Solvent-Independent Unifying Reducity

$\mathit{\boldsymbol{E}}_{\mathrm{\mathbf{abs}}}^{\mathrm{\mathbf{H_{2}O}}}$ of the redox system $\mathbf{H^{\mathbf{\boldsymbol{+}}}\mathbf{/}H_{2}}$

Below you can find $E_\mathrm{abs}$ and $E_\mathrm{{abs}}^\mathrm{H_{2}O}$ values at standard conditions (i.e. $a_\mathrm{S}\left(\mathrm{H}^{+},\mathrm{S}\right)=1$) for a variety of solvents. They are based on Gibbs transfer energies of the proton $\Delta_{\mathrm{tr}}G{^\circ}\left(\mathrm{H}^{+},\mathrm{H_{2}O\rightarrow S}\right)$, which we determined using our electrochemical ILSB method. Details are published here. The Gibbs hydration energy of the proton $\Delta_{\mathrm{solv}}G{^\circ}\left(\mathrm{H}^{+},\mathrm{H_2O}\right)$ is taken from the literature.^[1] All valus of $\Delta_{\mathrm{tr}}G{^\circ}\left(\mathrm{H}^{+},\mathrm{H_{2}O\rightarrow S}\right)$ and $\Delta_{\mathrm{solv}}G{^\circ}\left(\mathrm{H}^{+},\mathrm{S}\right)$ are given in kJ mol⁻¹, $\mathit{E}_\mathrm{abs}$ and $\mathrm{\mathit{E}_{H_{2}O}}$ values are given in V. Note, that the $\mathit{E}_\mathrm{abs}°$ of the $\mathrm{SHE_{H_{2}O}}$ deviates from the IUPAC value (4.44 V); the reason is that the latter one is based on $\alpha$ instead of $\mu$.

Literature

[1] M. D. Tissandier, K. A. Cowen, W. Y. Feng, E. Gundlach, M. H. Cohen, A. D. Earhart, J. V. Coe, T. R. Tuttle, J. Phys. Chem. A 1998, 102, 7787.

$\mathit{\boldsymbol{E}}_{\mathrm{\mathbf{abs}}}^{\mathrm{\mathbf{H_{2}O}}}$ of the redox system $\mathbf{Ag^{\mathbf{\boldsymbol{+}}}\mathbf{/}Ag}$

Below you can find $E_\mathrm{abs}$ and $E_\mathrm{{abs}}^\mathrm{H_{2}O}$ values (given in V) at standard conditions (i.e. $a_\mathrm{S}\left(\mathrm{Ag}^{+},\mathrm{S}\right)=1$) for a variety of solvents. They are based on Gibbs transfer energies of the silver ion $\Delta_{\mathrm{tr}}G{^\circ}\left(\mathrm{Ag}^{+},\mathrm{H_{2}O\rightarrow S}\right)$, which we determined using our electrochemical ILSB method. Details are published here and (together with $\Delta_{\mathrm{tr}}G{^\circ}\left(\mathrm{Cl}^{-},\mathrm{H_{2}O\rightarrow S}\right)$ values) here.

$\mathit{\boldsymbol{E}}_{\mathrm{\mathbf{abs}}}^{\mathrm{\mathbf{H_{2}O}}}$ of the redox systems $\mathbf{AgCl/Ag,Cl^{\mathbf{\boldsymbol{-}}}}$ and $\mathbf{\mathbf{Cl_{2}}/Cl^{\mathbf{\boldsymbol{-}}}}$

Below you can find $E_\mathrm{abs}$ and $E_\mathrm{{abs}}^\mathrm{H_{2}O}$ values of the redox system $\mathrm{AgCl/Ag,Cl^{-}}$ for a variety of solvents . Further below you can find $E_\mathrm{abs}$ and $E_\mathrm{{abs}}^\mathrm{H_{2}O}$ values of the redox system $\mathrm{Cl_2/Cl^{-}}$.

Both are valid at standard conditions (i.e. $a_\mathrm{S}\left(\mathrm{Cl}^{-},\mathrm{S}\right)=1$). They are based on Gibbs transfer energies of the chloride ion $\Delta_{\mathrm{tr}}G{^\circ}\left(\mathrm{Cl}^{-},\mathrm{H_{2}O\rightarrow S}\right)$, which we determined using our electrochemical ILSB method. Details are published here.

