Q.Using $E^{\circ}(\text{Ag}^{+}/\text{Ag}) = +0.80\ \text{V}$ and $E^{\circ}(\text{Cu}^{2+}/\text{Cu}) = +0.34\ \text{V}$, predict whether metallic copper placed in a solution of $\text{AgNO}_3$ will spontaneously reduce $\text{Ag}^+$ ions. Justify using the sign of $E^{\circ}_{cell}$.

The Intuition: Why Does a Metal "Want" to Dissolve?

Imagine a strip of zinc metal dipped in water. Some zinc atoms on the surface have a strong urge to leave the solid and go into solution as $Zn^{2+}$ ions, leaving their two electrons behind on the metal strip. That strip now has a surplus of negative charge. The water near the strip, meanwhile, gets a slight positive charge from the dissolved $Zn^{2+}$ ions.

This separation of charge creates an electric potential difference between the metal and the solution. That difference is the electrode potential of the zinc electrode. Different metals have different "urges" to lose electrons. Copper, for example, has almost no urge — in fact, $Cu^{2+}$ ions in solution prefer to grab electrons from the metal and plate out as copper atoms.

So the electrode potential is a measure of how strongly a metal (or any electrode) tends to lose or gain electrons relative to its own ions in solution.

The Problem: We Can Only Measure Differences

You cannot measure the absolute potential of a single electrode. If you connect a voltmeter to a zinc strip in a beaker, you get nothing — the circuit is incomplete. You need a second electrode to complete the circuit, and the voltmeter reads the difference between the two electrode potentials.

This is like measuring altitude. You cannot say "this hill is 500 meters tall" without a reference point — sea level. For electrode potentials, we need a universal "sea level."

The Reference: Standard Hydrogen Electrode (SHE)

The agreed-upon zero is the Standard Hydrogen Electrode. It consists of a platinum wire (coated with finely divided platinum) dipped in a solution of $H^+$ ions at 1 M concentration, with hydrogen gas at 1 bar pressure bubbling over the platinum surface. The temperature is fixed at 298 K (25 °C).

The half-reaction at this electrode is:

By international convention, the potential of this electrode is defined as exactly 0.00 V under standard conditions.

The Precise Definition

Standard Electrode Potential ($E^\ominus$) is the potential difference developed between an electrode and its surrounding electrolyte solution, measured against the Standard Hydrogen Electrode, when all species involved in the half-reaction are at unit activity (effectively 1 M concentration for dissolved ions, 1 bar pressure for gases) and the temperature is 298 K.

The notation $E^\ominus$ uses the plimsoll symbol (a superscript zero with a horizontal bar) to indicate standard conditions.

How It Works in Practice

To measure the standard electrode potential of zinc, you construct an electrochemical cell:

• Left electrode: Zinc strip dipped in 1 M $ZnSO_4$ solution
• Right electrode: Standard Hydrogen Electrode
• Salt bridge: Connects the two solutions

The voltmeter reads the cell potential. For zinc, the reading is -0.76 V. The negative sign tells you that the zinc electrode has a stronger tendency to lose electrons than the SHE — electrons flow from the zinc electrode to the SHE through the external circuit.

For copper, the reading is +0.34 V. The positive sign means copper has a weaker tendency to lose electrons than the SHE — electrons flow from the SHE to the copper electrode. …