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

*Munoz Ayala Israel and Vera Roberto Carlos*

## **Abstract**

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.

**Keywords:** 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

#### *Material Flow Analysis*

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].

a spent nuclear fuel and the TBP-IP6. In this reaction, the radiolitic effects are not

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

Considering that the distribution of water in the H2O–TBP/IP6–dodecane

*<sup>φ</sup>*<sup>2</sup> <sup>¼</sup> *<sup>x</sup>*2*V*<sup>2</sup>

*<sup>x</sup>*<sup>1</sup> <sup>¼</sup> *<sup>K</sup>*1*φ*2*a*<sup>1</sup> exp *<sup>b</sup>*1*φ<sup>n</sup>*

The study system comprises 30% of TBP and 10% of IP6 (TBP/IP6) in solution

Where *xi*, ai and φ<sup>i</sup> 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:

*x*2*V*<sup>2</sup> þ *x*3*V*<sup>3</sup>

**Table 1** present the value of *x1* calculated by Eq. (1). The following constants

were used: *K1* = 0.0795, *K2* = 0.0029 and *b1* = 1.783 (used for dodecane too);

*a1 x1* 1 0.044578274 0.9 0.040120447 0.8 0.035662619 0.7 0.031204792 0.6 0.026746965 0.5 0.022289137 0.4 0.01783131 0.3 0.013373482 0.2 0.008915655 0.1 0.004457827

*V2* = 273.8 cm<sup>3</sup> [1], *v3* = 228.6 cm3 [1], *n* = 2.10 and *k2* = 0.1.

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

2

<sup>þ</sup> *<sup>K</sup>*2*φ*3*a*<sup>1</sup> (1)

*φ*<sup>3</sup> ¼ 1 � *φ*<sup>2</sup> (3)

(2)

considered.

**Figure 2.**

**Table 1.**

**91**

with water and n-dodecane.

system be described using the Equation [7] (1)

*Full extraction reaction presented for the purpose PUREX system.*

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

*DOI: http://dx.doi.org/10.5772/intechopen.96992*

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**).

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

**Figure 1.** *Inositol polyphosphate (IP6) molecule.*

*Study of the Equilibrium of Nitric Acid with a Solution of TBP/IP6 DOI: http://dx.doi.org/10.5772/intechopen.96992*

$$
\begin{bmatrix}
\mathsf{U}\mathsf{\dot{O}}\_{2} \\
\mathsf{N}\mathsf{\dot{O}}\_{4} \\
\mathsf{P}\mathsf{\dot{O}}\_{4}
\end{bmatrix} + \mathsf{I}\mathsf{P}\mathsf{\dot{O}} + \mathsf{T}\mathsf{B}\mathsf{P}\begin{bmatrix}
\mathsf{0} \\
\mathsf{0} \\
\mathsf{0}^{4}
\end{bmatrix} \mathsf{N}\mathsf{\dot{O}}\_{2} \begin{bmatrix}
\mathsf{0}\mathsf{O}\_{2} \\
\mathsf{N}\mathsf{\dot{O}}\_{2}
\end{bmatrix} \begin{bmatrix}
\mathsf{0}\mathsf{O}\_{3} \\
\mathsf{N}\mathsf{\dot{O}}\_{3}
\end{bmatrix} \mathsf{I} \\
\mathsf{N}\mathsf{\dot{O}}\_{4} \begin{bmatrix}
\mathsf{0}\mathsf{O}\_{3} \\
\mathsf{N}\mathsf{\dot{O}}\_{4}
\end{bmatrix} \mathsf{I} \\
\mathsf{N}\mathsf{\dot{O}}\_{4}
\end{bmatrix} \mathsf{I} \begin{bmatrix}
\mathsf{0}\mathsf{O}\_{2} \\
\mathsf{N}\mathsf{\dot{O}}\_{4}
\end{bmatrix} \mathsf{I} \\
\mathsf{N}\mathsf{\dot{O}}\_{4} \begin{bmatrix}
\mathsf{0}\mathsf{O}\_{2} \\
\mathsf{N}\mathsf{\dot{O}}\_{2}
\end{bmatrix} \mathsf{I} = \begin{bmatrix}
\mathsf{0}\mathsf{O}\_{2} \\
\mathsf{N}\mathsf{\dot{O}}\_{2}
\end{bmatrix} \mathsf{I}
$$

