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We know that nitrates, sulfates and carbonates doesn't or hardly oxidized by anode in the aqueous solution.

What will be produced on anode in the electrolysis of molten salts of these ions?

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A common theme is disproportionation of the anion, and potential reactivity with the electrodes.


Nitrates

Electrochemical behavior of nickel electrodes in molten potassium nitrate with increased basicity, Electrochimica Acta, Vol. 36, No. 3/4, pp. 65S-660, 1991:

$\text{Ni}$ electrodes in a $\ce{KNO_3}$ melt [...] some ionic species of nickelite ($\ce{NiO_2^{2-}}$) and nickelate ($\ce{NiO_2^{-}}$) type

Voltammetric investigations of the oxygen electrochemical systems in molten sodium nitrate at 420°C, Electrochimica Acta, Vol. 33, No. 4, pp. 545-549, 1988:

the potential range is limited anodically by the electrochemical oxidation of nitrate ions into nitrogen dioxide and oxygen: $\ce{NO3-} \to \ce{NO2} + \frac{1}{2}\ce{O2} + \ce{e-}$ and cathodically by the electrochemical reduction of nitrate ions into nitrite ions: $\ce{NO3-} + \ce{2e-} \to \ce{NO2-} + \ce{O^2-}$

Carbonates

Electrochemical formation of carbon nano-powders with various porosities in molten alkali carbonates, Electrochimica Acta, Vol. 54, pp. 4566–4573, 2009:

reduction of carbonate ions: $\ce{CO3} + \ce{4e-} \to \ce{C} + \ce{3O^2-}$ [and reduction of metal ions, along with oxidation of carbonate ions:] $\ce{2CO3^2-} \to \ce{2CO2} + \ce{O2} + \ce{4e-}$

Sulfates

Polarization measurements on solid platinum-molten sodium sulphate-sodium chloride interfaces, EIectrochimica Acta, Vol. 23, pp. 381-388, 1978:

the limiting reactions [...] are suggested to be the $\ce{SO3}$ reduction to $\ce{S^2-}$ and $\ce{O2-}$ and the $\ce{SO4^2-}$ oxidation to $\ce{SO2}$ and $\ce{O2}$

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Carbonates will lose CO2 on melting and turn into oxides.

Nitrates usually decompose/blow up on melting. Electrolysis will speed up explosion. Before they blow up O2 will form. Water solutions at low temperatures can also form NO4$^-$ (pernitrates).

Sulfates will form O2. water solutions of sulfates also form persulfates at low temperature.

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