A deviation in the definition of distribution equilibrium potential between electrochemical and extraction-chemical phenomena was discussed and examined quantitatively.

Keywords: distribution equilibrium potential, inner potential, Nernst equation, conditional distribution constant, distribution ratio, distribution of simple salts

Org, organic; Dep, distribution equilibrium potential; ISE, Ion-selective electrode

In electrochemistry and analytical chemistry, the following equations have been employed.^1,2

$E=E^0{}^{´}-\left(RT/zF\right)ln\left(C_R*/C_O*\right)$ (1)

$Emf=constant+\left(0.05916\right)log{\left[M^{I}X\right]}_{t}at298K$ , (2)

$\Delta {\phi }_{{}^{1/2}}=\Delta {\phi }_M{}^o´+\left(RT/zF\right)ln\left\{\left(1+\xi K_D+{\beta }_1{}^w{c}_M*\right)/\xi K_D{\beta }_1{}^{org}{c}_{M_{*}}\right\}$ , (3)

And

$E_j=A\left(RT/F\right)ln\left\{\Sigma \left|z\right|uC\left(\alpha \right)/\Sigma \left|z\right|uC\left(\beta \right)\right\}$ (4)

With

$A=\left\{\Sigma \left(\left|z\right|u/z\right)\left[C\left(\beta \right)-C\left(\alpha \right)\right]\right\}/\left\{\Sigma \left|z\right|u\left[C\left(\beta \right)-C\left(\alpha \right)\right]\right\}$

These Equations 1,2,3, & 4 shown so-called the Nernst equation¹ for the electrode reaction O+ ze⁻→ R, a calibration curve based on potentiometric measurements with ISE¹, a polarographic half-wave potential for a facilitated ion transfer across liquid/liquid interfaces,² and the Henderson equation¹ for a liquid junction potential, respectively. The concentrations C_R*, C_O*, [M^IX]_t, c_M*, C(β), and C(α) in the equations denote bulk total concentrations of their ions (or salts). That is, they do not reflect net concentrations of individual ions (or ion pairs) in the bulk phase. In this opinion, we pointed a deviation in definition between the potentials^1,2 in Equation 1–4 and DEP³ obtained experimentally from the simple MX distribution systems and sub-quantitatively examined its correction procedure.

For example, considering the mass balances in the MCl aqueous solutions relevant to the above equations, the concentrations in Equation 2 to 4 must be more-precisely expressed by using the equilibrium concentrations as

${\left[MCl\right]}_t=\left[M^{+}\right]+\left[MCl\right]=\left[C{l}^{-}\right]+\left[MCl\right]$ , (2A)

${\text{c}}_{\text{M}}{\text{* = [M}}^{\text{+}}\text{] + [MCl]}$ , (3A)

And

$C\left(\alpha \right)=\left[M^{+}\right]\left(\alpha \right)+\left[MCl\right]\left(\alpha \right)$ (4A)

When dilute solutions are used for their experiments, the [MCl] and [MCl](α) (the concentration for the α phase at equilibrium) terms can be generally neglected. The same expression as those in Equation (2A) to (4A) essentially holds for C_R* and C_O* in Equation 1. So, the C_R*, C_O*, [M^IX]_t, C_M*, and C(α) terms do not necessarily equivalent to the ionic strength (I) for the phase. Accordingly, the E, emf, Δφ_1/2, and E_j values are defined as fundamentally the difference between inner potentials (φ) for the two phases, such as the phases with liquid/solid,¹ and liquid/liquid interfaces.^1,2 Namely, Equation 1 to 4 describe the differences Δφ in overall energy between the two phases.

On the other hand, in extraction and distribution systems, a conditional distribution constant (K_D,_i) of a single ion (i) between the two bulk phases has been defined as the ratio of the concentrations (or activities) of the individual i with DEP at equilibrium^1,3,4 and a standard distribution constant (K_D,_i^S) at DEP=0V.^3,4 It is

$K_D{,}_i={\left[i\right]}_{org}/\left[i\right]=K_D{,}_i{}^{S}exp\left\{\left(z_{i}F/RT\right)dep\right\}$ (5)
And this modified form is

(5A)

$dep=\left(RT/z_{i}F\right)\left(ln{K}_D{,}_i-ln{K}_D{,}_i{}^S\right)$

Here, z_i denotes the formal charge z with the sign of the ion i. In Equation (5) or (5A), the K_D,_i value contains only the amount of an ionic component, such as i=M⁺ or Cl⁻. These facts indicate that with the difference Δφ of only the individual M⁺ or Cl⁻ is expressed Equation (5A), while Equation 1 to 4 are done with the Δφ of the mixture of M⁺, Cl⁻, and MCl. This means that the electrochemical definition for E, emf, Δφ_1/2, and E_j,^1,2 can slightly deviate from the dep definition based on the experimental K_D,_i values.^1,3,4 Of course, the energetic states of the phases may influence the K_D,_i determination in the extraction experiments.