**Figure 2.** *Full extraction reaction presented for the purpose PUREX system.*

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 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

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

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

As has been said before, in this research just the equilibrium of the TBP/IP6 in

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

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

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

It is based on liquid–liquid extraction ion-exchange [3].

phosphates are partially ionized, resulting in the phytate anion [4].

nitric acid with n-dodecane is going to be study.

work.

*Material Flow Analysis*

mine water [5].

**2. Results and discussions**

**2.1 Propose system**

con dodecane (**Figure 1**).

**Figure 1.**

**90**

*Inositol polyphosphate (IP6) molecule.*

been obtained from the literature [6].

a spent nuclear fuel and the TBP-IP6. In this reaction, the radiolitic effects are not considered.

#### **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)

$$\mathcal{K}\_1 = K\_1 \rho\_2 a\_1 \exp\left(b\_1 \rho\_2^n\right) + K\_2 \rho\_3 a\_1 \tag{1}$$

Where *xi*, ai and φ<sup>i</sup> 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:

$$
\rho\_2 = \frac{\varkappa\_2 V\_2}{\varkappa\_2 V\_2 + \varkappa\_3 V\_3} \tag{2}
$$

$$
\rho\_3 = 1 - \rho\_2 \tag{3}
$$

**Table 1** present the value of *x1* calculated 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 cm<sup>3</sup> [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.

$$f\_1 = \frac{1}{\left[K\_1 \wp\_2 \exp\left(b\_1 \wp\_2^n\right) + K\_2 \wp\_3\right]}\tag{4}$$

*lnf* <sup>2</sup> ¼ *f* <sup>20</sup>

by (12).

**Table 2.**

**93**

� *m*<sup>1</sup>

8 ><

>:

*V*2*V*3*x* <sup>103</sup> *M*<sup>3</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.96992*

9 >=

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

*K*<sup>1</sup> exp *b*1*φ<sup>n</sup>*

Where *f20* is the TBP-IP6 activity coefficient in a binary (considering tri-nbutylphosphate 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

The deviations from the ideal values are moderate and increase with the activity

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

½ � *AB* <sup>¼</sup> ½ � *<sup>C</sup><sup>α</sup>* ½ � *<sup>C</sup><sup>α</sup>*

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

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

**a1 m1 Lnf2 f2** 1 0.2438 0.05711146 0.94448879 0.9 0.2190 0.05115063 0.95013554 0.8 0.1945 0.04529659 0.95571399 0.7 0.1697 0.03940556 0.96136074 0.6 0.1449 0.03354904 0.96700749 0.5 0.1201 0.02772661 0.97265424 0.4 0.0963 0.02217066 0.9780733 0.3 0.0721 0.01655281 0.98358344 0.2 0.0474 0.01085124 0.98920742 0.1 0.0227 0.005182 0.9948314

2

� � <sup>þ</sup> *<sup>K</sup>*1*φ*<sup>2</sup> exp *<sup>b</sup>*1*φ<sup>n</sup>*

*K*1*φ*<sup>2</sup> exp *b*1*φ<sup>n</sup>*

*HNO*<sup>3</sup> \$ *H*<sup>þ</sup> þ *NO*<sup>3</sup> (13)

*<sup>C</sup>*ð Þ <sup>1</sup> � *<sup>α</sup>* (14)

2 � �*x nb*1*φn*�<sup>1</sup>

2 � � <sup>þ</sup> *<sup>K</sup>*2*φ*<sup>3</sup>

( )

<sup>2</sup> � *K*<sup>2</sup>

(12)

>;

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

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

*<sup>K</sup>* <sup>¼</sup> *<sup>A</sup>*<sup>þ</sup> ½ � *<sup>B</sup>*� ½ �

calculation purposes, we have an equilibrium constant of K = 2.598.

complete dissociated acid and *α* = 1 a completely associated acid

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

*<sup>m</sup>*2*V*<sup>2</sup> <sup>þ</sup> *<sup>V</sup>*3*x*<sup>103</sup> *M*<sup>3</sup> h i<sup>2</sup>

of water and TBP/IP6 concentration.

