4.4 Electrochemical Cells: Galvanic & Electrolytic

Electrochemistry is where general chemistry and physics collide on the MCAT: redox (reduction–oxidation) reactions meet the circuit concepts — current, electromotive force (EMF), and resistance — introduced earlier in this chapter. An electrochemical cell is any device that either uses a spontaneous redox reaction to generate electrical energy, or uses electrical energy to force a non-spontaneous redox reaction to occur. The first type is a galvanic (voltaic) cell; the second is an electrolytic cell. Living cells exploit the same principles when ion gradients and membrane channels create and consume electrical energy.

Electrolytic Cells

An electrolytic cell uses an external power source (a battery or other EMF source) to drive a non-spontaneous redox reaction. This forced process is called electrolysis — literally, using electricity to split apart a compound, such as decomposing molten NaCl into liquid sodium metal and chlorine gas, or decomposing water into hydrogen and oxygen gas. Recharging a secondary battery is also electrolysis: the same physical cell is forced to run as an electrolytic cell.

Every electrochemical cell, electrolytic or galvanic, has two electrodes immersed in an electrolyte — a solution or molten substance containing free ions that can carry current between the electrodes:

• The anode is the electrode where oxidation occurs (loss of electrons)
• The cathode is the electrode where reduction occurs (gain of electrons)

This assignment never changes — memorize it with the mnemonic "AN OX, RED CAT" (ANode hosts OXidation; REDuction happens at the CAThode). What does change between cell types is the electrode's charge polarity, covered below once galvanic cells are introduced.

In an electrolytic cell, the external power source forces electrons to flow against their natural spontaneous direction: electrons are pulled out of the anode and pushed into the cathode. Because the driving EMF comes entirely from outside the cell, the anode is wired to the power source's positive terminal (making the electrolytic-cell anode positively charged), while the cathode is wired to the negative terminal.

Faraday's Law

Faraday's Law relates the amount of element deposited (or gas liberated) at an electrode to the total electric charge passed through the cell. The number of moles of electrons transferred equals the total charge divided by the Faraday constant (F), the charge carried by one mole of electrons, F ≈ 96,500 C/mol:

moles of e⁻ = Q / F, where Q = It (charge equals current multiplied by time)

Once moles of electrons are known, stoichiometry from the balanced half-reaction converts that figure into moles — and then mass — of the deposited element.

Worked example: A constant current of 2 A is passed through a solution of Cu²⁺ ions for 965 seconds, depositing copper metal at the cathode via Cu²⁺ + 2e⁻ → Cu (F ≈ 96,500 C/mol; molar mass of Cu = 63.5 g/mol).

• Charge passed: Q = It = (2 A)(965 s) = 1,930 C
• Moles of electrons: 1,930 C ÷ 96,500 C/mol = 0.02 mol e⁻
• Since each Cu²⁺ requires 2 electrons, moles of Cu deposited = 0.02 ÷ 2 = 0.01 mol Cu
• Mass deposited: (0.01 mol)(63.5 g/mol) = 0.635 g

The most common MCAT trap here is forgetting to divide by the number of electrons in the half-reaction — treating every mole of electrons as if it deposited a full mole of metal overstates the answer by a factor equal to that electron count (here, a wrong doubling to 1.27 g).

Galvanic (Voltaic) Cells

A galvanic cell (also called a voltaic cell) uses a spontaneous redox reaction to generate electrical energy — this is the operating principle behind every battery. A galvanic cell physically separates the oxidation and reduction half-reactions into two compartments (half-cells), each containing an electrode, forcing electrons to travel through an external wire to get from the oxidized species to the reduced species. That electron flow through the wire is the current available to power a device. A salt bridge or porous barrier allows ion migration that keeps each half-cell electrically neutral without mixing the bulk solutions completely.

Each half-reaction has a standard reduction potential (E°), a measured voltage (in volts) describing how strongly a species tends to be reduced (gain electrons) under standard conditions (1 M concentrations, 1 atm gases, usually 25 °C). Reduction potentials are tabulated as reductions by convention, even for the species that ends up being oxidized in a particular cell.

The species with the more positive (or less negative) reduction potential is reduced and becomes the cathode; the species with the more negative (or less positive) reduction potential is oxidized and becomes the anode. The overall cell potential is:

E°cell = E°cathode − E°anode

(using both values exactly as tabulated as reduction potentials — never flip the sign of the anode's value before subtracting). Equivalently, some texts write E°cell = E°reduction + E°oxidation after reversing the anode half-reaction's sign — both methods give the same number if done carefully.

Worked example: A galvanic cell pairs a zinc half-cell (Zn²⁺ + 2e⁻ → Zn, E° = −0.76 V) with a copper half-cell (Cu²⁺ + 2e⁻ → Cu, E° = +0.34 V). Copper's higher reduction potential means Cu²⁺ is reduced (copper is the cathode); zinc's lower reduction potential means Zn is oxidized (zinc is the anode).

E°cell = E°cathode − E°anode = 0.34 V − (−0.76 V) = 1.10 V

This is the classic Daniell cell, and 1.10 V is worth memorizing directly, since this exact pairing appears repeatedly across MCAT passages.