By the way, the distribution ratio (D) has been defined as

$D=c_t{,}_{org}/c_t=\left({\left[M^{+}\right]}_{org}+{\left[MX\right]}_{org}\right)/\left(\left[M^{+}\right]+\left[MX\right]\right)$ (6)

In the simple MX distribution systems.^3,5 Here, the symbols c_t and c_t,_org denote the total concentrations of the species with M(I) {or X(−I)} in the water and org phases, respectively.

Equation (6) can be rearranged as D=.

$\left({\left[M^{+}\right]}_{org}/\left[M^{+}\right]\right)\times \left(1+KMX{,}_{org}{\left[X^{-}\right]}_{org}\right)/\left(1+K_{MX}\left[X^{-}\right]\right)$ (6A)

With K_MX.org

$={\left[MX\right]}_{org}/{\left[M^{+}\right]}_{org}{\left[X^{-}\right]}_{\text{org}}and{K}_{MX}=\left[MX\right]/\left[M^{+}\right]\left[X^{-}\right]$ .^3,5

Using Equation (5) with the charge balance relations

${\text{[M}}^{\text{+}}{\text{] = [X}}^{\text{-}}\text{] = }I{\text{ and [M}}^{\text{+}}{\text{]}}_{\text{org }}{\text{= [X}}^{\text{-}}{\text{]}}_{\text{org}}\text{ (= }{I}_{\text{org}}\text{)}$ ,

Equation (6A) also becomes

$D=\left(1+K_{MX}{,}_{org}{K}_D{,}_{X}I\right)/\left(1+K_{MX}I\right)\times K_{D,M}=r{K}_{D,M}=r{K}_{D,X}$ (6B)

With $r=\left(1+K_{MX,}{}_{org}{K}_{D,X}I\right)/\left(1+K_{MX}I\right)$

Moreover, assuming that  at DEP=0, the following equation can be derived from Equations (5) & (6B):

$D=D^{S}exp\left\{\left(z_{i}F/RT\right)dep\right\}=c_t{,}_{org}/c_t$ (7)

This equation is very similar to the above electrochemical expression,^1,2 because the c_t and c_t,_org terms are equivalent with the expression of C_R*, C_O*, [M^IX]_t, c_M*, and C(α). That is, the dep values calculated from D, based on Equation (7), approach to the definition corresponding to E, emf, Δφ_1/2, and E_j. Also, the use of D is not in conflict with the above electrochemical definitions.

Table 1 summarizes some experimental K_D,± and D values,³ in the MX distribution into several diluents, where the relation ${\left(K_{D,M}{K}_{D,X}\right)}^{1/2}=K_{D,\pm }$ holds.^3,4 The plot of log K_D,± versus log D listed in Table 1 yielded log $K_{D,\pm }=\left(0.98\pm 0.04\right)logD-\left(0.10\pm 0.13\right)$ at the correlation coefficient of 0.996. This regression line show that the log K_D,± values are proportional to the log D ones, namely log K_D,±=log D–log r {see Equation (6B)}. In other words, this fact indicates that K_D,± is a function of D and r. When the r value is approximately equal to unity, we can immediately obtain D & K_D,± which equals K_D,M and K_D,X. The intercept (=log r≈0.1) of the regression line shows the possibility that the evaluated r values equal unity within the calculation error (≥0.1).

Consequently, the DEP in Equations (5) and (5A) satisfies the electrochemical definition in the case of r≈1. At the same time, the definition for C_R*, [M^IX]_t, and C(α) is reflected into indirectly the K_D,± values through the D ones. A similar discussion will be also needed for the more-complicated extraction systems,^4,6 with various extracting reagents.

None

The author declares that there are no conflicts of interest.

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