balancing half reactions and their cell potentials

[Brandon Li]

When you balance a half equation, i.e. scale it, why do you not multiply the standard E value by the same scalar? For example, given the half equation Mg2+ + 2e- -> Mg and we multiply by 3 to form 3Mg2+ + 6e- -> 3Mg2, why do we keep the same E =- 2.38 value?

[906013563]

When balancing a half-reaction equation by multiplying it by a scalar (such as your example of multiplying the magnesium half-reaction by 3), the standard reduction potential remains unchanged. This is because the standard reduction potential is an intrinsic property of the half-reaction and is independent of the stoichiometry of the reaction.
for your specific example:
when you multiply the magnesium half-reaction by 3 to balance it, you're essentially representing three individual magnesium ions (Mg 2+) being reduced to form three atoms of magnesium (Mg). However, the fundamental process of magnesium ion reduction (each Mg 2+ gaining two electrons to form Mg) remains the same, so the standard reduction potential associated with this process doesn't change.

[105717435]

When scaling a half-equation, the standard reduction potential (E°) remains unchanged because it represents the inherent tendency of the species involved to gain or lose electrons, independent of stoichiometric coefficients.