Galvanic Cell

How a galvanic cell produces voltage

A galvanic cell exploits the fact that metals differ in their willingness to give up electrons. Zinc gives them up easily (E° = −0.76 V); copper holds onto them tightly (E° = +0.34 V). Drop a zinc strip into copper sulfate and the difference manifests as a redox that proceeds on contact: Zn hands two electrons to Cu²⁺, plates copper onto the strip, and dissolves zinc into solution. The reaction is spontaneous and its energy normally escapes as heat.

The galvanic trick is to separate the two half-reactions in space and force electrons to take a long route between them — through an external wire — doing useful work along the way:

Anode (oxidation, left):     Zn(s) → Zn²⁺(aq) + 2e⁻
Cathode (reduction, right):  Cu²⁺(aq) + 2e⁻ → Cu(s)
Net:                         Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

The cell-diagram shorthand for this arrangement is:

Zn(s) │ Zn²⁺(aq, 1 M) ‖ Cu²⁺(aq, 1 M) │ Cu(s)
      anode               cathode
      |←  salt bridge →|

Single bars mark phase boundaries; the double bar is the salt bridge. Anode goes left, cathode right by convention. Electrons flow externally left-to-right. Inside, cations migrate through the salt bridge toward the cathode and anions toward the anode, completing the circuit and keeping each compartment neutral.

Worked example: EMF of the Daniell cell

To compute the standard EMF, look up each half-reaction in a table of standard reduction potentials and apply E°_cell = E°_cathode − E°_anode:

Cu²⁺(aq) + 2e⁻ → Cu(s)        E° = +0.34 V    (cathode, more positive)
Zn²⁺(aq) + 2e⁻ → Zn(s)        E° = −0.76 V    (anode, more negative)

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

The result is the open-circuit voltage you would measure with a high-impedance voltmeter. Two extra checks are routine. First, the sign: positive E°_cell means the reaction is spontaneous as written, which it had to be — copper plates onto zinc on contact in the lab. Second, the free-energy:

ΔG° = −nFE°cell
    = −(2)(96,485 C/mol)(1.10 V)
    = −212,267 J/mol
    ≈ −212 kJ/mol

Methane combustion releases ~800 kJ/mol; the Daniell cell delivers a fourth of that as recoverable electrical work, not heat — the whole reason batteries are useful.

For non-standard concentrations the Nernst equation handles things — at 25 °C:

E = E° − (0.0592 / n) · log10(Q)
Q = [Zn²⁺] / [Cu²⁺] = y / x

If [Cu²⁺] = 0.01 M and [Zn²⁺] = 1.0 M, Q = 100, log Q = 2, and the cell drops from 1.10 V to 1.10 − 0.0296·2 = 1.04 V. Real batteries always run below standard EMF for this reason: as the cell discharges, the Nernst correction grows.

Galvanic vs electrolytic vs concentration vs fuel cell

	Galvanic (voltaic)	Electrolytic	Concentration	Fuel cell
Driving force	Spontaneous redox	External voltage	Concentration gradient	Continuous fuel + oxidiser
E°cell	Positive	Negative (forced)	0 (Q drives EMF)	Positive
Anode polarity	Negative	Positive	Lower-concentration side	Negative (fuel side)
Energy direction	Chemical → electrical	Electrical → chemical	Mixing → electrical	Chemical → electrical (steady)
Reactants stored?	Yes, internal	Generated externally	Yes, two concentrations	No — supplied during use
Canonical example	Daniell, lead-acid, Li-ion	Hall-Héroult Al, electroplating	pH meter, ion-selective electrode	H2/O2 PEM, Toyota Mirai
Typical voltage	1-4 V per cell	2-12 V per bath (applied)	0-0.5 V (logarithmic in [ ])	0.6-1.0 V per cell at load

