Open access peer-reviewed chapter

Study of the Equilibrium of Nitric Acid with a Solution of TBP/IP6

By Munoz Ayala Israel and Vera Roberto Carlos

Submitted: September 6th 2020Reviewed: March 3rd 2021Published: March 29th 2021

DOI: 10.5772/intechopen.96992

Downloaded: 63


The behavior of the tri-n-butylphosphate (TBP) for a Liquid–liquid extraction (LLE) system is well known. To establish a new LLE system, the calculation of the equilibrium to establish an extraction system of TBP and inositol hexaphosphate (IP6) needs to be done. First, the change in the activity coefficient of TBP/IP6 related to the activity of water and TBP/IP6 concentration in the H2O–TBP/IP6–dodecane system, then the degradation of nitric acid in the system should be evaluated to assess the equilibrium. The proposed system consists of a solution of 30% of TBP and 10% of IP6 in nitric acid and dodecane. As main results, we discussed the value of the dissociation degree of nitric acid, the molar and volumetric fractions, the molar activity of the organic and aqueous phases and activities coefficients.


  • equilibrium
  • TBP
  • IP6
  • extraction system

1. Introduction

Liquid–liquid extraction ion-exchange (LLE-IE), also known as solvent extraction and partitioning, is a method to separate compounds or metal complexes, based on their relative solubilities in two different immiscible liquids, usually water (polar) and an organic solvent (non-polar) [1]. There is a net transfer of one or more species from one liquid into another liquid phase, generally from aqueous to organic. The transfer is driven by chemical potential, i.e., once the transfer is complete, the overall system of chemical components that make up the solutes and the solvents are in a more stable configuration (lower free energy). The solvent that is enriched in solute(s) is called extract. The feed solution that is depleted in solute(s) is called the raffinate. This type of process is commonly performed after a chemical reaction as part of the work-up, often including an acidic work-up [2].

From a hydrometallurgical perspective, solvent extraction is exclusively used in separation and purification of uranium and plutonium, zirconium and hafnium, separation of cobalt and nickel separation, and purification of rare earth elements etc., its greatest advantage being its ability to selectively separate out even very similar metals. One obtains high-purity single metal streams on ‘stripping’ out the metal value from the ‘loaded’ organic wherein one can precipitate or deposit the metal value.

One of the well-known applications of a LLE in hydrometallurgical techniques is the PUREX (plutonium uranium redox extraction) which is a chemical method used to purify fuel for nuclear reactors or nuclear weapons. PUREX is the de facto standard aqueous nuclear reprocessing method for the recovery of uranium and plutonium from used nuclear fuel (spent nuclear fuel or irradiated nuclear fuel). It is based on liquid–liquid extraction ion-exchange [3].

It is not the intention of this research work to stablish a new PUREX methodology but to study the equilibrium of a LLE-IE based on TBP and IP6. The behavior of TBP and nitric acid (HNO3) in the solvent extraction process has been studied, which has detected good stability, through laboratory tests, pilot tests and plant work.

IP6 is a unique natural substance found in plant seeds. It has received considerable attention due to its effects on mineral absorption. Impairs the absorption of iron, zinc and calcium and may promote mineral deficiencies. IP6 is a six-fold dihydrogenphosphate ester of inositol (specifically, of the myo isomer), also called inositol hexakisphosphate or inositol polyphosphate (IP6). At physiological pH, the phosphates are partially ionized, resulting in the phytate anion [4].

IP6 has had a high value for the nuclear industry, as it has studied as a complement to the recovery of uranium in seawater [3] and as a bio-recovery option in mine water [5].

As has been said before, in this research just the equilibrium of the TBP/IP6 in nitric acid with n-dodecane is going to be study.


2. Results and discussions

2.1 Propose system

The purpose of this work is to study an LLE-IE system to establish a new PUREX variant. Variants refer to change in some of the original conditions which in this case is adding a new molecule to the system. Original PUREX consist in TBP with HNO3 in a hydrocarbon. The proposed system consists in TBP with IP6 in solution con dodecane (Figure 1).

Figure 1.

Inositol polyphosphate (IP6) molecule.

The IP6 presents 6 phosphates, it is water soluble and lightly soluble in ethanol and has a boiling point of 150 °C. The respective constants for calculations have been obtained from the literature [6].