**2.3 Dissociation of nitric acid**

oxide species (NOX).

$$\ln \mathfrak{f}\_1 = -\ln \left[ K\_1 \wp\_2 \exp \left( b\_1 \wp\_2^n \right) + K\_2 \wp\_3 \right] \tag{5}$$

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

$$
\begin{bmatrix}
\frac{\partial \ln \mathcal{f}\_1}{\partial \ln \mathcal{f}\_2}
\end{bmatrix}\_{m1} = \begin{bmatrix}
\frac{\partial \ln \mathcal{f}\_2}{\partial \ln \mathcal{f}\_1}
\end{bmatrix}\_{m2} \tag{6}
$$

Where the derivatives with respect to the molar concentration *m2* y *m1* were calculated for constant *m1* and *m2* respectively. Differentiating (5), we obtain

$$\left[\frac{\delta \ln f\_1}{\delta m\_2}\right] m1 = -\left\{\frac{\left[K\_1 \exp\left(b\_1 \rho\_2^n\right) + K\_1 \rho\_2 \exp\left(b\_1 \rho\_2^n\right) n b\_1 \rho\_2^{n-1} - K\_2\right]}{\left[K\_1 \rho\_2 \exp\left(b\_1 \rho\_2^n\right) + K\_2 \rho\_3\right]}\right\} \left[\frac{\delta \rho\_2}{\delta m\_2}\right] \tag{7}$$

The value *m2* can be calculated from the mole fractions of TBP/IP6 and dodecane,

$$m\_2 = \left(\frac{\varkappa\_2}{\varkappa\_3}\right) \left(\frac{10^3}{M\_3}\right) = \left(\frac{\varkappa\_{20}}{\varkappa\_{30}}\right) \left(\frac{10^3}{M\_3}\right) \tag{8}$$

Where *x20* and *x30* are 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

$$\rho\_2 = \frac{V\_2}{\left[\frac{V\_2 + V\_3}{\frac{V\_2}{\ddots\_{\%}}}\right]} = \frac{m\_2 V\_2}{\left[m\_2 V\_2 + \frac{V\_3 x \ge 10^\circ}{M\_3}\right]}\tag{9}$$

From (9) we determinate the derivative *δφ2/ δm2* for (7),

$$\frac{\delta\rho\_2}{\delta m\_2} = \frac{V\_2 V\_3 \propto \frac{10^3}{M\_3}}{\left[m\_2 V\_2 + \frac{V\_3 x \mathbf{1} \mathbf{0}^3}{M\_3}\right]^2} \tag{10}$$

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

$$\frac{\partial \rho\_2}{\partial m\_2} = \left\{ \frac{V\_2 V\_3 \mathbf{x}^{\frac{10^3}{M\_3}}}{\left[ m\_2 V\_2 + \frac{V\_3 \mathbf{x} \mathbf{10}^3}{M\_3} \right]^2} \right\} \times \left\{ \frac{K\_1 \exp\left(b\_1 \rho\_2^n\right) + K\_1 \rho\_2 \exp\left(b\_1 \rho\_2^n\right) \mathbf{x} \ n b\_1 \rho\_2^{n-1} - K\_2}{K\_1 \rho\_2 \exp\left(b\_1 \rho\_2^n\right) + K\_2 \rho\_3} \right\} \tag{11}$$

