nitrate from the solvent definition and use of n a t e r only as the solvent, as is usual in connection \Yith aqueous systems. \vould greatly distort the usual meaning of the activity coefficients, because ammonium nitrate contributes significantly to mass: energy, and solvent properties of the sy-stern. \Vhile from a thennodynamic point of view activities of individual ionic species have no real physical significance, but only certain products and ratios of these individual ionic activities. i t is convenient to define “hypothetical” ionic activities. Equations 17 to 20 must be considered on this basis, a very convenient one. From Kielland’s data ( 6 ) , the hydrated ions concerned have a diameter of about 3.5 h. Therefore, activity coefficients of the monovalent ions calculated by Equations 18 to 20 are almost equal. Lsing the Bronsted Equation 20 for the hypothetical activity coefficient of the ammonium and bicarbonate ion, Equation 6 may be xvritten
Lvhich is not in
- ~ ]
BB
agreement \vith experiment. Huckel has therefore extended the theory, assuming that the dielectric constant of the solvent medium varies linearly with the ion concentration. The Huckel equation thus becomes :
log
nr,> in electrolyte solutions should be dirrct1)- proportional to the ionic strength. as indicatrd by the equation theoretically derived by Debye and hlc.4ulay ( 5 ) . At more concentrated w1ution.s. the equation
0
I
2
3
s
4
b
b
7
Ionic Strength I in grammoles/Kg( N
9
10
I1
H ~ N +o) ~ ~ +
Figure 3. Deviation of bicarbonate equilibrium constant, K1, from limiting DebyeHuckel law Untogged points from system C O ~ - N H J - H ~ O - N H ~ N O ~ Tagged points from system C02-NHa-HzO Points at 60’ and 40’ C. with N H i N O i from Levi and Vasilenko (7).All others from this investigation Temperature dependence of Brghsted coefficient, C’, in Equation 21 from slope of lines
40
t, OC.
0.30
C’
90 0.36
60
0.34
not exact. A more empirical approach is necessary, and \‘an Krevelen (74) suggested a n equation with two empirical terms : IS
log Y \ H B
+ 621
= 61 m x ~ 3
(24)
From a revieiv of the literature data and experimental meaaurernents ( 3 ) on the system ammonia-water-ammonium nitrate, the following values of these empirical constants were determined for a concentration range u p to 10 moles per kg. (HzO N H 4 N 0 3 ) in free ammonia concentration and ionic strength:
+
bl =
-0.00001t f 0.018 (10’ to 120’ C.)
0.035 (independent of temperature within accuracy of data)
62 =
(25)
150
120
0.39
0.41
These coefficients relate to a system without carbon dioxide, because it is impossible to obtain the Henry coefficient for free ammonia in a system where the ammonia can ionize to a large extent. Therefore, the assumption has to be applied that the ionic strength contribution of the ionized carbon dioxide is about the same as that of the other salts contributing to the total ionic strength. Data Evaluation Procedure
LZ’ith Equations 5, 13 to 16, and 21 to 25, the vapor pressures of ammonia and carbon dioxide over aqueous ammonium nitrate solutions can be calculated. if the empirical Brdnsted coefficient, C’, can be determined from experimental data. From the measurements of partial pressure of the aqueous VOL.
3
NO. 3
JULY
1964
275
system carbon dioxide-ammonia-Lvater and carbon dioxideammonia-water-ammonium nitrate, C' was evaluated in the following manner:
1. An ionic strength is assumed according to: 1
=
+ 21c0:121 +
C(1
mSH~s0:j
(26)
Since msliiso,i and C are knoivn quantities. this becomes equivalent to assuming the fraction of the total carbon dioxide which is in the form of carbonate. 'I'his assumption has to be checked later. 2. 'l'here is also assumed mSilj. Then log ysEIi is calculated from Equationr 24 and 25. L-sing the experimentally determined ammonia partial pressure. v/h-lri is recalculated by Equations 5 and 13. 3. A trial and error calculation is continued until the assumed and calculated values for m s H i are in close agreement. Becau5e of the stoichiometric relation.