A working table of standard reduction potentials

Half-reaction (reduction)	E° (V vs SHE)	Role
F2(g) + 2e⁻ → 2F⁻	+2.87	Strongest practical oxidiser
MnO4⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H2O	+1.51	Lab oxidiser (titrations)
O2(g) + 4H⁺ + 4e⁻ → 2H2O	+1.23	Atmospheric oxidiser
Cu²⁺ + 2e⁻ → Cu	+0.34	Daniell cathode
2H⁺ + 2e⁻ → H2(g)	0.00 (reference)	Standard hydrogen electrode
Fe²⁺ + 2e⁻ → Fe	−0.44	Iron rusts (anode in air)
Zn²⁺ + 2e⁻ → Zn	−0.76	Daniell anode; sacrificial coating
Al³⁺ + 3e⁻ → Al	−1.66	Hall-Héroult electrolysis
Li⁺ + e⁻ → Li	−3.04	Strongest standard reducer; Li-ion anode

Pick any two rows: the higher (as reduction) runs at the cathode, the lower (reversed, as oxidation) at the anode, and the EMF is the row-difference. Cu²⁺/Cu with Zn²⁺/Zn gives 1.10 V. F₂/F⁻ with Li⁺/Li would deliver 5.91 V — impossible to build because no electrolyte survives both half-cells.

Real-world galvanic cells

• Lead-acid car battery. Pb anode and PbO₂ cathode in 4.5 M H₂SO₄. Each cell delivers 2.05 V; six in series make 12.3 V. Energy density 35 Wh/kg but very high peak current — a 600 A cold-crank pulse is routine.
• Lithium-ion phone battery. LiC₆ anode and layered-oxide cathode (NCM, LiNi_xCo_yMn_zO₂). Open-circuit 3.7-4.2 V; energy density 250 Wh/kg, the highest in commercial use. Powers ~5 billion active smartphones.
• Lemon clock cell. Zn nail + Cu coin in citric-acid juice. Open-circuit ~0.9 V — slightly under 1.10 V because the cathode reaction is 2H⁺ + 2e⁻ → H₂ (E° = 0) rather than Cu²⁺/Cu. Two lemons in series run an LCD clock drawing under 50 μA.
• Pacemaker Li-iodine cell. Sealed solid-state Li anode + I-polymer cathode. Self-discharge so low that a single cell powers an implanted pacemaker for 7-10 years.

Variants

• Concentration cell. Same half-reaction both sides, different concentrations. EMF is a pure Nernst effect: E = (0.0592 / n) · log([cathode]/[anode]). Underlies the pH meter.
• Daniell with porous frit. Original 1836 design used a porous earthenware pot instead of a salt bridge — powered telegraph networks across Europe and the US for forty years.
• Primary vs secondary cells. Primary (alkaline AA, lithium coin) are one-discharge — cathode reactions cannot be reversed practically. Secondary (Li-ion, NiMH, lead-acid) cycle hundreds to thousands of times.
• Flow battery. Electrolytes stored externally and pumped through the cell. Energy and power scale independently; vanadium redox stacks reach 500 kWh and serve as grid storage.

Common pitfalls

• Sign errors in E°_anode. Look up the reduction potential, then subtract — don't flip the anode reaction's sign yourself. The formula E°_cell = E°_cathode − E°_anode already encodes the reversal.
• Polarity confusion. Galvanic anode is negative (electrons leave); electrolytic anode is positive (driven externally). Half-reaction labels stay the same — anode is always oxidation — but polarity flips.
• Forgetting concentration effects. A "1.10 V" Daniell cell delivers 1.10 V only at 1 M and 25 °C. Use Nernst otherwise; expect tens of mV of drift across a real discharge.
• EMF vs terminal voltage. EMF is open-circuit. Under load, internal resistance and polarisation drop terminal voltage — a 12.6 V car battery can drop to 9 V during cranking.
• Omitting the salt bridge. Without it the cell delivers a microsecond burst and stops as compartments charge up. Every working galvanic cell has an ion-permeable internal path.