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

*Study of the Equilibrium of Nitric Acid with a Solution of TBP/IP6 DOI: http://dx.doi.org/10.5772/intechopen.96992*

$$\begin{aligned} \ln \mathfrak{f}\_{2} &= f\_{20} \\ &- m\_{1} \left\{ \frac{V\_{2} V\_{3} \mathfrak{x} \frac{10^{3}}{M\_{3}}}{\left[ m\_{2} V\_{2} + \frac{V\_{3} \mathfrak{x} 10^{3}}{M\_{3}} \right]^{2}} \right\} \left\{ \frac{K\_{1} \exp \left( b\_{1} \mathfrak{p}\_{2}^{\mathfrak{n}} \right) + K\_{1} \mathfrak{p}\_{2} \exp \left( b\_{1} \mathfrak{p}\_{2}^{\mathfrak{n}} \right) \ge n b\_{1} \mathfrak{p}\_{2}^{\mathfrak{n}-1} - K\_{2}}{K\_{1} \mathfrak{p}\_{2} \exp \left( b\_{1} \mathfrak{p}\_{2}^{\mathfrak{n}} \right) + K\_{2} \mathfrak{p}\_{3}} \right\} \end{aligned} \tag{12}$$

Where *f20* is the TBP-IP6 activity coefficient in a binary (considering tri-nbutylphosphate 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).

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**

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

2 � � <sup>þ</sup> *<sup>K</sup>*2*φ*<sup>3</sup>

<sup>¼</sup> *<sup>∂</sup>lnf* <sup>2</sup> *<sup>∂</sup>lnf* <sup>1</sup> � �

2 � � <sup>þ</sup> *<sup>K</sup>*2*φ*<sup>3</sup>

*m*2

2 � �*nb*1*φ<sup>n</sup>*�<sup>1</sup>

> *M*<sup>3</sup> � �

<sup>2</sup> � *K*<sup>2</sup>

h i (9)

h i<sup>2</sup> (10)

2 � � <sup>þ</sup> *<sup>K</sup>*2*φ*<sup>3</sup>

( )

2 � �*x nb*1*φ<sup>n</sup>*�<sup>1</sup>

<sup>2</sup> � *K*<sup>2</sup>

(11)

*δφ*<sup>2</sup> *δm*<sup>2</sup> � �

� � (4)

� � (5)

(6)

(7)

(8)

*<sup>f</sup>* <sup>1</sup> <sup>¼</sup> <sup>1</sup>

*lnf* <sup>1</sup> ¼ � ln *<sup>K</sup>*1*φ*<sup>2</sup> exp *<sup>b</sup>*1*φ<sup>n</sup>*

*<sup>∂</sup>lnf* <sup>1</sup> *<sup>∂</sup>lnf* <sup>2</sup> � �

2

*<sup>m</sup>*<sup>2</sup> <sup>¼</sup> *<sup>x</sup>*<sup>2</sup> *x*3 � � 10<sup>3</sup>

*<sup>φ</sup>*<sup>2</sup> <sup>¼</sup> *<sup>V</sup>*<sup>2</sup>

From (9) we determinate the derivative *δφ2/ δm2* for (7),

*∂φ*<sup>2</sup> *δm*<sup>2</sup>

9 >=

>; *x*

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

*M*<sup>3</sup>

*<sup>m</sup>*2*V*<sup>2</sup> <sup>þ</sup> *<sup>V</sup>*3*x*10<sup>3</sup> *M*<sup>3</sup> h i<sup>2</sup>

integrating the Eq. (6), we obtain

<sup>¼</sup> *<sup>V</sup>*2*V*3*<sup>x</sup>* <sup>10</sup><sup>3</sup>

8 ><

>:

*<sup>V</sup>*2þ*V*<sup>3</sup> *<sup>x</sup>*<sup>20</sup> *x*30

The result of the Eq. (4) is a molar coefficient of *aw f1 = 22.432452* and *lnf1 = 3.11050866*. To derive an equation for the molal coefficient of the activity of

*m*1

Where the derivatives with respect to the molar concentration *m2* y *m1* were calculated for constant *m1* and *m2* respectively. Differentiating (5), we obtain

� �

2 � � <sup>þ</sup> *<sup>K</sup>*2*φ*<sup>3</sup> � � ( )

> <sup>¼</sup> *<sup>x</sup>*<sup>20</sup> *x*<sup>30</sup> � � 10<sup>3</sup>

*<sup>m</sup>*2*V*<sup>2</sup> <sup>þ</sup> *<sup>V</sup>*3*x*10<sup>3</sup> *M*<sup>3</sup>

