Assuming that at equilibrium all aqueous HN03 is fully ionized and all organic HN03 is in the form of HN03 "TBP, the distribution coefficient of nitric acid is

о = [HNOsjTBPCg)] (4.19)

H [H+(*?)3

and combining with Eq. (4.16),

DH = KH [N03′(«?)] [TBP(o)] (4.20)

For a uranium-nitric acid system, the concentration of uncombined TBP in terms of concentrations of uranium and acid in the organic phase is

[TBP(o)] = C — [HN03 — TBP(o)] — 2 [U02 (N03 )2-2TBP(o)] (4.21)

where C is the concentration of total TBP, both combined and uncombined, in the organic phase. The distribution coefficient of uranium in terms of total TBP concentration and aqueous concentrations is obtained by combining Eqs. (4.16), (4.18), and (4.21):

Dy________ = Ац [МОГИ)]2

(С — 2DV [U(V+(<zq)] Г (1 + AH [H>?)] [N03 ‘(aq)] f ‘ ‘

and solving for Dy,

Only the negative sign of the square root is used in Eq. (4.23); the positive value of the root yields a trivial solution that implies negative concentrations of uncombined TBP in the organic phase.

The extraction of nitric acid with TBP from aqueous solutions free of other extractable species has been studied by several investigators [G7, М2], and the equilibrium data lead to an average value of 0.145 for the acid equilibrium constant, assuming activity coefficients of unity. The correlation of nitric acid on the basis of Eq. (4.16) is poor when the acid concentration in the aqueous phase is greater than about 7 Af, possibly because of the formation of the dinitrato and trinitrato complexes 2HN03*TBP and 3HN03*TBP or possibly because of solution of nitric acid in the organic without complexing [S4].

The uranium distribution data in Table 4.3 can be correlated reasonably well by using the following equilibrium constants in Eq. (4.23) and assuming activity coefficients of unity:

KH = 0.145

Au = 5.5

The concentration C of total TBP is obtained from the volume percent (v/o) TBP in the organic phase by

where 0.972 is the density of pure TBP [G4, Ml, S4] and 266.3 is the molecular weight of TBP, which has the chemical formula (C4H9)3P04. Equation (4.25) neglects the small volume change resulting from water solubility in the organic phase and from extraction of the uranium and acid complexes, and it neglects the solubility of TBP in the aqueous phase [S4]. At 40 percent TBP by volume, the total TBP molar concentration Cis 1.464 mol/liter.

Uranium distribution coefficients calculated from Eq. (4.23) and from the above data are listed in Table 4.3.

The close agreement between observed and calculated distribution coefficients in Table 4.3 is surprising in view of the wide range of aqueous concentration and the assumption of unity for the activity coefficients. Distribution coefficients for an even greater range of parameters in the TBP extraction system are given in Chap. 10.

A number of attempts have been made to establish correlations of distribution coefficients in the U0j(N03)2-HN03-TBP system on a more fundamental thermodynamic basis. One approach [Bl, H2, R4] has been to correlate on the basis of ionic strength in the aqueous
phase, with assumed constant activity coefficients in the organic phase. A more advanced approach by Goldberg et al. [G2a] involved the correlation of distribution data based on the ratio of the activity of the U02(N03)2 ‘2TBP complex to the activity of free TBP in the organic phase, using activity coefficients derived from experimental data for the partial pressure of HN03 over aqueous solutions of HNO3 and иОзСЮз^. With this approach the data of Codding et al, [C3] for the distribution coefficients of UC^CNCb^ in TBP extraction were correlated over a wide range of concentrations, with an average deviation of 5.8 percent.