DAT General Chemistry: Calculating the Standard Cell Potential

DAT High-Yield Concept

Standard Cell Potential Formula: Calculate using standard reduction potentials: $E^\circ_{\text{cell}} = E^\circ_{\text{red}}(\text{cathode}) - E^\circ_{\text{red}}(\text{anode})$ or by adding oxidation potential: $E^\circ_{\text{cell}} = E^\circ_{\text{red}}(\text{cathode}) + E^\circ_{\text{ox}}(\text{anode})$ .
Sign Reversal: Reversing a reduction half-reaction to express it as an oxidation reverses the sign of its potential ( $E^\circ_{\text{ox}} = -E^\circ_{\text{red}}$ ).
Intensive Property: Voltage measures potential difference (joules per coulomb). Scaling stoichiometric coefficients in a half-reaction does not change its $E^\circ$ .
Predicting Spontaneity: A positive standard cell potential ( $E^\circ_{\text{cell}} > 0$ ) corresponds to a spontaneous redox reaction under standard conditions.

Calculating Standard Cell Potential ( $E^\circ_{\text{cell}}$ )

An electrochemical cell converts chemical energy into electrical energy through redox reactions. Under standard conditions— $\pu{1.0 M}$ solute concentrations, $\pu{1.0 atm}$ gas partial pressures, and a temperature of $\pu{25 degC}$ ( $\pu{298 K}$ )—the electric potential difference between electrodes is the standard cell potential ( $E^\circ_{\text{cell}}$ ).

Standard potentials for individual half-reactions are measured relative to the Standard Hydrogen Electrode (SHE), which is assigned an arbitrary potential of $E^\circ = \pu{0.00 V}$ .

standard electrode potential of Zn2+/Zn half-cell (Source: Andyrendall · Public domain · Wikimedia Commons)

Standard reduction potentials (covered in depth in their own lesson) are compiled into reference tables listing species by their tendency to gain electrons.

Table of standard electrode potentials (Source: Tem5psu · CC BY-SA 3.0 · Wikimedia Commons)

To calculate overall cell voltage, identify the reduction occurring at the cathode and oxidation occurring at the anode. You can calculate $E^\circ_{\text{cell}}$ using directly tabulated reduction potentials:

E^\circ_{\text{cell}} = E^\circ_{\text{red}}(\text{cathode}) - E^\circ_{\text{red}}(\text{anode})

Alternatively, express the anode reaction as an oxidation and sum the two potentials:

E^\circ_{\text{cell}} = E^\circ_{\text{red}}(\text{cathode}) + E^\circ_{\text{ox}}(\text{anode})

Sign Reversal and the Intensive Nature of Potential

When reversing a standard reduction half-reaction to write it as an oxidation, change the sign of its potential:

E^\circ_{\text{ox}} = -E^\circ_{\text{red}}

Crucially, standard cell potential is an intensive property. Voltage represents energy per unit charge ( $\pu{1 V} = \pu{1 J/C}$ ). Multiplying a half-reaction by stoichiometric coefficients to balance electron transfer increases both total energy and total charge proportionately, leaving the potential difference unchanged. Never multiply $E^\circ$ by stoichiometric factors.

Combining two half-reactions: flip the sign once, and never scale the potential — To combine two half-reactions, first look both of them up in the table exactly as printed, which means both as reductions. The one with the more positive standard reduction potential is the half that actually gets reduced, so it is the cathode; the other is forced to run backwards and is the anode. Reversing that half-reaction reverses the sign of its potential but leaves the magnitude alone, and the two potentials are then added. The shortcut, standard cell potential equals cathode minus anode with both values taken as reduction potentials, gives the same number without any reversing, but you must not reverse a sign and subtract as well or the answer comes out backwards. Multiplying a half-reaction by a coefficient does not change its potential, because potential is energy per unit charge and scaling multiplies both. A positive standard cell potential means a negative standard free-energy change, so the reaction as written is spontaneous.

DAT Mnemonic: Remember RED CAT (REDuction at CAThode) and AN OX (ANode is OXidation).

Intensive vs. Extensive Thermodynamic Properties:

Property	Classification	Depends on Amount?	Scaled by Stoichiometry?
Cell Potential ( $E^\circ$ )	Intensive	No	No
Gibbs Free Energy ( $\Delta G^\circ$ )	Extensive	Yes	Yes
Enthalpy ( $\Delta H^\circ$ )	Extensive	Yes	Yes

Predicting Reaction Spontaneity from $E^\circ_{\text{cell}}$

References

Sources returned by Google Search grounding during lesson verification.

Chad's Prep: Standard Cell Potentials — chadsprep.com
LibreTexts: Calculating Standard Cell Potentials — chem.libretexts.org

Calculating the Standard Cell Potential

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