*M*<sup>3</sup>

� � <sup>þ</sup> *<sup>K</sup>*1*φ*<sup>2</sup> exp *<sup>b</sup>*1*φ<sup>n</sup>*

*K*1*φ*<sup>2</sup> exp *b*1*φ<sup>n</sup>*

� � <sup>þ</sup> *<sup>K</sup>*1*φ*<sup>2</sup> exp *<sup>b</sup>*1*φ<sup>n</sup>*

*K*1*φ*<sup>2</sup> exp *b*1*φ<sup>n</sup>*

The value *m2* can be calculated from the mole fractions of TBP/IP6 and

*M*<sup>3</sup> � �

Where *x20* and *x30* are 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).

� � <sup>¼</sup> *<sup>m</sup>*2*V*<sup>2</sup>

<sup>¼</sup> *<sup>V</sup>*2*V*3*<sup>x</sup>* <sup>103</sup>

*K*<sup>1</sup> exp *b*1*φ<sup>n</sup>*

*<sup>m</sup>*2*V*<sup>2</sup> <sup>þ</sup> *<sup>V</sup>*3*x*<sup>103</sup> *M*<sup>3</sup>

2

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

*K*1*φ*<sup>2</sup> exp *b*1*φ<sup>n</sup>*

of water.

*Material Flow Analysis*

*δln f* <sup>1</sup> *δm*<sup>2</sup> � �

dodecane,

*∂φ*<sup>2</sup> *δm*<sup>2</sup>

**92**

Then from (2), we obtain

TBP, we used the cross-equation.

*<sup>m</sup>*<sup>1</sup> ¼ � *<sup>K</sup>*<sup>1</sup> exp *<sup>b</sup>*1*φ<sup>n</sup>*

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.

$$\text{HNO}\_3 \leftrightarrow H^+ + \text{NO}\_3 \tag{13}$$

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

$$K = \frac{[\mathcal{A}^+][B^-]}{[AB]} = \frac{[\mathcal{C}a][\mathcal{C}a]}{\mathcal{C}(1-a)}\tag{14}$$

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


**Table 2.** *Molalities of water m1 and TBP/IP6 activity coefficient f2 for a solution in n-dodecane.*

$$a = -2.64 \text{x} \text{10}^{-6} [\text{C}]^4 + 2.633 \text{x} \text{10}^{-4} [\text{C}]^3 - 5.8558 \text{x} \text{10}^{-3} [\text{C}]^2 - 1.54199 \text{x} \text{10}^{-2} [\text{C}] + 1 \tag{15}$$

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

$$\left[\mathrm{NO}\_{3}^{-}\right] = a \cdot \left[\mathrm{HNO}\_{3\ \mathrm{total}}\right] \tag{16}$$

Eq. (21) is very similar to Eq. (1). As in (1), *xi*, *ai*, and *ϕ<sup>i</sup>* are 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).

 0.97898485 0.97898485 0.02101515 0.94780094 1.89560188 0.10439812 0.90793309 2.72379927 0.27620073 0.86080276 3.44321104 0.55678896 0.80776805 4.03884025 0.96115975 0.80776805 4.03884025 0.96115975 0.7501237 4.5007422 1.4992578 0.68910109 4.82370763 2.17629237 0.62586824 5.00694592 2.99305408 0.56152981 5.05376829 3.94623171 0.4971271 4.971271 5.028729 0.43363805 4.77001855 6.22998145 0.37197724 4.46372688 7.53627312 0.31299589 4.06894657 8.93105343 0.25748186 3.60474604 10.39525396 0.20615965 3.09239475 11.90760525 0.1596904 2.5550464 13.4449536 0.11867189 2.01742213 14.98257787 0.08363854 1.50549372 16.49450628 0.05506141 1.04616679 17.95383321 0.0333482 0.666964 19.333036 0.01884325 0.39570825 20.60429175 0.01182754 0.26020588 21.73979412 0.01251869 0.28792987 22.71207013 0.02107096 0.50570304 23.49429696 0.03757525 0.93938125 24.06061875 0.0620591 1.6135366 24.3864634 0.09448669 2.55114063 24.44885937 0.13475884 3.77324752 24.22675248 0.18271301 5.29867729 23.70132271 0.2381233 7.143699 22.856301