In a galvanic cell, the spontaneous reaction pushes electrons out of the anode on its own — no external power source is needed. Electrons flow through the external circuit from anode to cathode, making the galvanic-cell anode the negative terminal and the cathode the positive terminal. This is the opposite polarity assignment from the electrolytic cell described above, even though the oxidation-at-anode / reduction-at-cathode rule never changes:

Free Energy, Spontaneity & the Nernst Equation

Cell potential is not a separate universe from thermodynamics. Under standard conditions:

ΔG° = −nFE°cell

where n is moles of electrons transferred in the balanced reaction and F is Faraday's constant. A positive E°cell means ΔG° is negative — the reaction is spontaneous as written under standard conditions (galvanic discharge). A negative E°cell means the reverse reaction is spontaneous; running the cell as written would require an external voltage (electrolytic mode).

Real cells are rarely at standard concentrations. The Nernst equation adjusts cell potential for nonstandard reaction quotient Q:

E = E° − (RT/nF) ln Q

At 25 °C, a convenient base-10 form is:

E ≈ E° − (0.059 V / n) log Q

If Q < 1 (reactants in excess relative to products), log Q is negative and E > E°. If Q > 1, E < E°. At equilibrium Q = K and E = 0, which recovers the relation between E° and the equilibrium constant. The MCAT rarely demands heavy log arithmetic, but it does test the direction: raising product concentration or lowering reactant concentration decreases E for the forward cell reaction.

Concentration cells are the purest application. A concentration cell is a special galvanic cell built from two half-cells using the same electrode material and the same ion, differing only in ion concentration. Because both half-reactions are identical, E° = 0 V — yet the cell still generates a real, nonzero voltage driven purely by the concentration difference. In Nernst terms, E° = 0 and E = −(0.059/n) log Q, with Q equal to the concentration ratio between the two sides.

The dilute half-cell's electrode becomes the anode (oxidation releases more ions into the dilute solution), and the concentrated half-cell's electrode becomes the cathode (reduction removes ions from the concentrated solution). Net transfer equalizes concentrations. This exact mechanism — a voltage generated by an ion concentration difference across a barrier, rather than by different electrode materials — is the conceptual parent of the nerve cell's resting membrane potential, developed in the next section.

Membrane Nernst potential (preview): for a single ion permeable across a membrane, the equilibrium potential is the voltage at which chemical and electrical driving forces balance. At body temperature the often-quoted rule of thumb is about 61/z mV times log([ion]out/[ion]in) for cation z (sign conventions vary with form of the equation). K⁺'s equilibrium potential is strongly negative because [K⁺]in ≫ [K⁺]out; Na⁺'s is positive because [Na⁺]out ≫ [Na⁺]in. You will apply this fully in the nerve conduction section.

Batteries

A battery is one or more galvanic cells connected together to supply usable electrical energy. Two related but distinct voltage concepts describe a battery's output:

• Electromotive force (EMF) is the maximum possible voltage a cell can produce, measured when no current is flowing
• Terminal voltage is the actual voltage available at the battery's terminals once current is flowing, always slightly lower than the EMF because of the battery's own internal resistance

Batteries are classified as primary cells (non-rechargeable — the redox reaction cannot easily be reversed, as in a standard alkaline battery) or secondary cells (rechargeable — an external power source can force the reaction to run in reverse, restoring the original reactants, essentially operating the same physical cell as an electrolytic cell during charging).

Two secondary-cell chemistries are frequently tested:

Lead-storage battery (the standard car battery): uses a lead (Pb) anode, a lead dioxide (PbO₂) cathode, and sulfuric acid (H₂SO₄) as the electrolyte. Each cell produces roughly 2 V; six cells connected in series produce the familiar 12 V automotive battery. Discharging converts both electrodes toward lead sulfate (PbSO₄); recharging (which runs the cell as an electrolytic cell) reverses this reaction.

Nickel-cadmium (NiCad) battery: uses a cadmium (Cd) anode and a nickel oxide hydroxide (NiO(OH)) cathode, producing roughly 1.2 V per cell. NiCad batteries are rechargeable and were historically common in portable electronics before being largely displaced by lithium-ion chemistry.

A useful test-day check: since batteries in series add their individual voltages, a battery's total voltage divided by its per-cell voltage tells you how many cells are inside — 12 V ÷ 2 V per cell = 6 cells for a lead-storage battery, a relationship the MCAT can test directly.

Common MCAT Traps

• Flipping oxidation/reduction site when cell type changes. Anode is always oxidation; only the sign (polarity) flips between galvanic and electrolytic.
• Subtracting reduction potentials incorrectly (forgetting the double negative when the anode E° is negative).
• Ignoring n (electrons per ion) in Faraday stoichiometry.
• Assuming concentration cells have zero voltage because E° = 0. Nonzero E exists whenever concentrations differ.
• Confusing ΔG = −nFE with the need for a positive E for spontaneity. Positive E → negative ΔG → spontaneous galvanic discharge.