A negative cell potential means a reaction will not run on its own. An outside power source can force it: that is electrolysis, used to make aluminum, chlorine and sodium hydroxide, and to plate metals.
🔑 Key idea
In an electrolytic cell, a power supply pushes electrons into one electrode, making it the negative cathode, where reduction happens. The other electrode, connected to the positive terminal, is the anode, where oxidation happens. The applied voltage must be at least the size of the (negative) cell potential, and in practice more.
💡 Why it works
Anode always means oxidation and cathode always means reduction, in every cell. What differs is the source of the push. In a galvanic cell, the reaction itself makes the anode negative by leaving electrons there. In an electrolytic cell, the power supply drags electrons out of the anode, so it is positive, and pumps them into the cathode, which is negative. The extra voltage beyond the minimum (the overpotential) is needed to drive the reactions at a useful rate.
Copper plating: the power supply drives $\mathrm{Cu^{2+}}$ to copper metal at the negative cathode.
Worked examples
✏️ Worked example: Molten magnesium chloride
Molten $\mathrm{MgCl_2}$ is electrolyzed. What forms at each electrode, and what are their signs?
Only $\mathrm{Mg^{2+}}$ and $\mathrm{Cl^-}$ are present (no water).
$E^\circ_\text{cell} = 0.34 - 1.36 = -1.02\ \text{V}$. Not favored, so at least $1.02\ \text{V}$ must be applied (more in practice).
Answer: $1.02\ \text{V}$.
In water, the solvent can react too. At the cathode, water is reduced to $\mathrm{H_2}$ in preference to active-metal ions such as $\mathrm{Na^+}$, so electrolysis of salt water gives hydrogen, not sodium. At the anode, chlorine forms from concentrated brine even though oxidizing water has a lower standard potential, because making oxygen needs a large overpotential. This chlor-alkali process makes chlorine and sodium hydroxide on a huge scale.
Recharging a battery is electrolysis: the charger pushes the battery's reaction backward, restoring its reactants.
⚠️ Common mistake
Thinking the anode is negative in every cell. It is negative in a galvanic cell and positive in an electrolytic cell. Check: the anode is always where oxidation happens; the sign follows from what drives the electrons.
Practice
Pass with 3 right answers, the last 2 in a row. Each right answer earns 2 XP.