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

calculated as

**Table 3.**

**95**

**Molarity α NO3**

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

*DOI: http://dx.doi.org/10.5772/intechopen.96992*

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

*fs* <sup>¼</sup> exp �*b*<sup>2</sup> <sup>1</sup> � *<sup>φ</sup>*<sup>2</sup> ð Þ2*:*<sup>1</sup> h i (22)

� **HNO3**

$$\left[H\text{NO}\_3\right] = \left[H\text{NO}\_3\text{ total}\right] - \left[\text{NO}\_3^-\right] \tag{17}$$

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

$$4HNO\_3 \leftrightarrow 4NO\_2^\* + 2H\_2O + O\_2 \tag{18}$$

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. Nondissociated 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**).

#### **2.4 Calculations of the equilibrium**

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


$$\mathbf{x}\_{\vec{\eta}} = \frac{\mathbf{K}\_{\vec{\eta}} a\_a^i a\_2^j}{f\_{\vec{\eta}}} \tag{19}$$

where aa and *a2* are the nitric acid and TBP/IP6 activities, *xij* and *fij* are the molar fraction and rational activity coefficient of a solvate consisting of i acid molecules and j complex molecules (TBP/IP6). The parameter *fij* is calculated within the nonstoichiometric hydration concept by the equation

$$f\_{\vec{\eta}} = \exp\left[h\_{\vec{\eta}}(\mathbf{1} - a\_1)\right] \tag{20}$$

where *hij* is the hydrate number of a solvate, and *a1* is the water activity.

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

$$\infty\_1 = K\_1 \rho\_1 a\_1 \exp\left(b\_1 \rho\_1^n\right) + k\_2 \left[K\_1 \rho\_2 a\_1 \exp\left(b\_1 \rho\_2^n\right)\right]^2 + K\_2 \rho\_3 a\_1 \tag{21}$$

*Study of the Equilibrium of Nitric Acid with a Solution of TBP/IP6 DOI: http://dx.doi.org/10.5772/intechopen.96992*

*<sup>α</sup>* ¼ �2*:*64*x*10�6½ � *<sup>C</sup>* <sup>4</sup> <sup>þ</sup> <sup>2</sup>*:*6331*x*10�4½ � *<sup>C</sup>* <sup>3</sup> � <sup>5</sup>*:*8558*x*10�<sup>3</sup>

*NO*� 3

<sup>4</sup>*HNO*<sup>3</sup> \$ <sup>4</sup>*NO*<sup>∙</sup>

of saturation of nitric acid and coexistence with non-associated species.

or radiation is attributed to the thermal decomposition of nitric acid. Non-

concentrations, high acidity and at high temperatures (**Table 3**).

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

*xij* <sup>¼</sup> *Kija<sup>i</sup>*

where aa and *a2* are the nitric acid and TBP/IP6 activities, *xij* and *fij* are the molar fraction and rational activity coefficient of a solvate consisting of i acid molecules and j complex molecules (TBP/IP6). The parameter *fij* is calculated within the

*fij* ¼ exp *hij*ð Þ 1 � *a*<sup>1</sup>

3.The molar fraction of free water (nonbonded with solvates) is calculated by

<sup>þ</sup> *<sup>k</sup>*<sup>2</sup> *<sup>K</sup>*1*φ*2*a*<sup>1</sup> exp *<sup>b</sup>*1*φ<sup>n</sup>*

where *hij* is the hydrate number of a solvate, and *a1* is the water activity.

*aa j* 2 *fij*

**2.4 Calculations of the equilibrium**

obeys the mass action law.

the equation

**94**

*<sup>x</sup>*<sup>1</sup> <sup>¼</sup> *<sup>K</sup>*1*φ*1*a*<sup>1</sup> exp *<sup>b</sup>*1*φ<sup>n</sup>*

nonstoichiometric hydration concept by the equation

1

ated nitric acid.