$\mathit{\boldsymbol{E}}_{\mathrm{\mathbf{abs}}}^{\mathrm{\mathbf{H_{2}O}}}$ of the redox system $\mathbf{Fc^{\mathbf{\boldsymbol{+}}}\mathbf{/}Fc}$

Coming soon.

$\mathit{\boldsymbol{E}}_{\mathrm{\mathbf{abs}}}^{\mathrm{\mathbf{H_{2}O}}}$ of the redox systems determined with the ILSB Method

Below you can find the overview of our $E_\mathrm{abs}$ and $E_\mathrm{{abs}}^\mathrm{H_{2}O}$ values (given in V) at standard conditions (i.e. $a_\mathrm{S}\left(\mathrm{i},\mathrm{S}\right)=1$) for a variety of solvents. They are based on Gibbs transfer energies of the relevant ion i $\Delta_{\mathrm{tr}}G{^\circ}\left(\mathrm{i},\mathrm{H_{2}O\rightarrow S}\right)$, which we determined using our electrochemical ILSB method.

Remarks to $\mathit{\boldsymbol{E}}_{\mathrm{\mathbf{abs}}}^{\mathrm{\mathbf{H_{2}O}}}$

The distinction between the $\mathrm{\mathit{E}_{abs}}$ scales (i.e. $\mathrm{\mathit{E}_{abs}}$ and $\mathrm{\mathit{E}_{abs}^{H_{2}O}}$ ) and the $\mathrm{\mathit{E}_{S}}$ scales (i.e. $\mathrm{\mathit{E}_{H_{2}O}}$, $\mathrm{\mathit{E}_{MeCN}}$, $\mathrm{\mathit{E}_{H_{2}SO_{4}}}$, etc.) is the reference state of the electron: For the latter actually no electrons are used explicitly as reference, as the redox system $\mathrm{H^+}/\mathrm{H_2}$ (i.e. the Standard Hydrogen Electrode, $\mathrm{SHE_{S}}$) is used, and hence, the ideal dilute proton solution in the solvent S with the relative activity $a_\mathrm{S}(\mathrm{{H^+},S})=1$. Therefore, these scales are relative scales only applicable for the solvent under consideration S. As pointed out by Trasatti, different reference states of the electron can be associated to this single electrode. What he called $E_\mathrm{k}$ and $_{3}E_{\mathrm{a}}^{\mathrm{M}}$, respectively,^[1] is based on the real potential $\alpha$ of the proton, and is used by the IUPAC for the definition of the absolute electrode potential for reasons of measurability;^[2] for an annotation click here. The $\mathrm{pe_{abs}}$, $\mathrm{\mathit{E}_{abs}}$, and the $\mathrm{\mathit{E}_{abs}^{H_{2}O}}$ scales are based on the chemical potential $\mu$ of the proton, and $\mathrm{\mathit{E}_{abs}}$ essentially corresponds to Trasatti’s single electrode potential $\mathrm{\mathit{E}_{T}}$ and $_{2}E_{\mathrm{a}}^{\mathrm{M}}$, respectively, that can be traced back to Kanevskii.^[3] Thus, the reference state is the ideal electron gas at 298.15 K and 10$^{5}$ Pa where the chemical potential of the electron $\mu_{\mathrm{abs}}\left(\mathrm{e}^{-}\right)$ arbitrarily is set to 0 kJ mol$^{-1}$. This state is independent on any solvent or medium ensuring the comparability of all values within these scales.

The defintion of the pe_abs is:

Usually, the chemical potential of the electron is unknown. Nevertheless, the pe_abs can be calculated. For example, if the electrode reaction of the redox system $\mathrm{H^+}/\mathrm{H_2}$ is given as Eq. rv2,

the following BFHC belongs to the $\mathrm{\mathit{E}_{abs}}$ scales; at constant pressure and temperature, the absolute chemical potential of the proton equals the Gibbs energy of solvation.