The full chemical reaction with the purpose LLE-IE system is as present in Figure 2. It can be observed the interaction between the characteristic’s actinides of a spent nuclear fuel and the TBP-IP6. In this reaction, the radiolitic effects are not considered.

Figure 2.

Full extraction reaction presented for the purpose PUREX system.

2.2 Effects of water on the activity of TBP/IP6 in the H2O-dodecane system

The study system comprises 30% of TBP and 10% of IP6 (TBP/IP6) in solution with water and n-dodecane.

Considering that the distribution of water in the H2O–TBP/IP6–dodecane system be described using the Equation [7] (1)


Where xi, ai and φi are the molar fraction, activity, and volume fraction of the i component in solution respectively; indices 1, 2 and 3 refer to water, TBP/IP6 and dodecane respectively; in this work, by recommendation, we used n = 2.10; and the volume fractions of TBP/IP6 and dodecane were calculated neglecting water by:


Table 1 present the value of x1calculated by Eq. (1). The following constants were used: K1 = 0.0795, K2 = 0.0029 and b1 = 1.783 (used for dodecane too); V2 = 273.8 cm3 [1], v3 = 228.6 cm3 [1], n = 2.10 and k2 = 0.1.


Table 1.

Calculate mole fractions of water in TBP/IP6 solution with dodecane.

From Eq. (1) we can derive an equation for the molar coefficient of the activity of water.


The result of the Eq. (4) is a molar coefficient of aw f1 = 22.432452and lnf1 = 3.11050866. To derive an equation for the molal coefficient of the activity of TBP, we used the cross-equation.


Where the derivatives with respect to the molar concentration m2y m1were calculated for constant m1and m2respectively. Differentiating (5), we obtain


The value m2can be calculated from the mole fractions of TBP/IP6 and dodecane,


Where x20and x30are the mole fraction of TBP/IP6 and diluent in anhydrous solution; x30 = 1-x20; and M3 is the molecular mass of the solvent (170.33 g/mol). Then from (2), we obtain


From (9) we determinate the derivative δφ2/ δm2for (7),


Now, substituting the Eq. (10) in (7),


The right side of the Eq. (11) does not contain any value dependent on m1. Then, integrating the Eq. (6), we obtain


Where f20is the TBP-IP6 activity coefficient in a binary (considering tri-n-butylphosphate and inositol hexaphosphate as one) anhydrous solution, which can be set at 1 in the first approximation. Table 2 presents the results of the calculation by (12).


Table 2.

Molalities of water m1 and TBP/IP6 activity coefficient f2 for a solution in n-dodecane.

The deviations from the ideal values are moderate and increase with the activity of water and TBP/IP6 concentration.

2.3 Dissociation of nitric acid

Nitric acid is integral to the reprocessing of irradiated fuel and other LLE, the understandings its behavior is important. Nitric acid undergoes thermal and radiolytic degradation, the products of which include nitrous acid (HNO2) and nitrogen oxide species (NOX).

Eq. 13 shows the generic dissociation reaction of nitric acid.


The equation for calculating the degree of dissociation is as follows:


Where K is the equilibrium constant, AB is the reagent, A+ and B- ions (cation and anion respectively), C acid concentration and α dissociation degree. For alpha calculation purposes, we have an equilibrium constant of K = 2.598.

We will consider the dissociation of nitric acid using the polynomial Eq. (15), which has been adjusted from the data reported by [8]. In Eq. 15, the concentration of nitric acid [C] is in mol/dm3 and α the dissociation degree where α = 1 shows a complete dissociated acid and α = 1 a completely associated acid


The following calculation describes the concentration of associated and dissociated nitric acid.


Where [HNO3total] is the sum of dissociated and associated nitric acid, [NO3] and [HNO3] are respectively the associated and dissociated acid concentration.


It can be observed that after the 23 M the value increases again: due to the point of saturation of nitric acid and coexistence with non-associated species.

In nitric acid solutions, nitrogen oxide species, including HNO2, NO2 and NO, have been observed. The presence of these species in the absence of other reactants or radiation is attributed to the thermal decomposition of nitric acid. Non-dissociated nitric acid is thermally decomposed to produce NO2• as shown in Eq. 18; notice that this reaction is non-elementary. This thermal decomposition of nitric acid in aqueous solution has been widely reported in the literature for different concentrations, high acidity and at high temperatures (Table 3).


Table 3.