*Material Flow Analysis*

The following calculation describes the concentration of associated and dissoci-

½ �¼ *HNO*<sup>3</sup> *HNO*<sup>3</sup> *total* ½ �� *NO*�

Where [HNO3total] is the sum of dissociated and associated nitric acid, [NO3

It can be observed that after the 23 M the value increases again: due to the point

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

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

and [HNO3] are respectively the associated and dissociated acid concentration.

½ � *<sup>C</sup>* <sup>2</sup> � <sup>1</sup>*:*54199*x*10�<sup>2</sup>

(17)

<sup>2</sup> þ 2*H*2*O* þ *O*<sup>2</sup> (18)

(20)

2

<sup>2</sup> <sup>þ</sup> *<sup>K</sup>*2*φ*3*a*<sup>1</sup> (21)

<sup>¼</sup> *<sup>α</sup>* � *HNO*<sup>3</sup> *total* ½ � (16)

3

½ �þ *C* 1 (15)

�]

(19)

Eq. (21) is very similar to Eq. (1). As in (1), *xi*, *ai*, and *ϕ<sup>i</sup>* are 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


$$f\_s = \exp\left[-b\_2(1-\rho\_2)^{2.1}\right] \tag{22}$$

**Table 3.**

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

5. The molar fraction *xi* is determined as

$$\mathbf{x}\_{i} = \frac{c\_{i}(\mathbf{1} - \mathbf{x}\_{1})}{\sum c\_{j}} \tag{23}$$

where the sum Σ*cj* is calculated for the first time as

$$\sum \mathbf{c}\_{j} = \mathbf{c}\_{a} + \mathbf{c}\_{2} + \mathbf{c}\_{3} \tag{24}$$

*ca*, *c2*, and *cd* are the molar acid, TBP/IP6, and dodecane concentrations, respectively, and

$$\mathcal{c}\_2 = \mathcal{c}\_T \mathcal{c}\_a \tag{25}$$

where *d* is the density of a solution, and *xi* and *Mi* are the molar fraction and

The values of *cj* are used to correct the molar fractions in compliance with

**Parameter Value** d complex TBP/IP6 1.06984 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 phase 0.4245719 Complex molar activity coefficient [*f2*] 0.96700749

The calculated acid molar concentration *cac* is further found as (28) and the

**Table 4** presents all the principal input parameters. The values presented in the

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 *f2* are moderate and increase with the activity of water and TBP/IP6 concentration. The density of the complex makes precipitation possible and enough availability of

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

*cac* ¼ *c*<sup>11</sup> þ *c*<sup>12</sup> þ 2*c*<sup>21</sup> (28) *ctc* ¼ *c*2*<sup>f</sup>* þ *c*<sup>11</sup> þ 2*c*<sup>12</sup> þ *c*<sup>21</sup> (29)

calculated complex molar concentration *ctc* is estimated as (29)

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

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

*DOI: http://dx.doi.org/10.5772/intechopen.96992*

have the total disposition of water to hydrate.

table are the one who has been used to solve the equilibrium equations.

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

dissociated acid makes this complex suitable for redox reactions.

mass of the ith component.

Eqs. (23) and (24).

**Table 5.**

**3. Conclusions**

**97**

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

$$\begin{aligned} &\mathbf{x}\_1 + \mathbf{x}\_{2'} + \mathbf{x}\_3 \\ &+ \left\{ K\_{11} a\_d \mathbf{x}\_{2'} f\_2 + K\_{21} a\_d^2 \mathbf{x}\_{2'} f\_2 \exp\left[ h\_{21} (a\_1 - \mathbf{1}) \right] + K\_{12} a\_d \mathbf{x}\_{2'}^2 f\_2^2 \exp\left[ h\_{12} (a\_1 - \mathbf{1}) \right] \right\} \\ &+ \exp\left[ -b\_2 (1 - \rho\_2)^{21} \right] = \mathbf{1} \end{aligned} \tag{26}$$

