In the context of the Hall-Heroult process for the extraction of Al, which of the following statements is false?

First, recall that in the Hall-Héroult electrolytic reduction of alumina, the electrolytic bath is not made of pure alumina. Pure $$Al_2O_3$$ has an extremely high melting point, close to $$2050^\circ{\rm C}$$, and also possesses very low electrical conductivity in the molten state. To overcome these difficulties, a molten mixture is prepared which can both dissolve alumina and conduct current at a much lower temperature (about $$950^\circ{\rm C}$$).

The principal constituent of this bath is molten cryolite, whose formula is $$Na_3AlF_6$$. Alumina is added to this cryolite. To further decrease the melting point and improve conductivity, small amounts of $$CaF_2$$ are also mixed in. Thus the real electrolyte is the molten solution of alumina in cryolite (often with added $$CaF_2$$), not cryolite by itself.

We now examine each option:

Option A states, “$$Na_3AlF_6$$ serves as the electrolyte.” Because the actual electrolyte is the mixture of $$Al_2O_3$$ dissolved in molten $$Na_3AlF_6$$ (sometimes with $$CaF_2$$), it is incorrect to say that cryolite alone is the electrolyte. Hence, this statement is false.

Option B claims that CO and $$CO_2$$ are produced. At the carbon anode, oxide ions released from alumina react as

$$\text{C (s) } + 2\,O^{2-} \rightarrow CO_2 \, + \, 4\,e^-$$

or, under slightly different conditions,

$$\text{C (s) } + O^{2-} \rightarrow CO \, + \, 2\,e^-$$

Thus both CO and $$CO_2$$ can indeed form, so Option B is true.

Option C says that $$Al_2O_3$$ is mixed with $$CaF_2$$ which lowers the melting point of the mixture and provides conductivity. This effect of $$CaF_2$$ is well documented, so the statement is true.

Option D asserts that $$Al^{3+}$$ ions are reduced at the cathode to metallic aluminium. At the cathode the reaction is

$$Al^{3+} \; + \; 3\,e^- \; \rightarrow \; Al$$

This is exactly what happens, so Option D is also true.

Only Option A is inconsistent with the detailed chemistry of the process.

Hence, the correct answer is Option A.