DAT General Chemistry: Electrolytic Cells

DAT High-Yield Concept

Nonspontaneous Redox: Electrolytic cells use an external power source to drive nonspontaneous chemical reactions ( $\Delta G > 0$ , $E^\circ_{\text{cell}} < 0$ ).
Universal Rule (AN OX / RED CAT): Oxidation always occurs at the anode, and reduction always occurs at the cathode in both galvanic and electrolytic cells.
Electron Direction: Electrons always flow through the external wire from anode to cathode in all electrochemical cells.
Electrode Sign Inversion: In electrolytic cells, the anode is positive (+) and the cathode is negative (-)—the opposite of galvanic cells.

Principles of Electrolytic Cells

An electrolytic cell converts electrical energy into chemical energy through a process called electrolysis. While galvanic cells generate electricity spontaneously from chemical reactions, electrolytic cells require an external direct current (DC) power source (such as a battery) to force a nonspontaneous redox process to occur.

For electrolysis to proceed, the external voltage supplied must exceed the magnitude of the cell's negative standard cell potential ( $|E^\circ_{\text{cell}}|$ ). Common applications tested on the DAT include the electrolysis of water into hydrogen and oxygen gas, or molten ionic compounds into their pure elemental forms.

Key Definition: Electrolysis is the decomposition of a compound using electric current. The process requires continuous external voltage input because thermodynamic criteria dictate

\Delta G > 0

and

E^\circ_{\text{cell}} < 0

Comparing Galvanic and Electrolytic Cells

A central DAT objective is contrasting galvanic (voltaic) cells with electrolytic cells. Both cell types share foundational operational rules: oxidation occurs at the anode, reduction occurs at the cathode, cations migrate toward the cathode, and anions migrate toward the anode.

A revised copy of the Wikimedia Commons galvanic cell diagram/image http://commons.wikimedia.org/wiki/Image:Galvanic_cell.png as it existed there on 15 March 2007. (Source: The original uploader was Ohiostandard at English Wikipedia . · CC BY-SA 3.0 · Wikimedia Commons)

However, the direction of energy flow, reaction spontaneity, and electrode sign assignments differ completely between the two cells.

Property	Galvanic (Voltaic) Cell	Electrolytic Cell
Reaction Spontaneity	Spontaneous ( $\Delta G < 0$ )	Nonspontaneous ( $\Delta G > 0$ )
Standard Cell Potential	Positive ( $E^\circ_{\text{cell}} > 0$ )	Negative ( $E^\circ_{\text{cell}} < 0$ )
Energy Conversion	Chemical $\rightarrow$ Electrical	Electrical $\rightarrow$ Chemical
Anode (Oxidation) Charge	Negative ( $-$ )	Positive ( $+$ )
Cathode (Reduction) Charge	Positive ( $+$ )	Negative ( $-$ )
Electron Flow (External Wire)	Anode $\rightarrow$ Cathode	Anode $\rightarrow$ Cathode

Electrode Signs in Electrochemical Cells

To determine electrode signs correctly on the DAT, analyze how electrons are moved in each system:

In a galvanic cell, spontaneous oxidation releases electrons at the anode, making it electron-dense (negative, -). Electrons flow spontaneously toward the cathode, making it electron-deficient (positive, +).
In an electrolytic cell, an external battery forcibly pulls electrons away from the anode, rendering the anode electron-deficient (positive, +). The battery pumps electrons onto the cathode, rendering the cathode electron-dense (negative, -).

Galvanic against electrolytic: what stays the same and what flips — Both kinds of cell obey the same two definitions: oxidation happens at the anode, reduction happens at the cathode, and electrons therefore travel from anode to cathode through the external wire. What differs is the direction of the energy flow. A galvanic cell runs a spontaneous reaction, so its standard cell potential is positive, its free-energy change is negative, and it delivers electrical energy; the anode is the negative terminal because the reaction is pushing electrons out of it. An electrolytic cell forces a non-spontaneous reaction with an external power supply, so the anode is connected to the supply's positive terminal and is the positive electrode while the cathode is negative. The electrode signs flip between the two cell types, but the anode-oxidation and cathode-reduction pairings never do.

DAT Memory Aids:
• AN OX & RED CAT: Anode = Oxidation, Reduction = Cathode (true for ALL cells).
• EPA in Electrolytic Cells: Electrolytic = Positive Anode.
• ANO in Galvanic Cells: Anode = Negative in Ordinary batteries.

Worked Example: Electrolysis of Molten Magnesium Chloride

Problem: Molten magnesium chloride ( $\ce{MgCl2(l)}$ ) is electrolyzed in an electrolytic cell. Given the standard reduction potentials: $E^\circ(\ce{Mg^{2+} / Mg}) = \pu{-2.37 V}$ $E^\circ(\ce{Cl2 / Cl^-}) = \pu{+1.36 V}$ Identify the half-reactions, write the balanced net reaction, calculate $E^\circ_{\text{cell}}$ , state the minimum required external voltage, and assign electrode polarities.

Step-by-Step Solution:

Identify species present: Molten $\ce{MgCl2}$ contains $\ce{Mg^{2+}(l)}$ and $\ce{Cl^-(l)}$ ions.
Cathode Half-Reaction (Reduction): Cations ( $\ce{Mg^{2+}}$ ) gain electrons at the cathode: $\ce{Mg^{2+}(l) + 2e^- -> Mg(s)}$
Anode Half-Reaction (Oxidation): Anions ( $\ce{Cl^-}$ ) lose electrons at the anode: $\ce{2Cl^-(l) -> Cl2(g) + 2e^-}$
Net Cell Reaction & Potential: $\ce{Mg^{2+}(l) + 2Cl^-(l) -> Mg(s) + Cl2(g)}$ $E^\circ_{\text{cell}} = E^\circ_{\text{reduction, cathode}} - E^\circ_{\text{reduction, anode}} = \pu{-2.37 V} - \pu{1.36 V} = \pu{-3.73 V}$
Minimum External Voltage: The power supply must deliver a potential exceeding $\pu{3.73 V}$ to force the nonspontaneous reaction forward.
Electrode Signs: In this electrolytic cell, the anode is positive (+) and the cathode is negative (-).

Common Exam Trap: Students often mistakenly swap the sites of oxidation and reduction when electrode signs flip. Remember: the definitions of anode (oxidation) and cathode (reduction) never change; only the assigned electrical polarities ( $+$ / $-$ ) reverse!

Critical Thinking Questions

Why do electrons always travel through the wire from anode to cathode in both cell types, despite opposite electrode sign assignments?
In the electrolysis of aqueous $\ce{NaCl(aq)}$ versus molten $\ce{NaCl(l)}$ , why does reduction of water occur at the cathode instead of reduction of $\ce{Na^+}$ ?
When a rechargeable secondary battery discharges, it acts as a galvanic cell. What type of cell does it become while being recharged, and how do its electrode polarities change?

References

Sources returned by Google Search grounding during lesson verification.

17.7: Electrolysis - Chemistry LibreTexts — chem.libretexts.org
19.7 Electrolytic Cells - Chad's Prep — chadsprep.com

Electrolytic Cells

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