Calculation of values for the dissociation degree of nitric acid with to molarity in the solution.

2.4 Calculations of the equilibrium

The calculation method used in this research work is as follow:

  1. The nitric acid and water activities are calculated from the data of [8].

  2. The calculation of equilibrium implies the formation of the non-hydrated HNO3·TBP/IP6 monosolvate and the hydrated HNO3·2TBP/IP6 disolvate and 2HNO3·TBP/IP6 semisolvate of nitric acid, and the equilibrium between them obeys the mass action law.


where aa and a2are the nitric acid and TBP/IP6 activities, xijand fijare the molar fraction and rational activity coefficient of a solvate consisting of i acid molecules and j complex molecules (TBP/IP6). The parameter fijis calculated within the nonstoichiometric hydration concept by the equation


where hijis the hydrate number of a solvate, and a1is the water activity.

  1. The molar fraction of free water (nonbonded with solvates) is calculated by the equation


Eq. (21) is very similar to Eq. (1). As in (1), xi, ai, and ϕiare the molar fraction, activity, and volumetric fraction of the ith component in a solution. The volumetric TBP/IP6 and n-dodecane fractions are calculated without allowance for water as (2) and (3).

4. Organic phase nonideality is considered using the activity solvate coefficients calculated as


5. The molar fraction xiis determined as


where the sum Σcjis calculated for the first time as


ca, c2, and cdare the molar acid, TBP/IP6, and dodecane concentrations, respectively, and


where cT is the total complex (TBP/IP6) concentration in a solution, i.e., the formation of the monosolvate alone was initially assumed.

6. To calculate the molar fraction of free complex x2f, we write the equation


7. The value of x2fcalculated by the Eq. (26) is used to determine the molar fractions xij. The molar concentrations cijare then estimated by the equations


where dis the density of a solution, and xiand Miare the molar fraction and mass of the ith component.

The values of cjare used to correct the molar fractions in compliance with Eqs. (23) and (24).

The calculated acid molar concentration cacis further found as (28) and the calculated complex molar concentration ctcis estimated as (29)


Table 4 presents all the principal input parameters. The values presented in the table are the one who has been used to solve the equilibrium equations.

% TBP30.00%%
% Dodecane60.00%%
% IP610.00%%
Molarity HNO3 [M]9mol/L
Water activity [aw]0.6
Molecular weight HNO363.01g/mol
Molecular weight Dodecane170.34g/mol
Molecular weight TBP266.29g/mol
Molecular weight IP6660.04g/mol
ρ HNO31.5129g/cm3
ρ Dodecane [d0]0.73526g/cm3
ρ TBP0.973g/cm3
ρ IP61.3g/cm3
Acid concentration [ca]9mol/dm3

Table 4.

Principal input parameters and its values.

The concentration of the acid allowed to know the activity of water in the system, which have a value of 0.6 which represents a large amount of water to form the aqueous phase, since a water activity value equal to 1 would represent that we have the total disposition of water to hydrate.

Table 5 presents the results of the calculation in the equilibrium.

d complex TBP/IP61.06984
HNO3 Dissociation degree [α]0.5615298
Volumetric fraction of complex [ϕ2]0.4
Volumetric fraction of dodecane [ϕ3]0.6
Molar fraction of water [x1]0.0257969
Molar activity coefficient water [f1]0.9583666
Solvate molar activity coefficient [fs] Organic phase0.4245719
Complex molar activity coefficient [f2]0.96700749

Table 5.

Principal results for the equilibrium calculation with 30% TBP/10% IP6 in.


3. Conclusions

As first step in the overall objective of the study of the equilibrium in the LLE-IE, the kinetic data and constants values has been investigated to produce an initial dynamic model of the interaction of the TBP/IP6 in aqueous conditions. The effects of water in the activity of the TBP/IP6 has been evaluated. As it can be seen, the deviations from the ideal values of the molar coefficient of the system TBP/IP6 f2are moderate and increase with the activity of water and TBP/IP6 concentration. The density of the complex makes precipitation possible and enough availability of dissociated acid makes this complex suitable for redox reactions.

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Munoz Ayala Israel and Vera Roberto Carlos (March 29th 2021). Study of the Equilibrium of Nitric Acid with a Solution of TBP/IP6, Material Flow Analysis, Sanjeev Kumar, IntechOpen, DOI: 10.5772/intechopen.96992. Available from:

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