It follows at standard conditions (take note of our used standard states):

Or, since the Gibbs energies of atomization and ionization, $\Delta_{\mathrm{at}}G{^\circ}\left(\mathrm{H}\right)$ and $\Delta_{\mathrm{ion}}G{^\circ}\left(\mathrm{H}\right)$, respectively, are solvent-independent, at any proton activities and hydrogen pressures:

In this way any redox system can be implemented into the $\mathrm{pe_{abs}}$ scale, knowing the relevant Gibbs energies for the processes given in the BFHC. The $\mathrm{pe_{abs}}$ can be calculated into the $\mathrm{\mathit{E}_{abs}}$:

As for the $\mathrm{pH_{abs}}$, we use the value for the Standard Gibbs energy of hydration of the proton obtained by Tissandier et al., $\Delta_{\mathrm{solv}}G{^\circ}\left(\mathrm{H}^{+},\mathrm{H_{2}O}\right)=-1104.8\:\mathrm{kJ\,mol^{-1}}$.^[4] Thus, an aqueous solution with the $\mathrm{\mathit{E}_{H_{2}O}}=0\:\mathrm{V}$ has the $\mathrm{\mathit{E}_{abs}}=4.28\:\mathrm{V}$ at 198.15 K. To align the zero point of the $\mathrm{\mathit{E}_{abs}}$ scale with that of the $\mathrm{\mathit{E}_{H_{2}O}}$ scale, thereby obtaining the $\mathrm{\mathit{E}_{abs}^{H_{2}O}}$ scale, this value has to be subtracted from the $\mathrm{\mathit{E}_{abs}}$ value:

In addition to the “familiarity” of the values (e.g. 0 V vs. 72.3 or 4.28 V, respectively), this has the advantage that if a more reliable value for the Gibbs energy of the proton hydration is available, in a majority of cases it is not required to recalculate the $\mathrm{\mathit{E}_{H_{2}O}}$ values. This is the case when the values were determined using Gibbs transfer energy values $\Delta_{\mathrm{tr}}G{^\circ}\left(\mathrm{H}^{+},\mathrm{H_{2}O}\rightarrow\mathrm{S}\right)$ for the transfer of the proton from water to solvent S:

The $\mathit{E}_{\mathrm{abs}}^{\mathrm{H_{2}O}}\left(\mathrm{H}^{+}/\mathrm{H}_{2}\right)$ value is connected to the $\mathrm{pH_{abs}^{H_{2}O}}$ value:

Final note: Since ions are electrically charged they are affected by electric fields. Thus, in principle, one is free to choose a quantity including the energy contribution of the electric field; it is in this way that the IUPAC defines the absolute electrode potential of the $\mathrm{SHE_{H_{2}O}}$ (see above). Click here for implications if the $\mathrm{SHE_{H_{2}O}}$ was defined with $\mu$, as done here.

Literature

[1] a) S. Trasatti, J. Electroanal. Chem. 1982, 139, 1. b) S. Trasatti, Electrochim. Acta 1990, 35, 369.

[2] S. Trasatti, Pure Appl. Chem. 1986, 58, 955.

[3] E. Kanevskii, Zh. Fiz. Khim. 1948, 22, 1397.

[4] M. D. Tissandier, K. A. Cowen, W. Y. Feng, E. Gundlach, M. H. Cohen, A. D. Earhart, J. V. Coe, T. R. Tuttle, J. Phys. Chem. A 1998, 102, 7787.

Calculation of $\mathit{\boldsymbol{E}}_{\mathrm{\mathbf{abs}}}^{\mathrm{\mathbf{H_{2}O}}}$

To get other $\mathrm{\mathit{E}_{abs}^{H_{2}O}}$ values in the solvent S than at standard conditions, use the Nernst Equation as you are accustomed to, e.g. with Eq. cr1.

Find here the $E_\mathrm{{abs}}^\mathrm{H_{2}O}\,°$ values for the redox system $\mathrm{H}^+/\mathrm{H}_2$, for the redox system $\mathrm{Ag}^+/\mathrm{Ag}$, for the redox system $\mathrm{AgCl/Ag,Cl^{-}}$, and for the redox system $\mathrm{Cl_2/Cl^{-}}$. Click here for $E_\mathrm{{abs}}^\mathrm{H_{2}O}\,°$ values of redox systems that we have not determined with our ILSB method. $a_{\mathrm{ox}}$ and $a_{\mathrm{red}}$ are the relative activity coefficients of the deelectronated and electronated form of the redox system. R, T, n, and F have their usual meaning.