7. The value of *x2f* calculated by the Eq. (26) is used to determine the molar fractions *xij*. The molar concentrations *cij* are then estimated by the equations


$$\omega\_{j} = \frac{\varkappa\_{j}d \ast 1000}{\Sigma \varkappa\_{i} \mathcal{M}\_{i}} \tag{27}$$

**Table 4.**

*Principal input parameters and its values.*

*Study of the Equilibrium of Nitric Acid with a Solution of TBP/IP6 DOI: http://dx.doi.org/10.5772/intechopen.96992*


#### **Table 5.**

5. The molar fraction *xi* is determined as

tively, and

*Material Flow Analysis*

**Table 4.**

**96**

*Principal input parameters and its values.*

*x*<sup>1</sup> þ *x*2*<sup>f</sup>* þ *x*<sup>3</sup>

<sup>þ</sup> *<sup>K</sup>*11*aax*2*<sup>f</sup> <sup>f</sup>* <sup>2</sup> <sup>þ</sup> *<sup>K</sup>*21*a*<sup>2</sup>

<sup>∗</sup> *exp* �*b*<sup>2</sup> <sup>1</sup> � *<sup>φ</sup>*<sup>2</sup> ð Þ<sup>2</sup>*:*<sup>1</sup> h i

where the sum Σ*cj* is calculated for the first time as

formation of the monosolvate alone was initially assumed.

¼ 1

Water activity [aw] 0.6

*xi* <sup>¼</sup> *ci*ð Þ P 1 � *x*<sup>1</sup> *cj*

*ca*, *c2*, and *cd* are the molar acid, TBP/IP6, and dodecane concentrations, respec-

where cT is the total complex (TBP/IP6) concentration in a solution, i.e., the

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

*ax*2*<sup>f</sup> <sup>f</sup>* <sup>2</sup> exp ½ �þ *<sup>h</sup>*21ð Þ *<sup>a</sup>*<sup>1</sup> � <sup>1</sup> *<sup>K</sup>*12*aax*<sup>2</sup>

7. The value of *x2f* calculated by the Eq. (26) is used to determine the molar fractions *xij*. The molar concentrations *cij* are then estimated by the equations

> *cj* <sup>¼</sup> *<sup>x</sup> jd* <sup>∗</sup> <sup>1000</sup> Σ*xiMi*

**Parameter Value Units** % TBP 30.00% % % Dodecane 60.00% % % IP6 10.00% % Molarity HNO3 [M] 9 mol/L

Molecular weight HNO3 63.01 g/mol Molecular weight Dodecane 170.34 g/mol Molecular weight TBP 266.29 g/mol Molecular weight IP6 660.04 g/mol ρ HNO3 1.5129 g/cm3 ρ Dodecane [d0] 0.73526 g/cm3 ρ TBP 0.973 g/cm3 ρ IP6 1.3 g/cm3 Acid concentration [ca] 9 mol/dm<sup>3</sup>

n o

<sup>X</sup>*cj* <sup>¼</sup> *ca* <sup>þ</sup> *<sup>c</sup>*<sup>2</sup> <sup>þ</sup> *<sup>c</sup>*<sup>3</sup> (24)

*c*<sup>2</sup> ¼ *cT*–*ca* (25)

2*f f* 2

<sup>2</sup> *exp h*½ � <sup>12</sup>ð Þ *a*<sup>1</sup> � 1

(26)

(27)

(23)

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

where *d* is the density of a solution, and *xi* and *Mi* are the molar fraction and mass of the ith component.

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

The calculated acid molar concentration *cac* is further found as (28) and the calculated complex molar concentration *ctc* is estimated as (29)

$$
\mathcal{L}\_{\rm act} = \mathcal{c}\_{11} + \mathcal{c}\_{12} + \mathcal{2}\mathcal{c}\_{21} \tag{28}
$$

$$\mathcal{c}\_{tc} = \mathcal{c}\_{\mathcal{Y}} + \mathcal{c}\_{11} + \mathcal{2}\mathcal{c}\_{12} + \mathcal{c}\_{21} \tag{29}$$

**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.

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.

#### **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 *f2* are 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.

*Material Flow Analysis*
