Measurement of Electrode Potential — Revision Notes

⚡ 30-Second Revision

Electrode Potential ($E$): — Potential difference at electrode-electrolyte interface.
Standard Electrode Potential ($E^circ$): — $E$ at $298,\text{K}$, $1,\text{M}$ ions, $1,\text{atm}$ gases.
Standard Hydrogen Electrode (SHE): — Reference electrode, $E^circ_{\text{SHE}} = 0.00,\text{V}$.
Cell Potential ($E_{ ext{cell}}$): — $E_{\text{cathode}} - E_{\text{anode}}$.
Nernst Equation (at $298, ext{K}$): — $E = E^circ - \frac{0.0592}{n} \log Q$ (for half-cell) or $E_{\text{cell}} = E^circ_{\text{cell}} - \frac{0.0592}{n} \log Q$ (for cell).
Stronger Reducing Agent: — More negative $E^circ_{\text{red}}$.
Stronger Oxidizing Agent: — More positive $E^circ_{\text{red}}$.
Spontaneous Reaction: — $E_{\text{cell}} > 0$.

2-Minute Revision

Electrode potential is the potential difference at the interface of an electrode and its electrolyte, arising from redox tendencies. Since absolute potential cannot be measured, we use a reference: the Standard Hydrogen Electrode (SHE), whose standard potential ($E^circ_{\text{SHE}}$) is arbitrarily set to $0.

00, ext{V}$. Standard conditions for$E^circ$are$298, ext{K}$,$1, ext{M}$ion concentration, and$1, ext{atm}$gas pressure. To measure an unknown$E^circ$, we couple it with SHE and measure the cell potential.

By convention, potentials are reported as standard reduction potentials. A more positive $E^circ_{\text{red}}$ indicates a stronger oxidizing agent (easier reduction), while a more negative $E^circ_{\text{red}}$ indicates a stronger reducing agent (easier oxidation).

For a complete galvanic cell, the standard cell potential ($E^circ_{\text{cell}}$) is calculated as $E^circ_{\text{cathode}} - E^circ_{\text{anode}}$. The cathode is where reduction occurs (higher $E^circ_{\text{red}}$), and the anode is where oxidation occurs (lower $E^circ_{\text{red}}$).

If $E^circ_{\text{cell}}$ is positive, the reaction is spontaneous. When conditions are non-standard, the Nernst equation is used: $E = E^circ - \frac{0.0592}{n} \log Q$ (at $298,\text{K}$), where $n$ is electrons transferred and $Q$ is the reaction quotient.

This equation allows us to calculate actual potentials and understand how concentration changes affect cell voltage.

5-Minute Revision

The measurement of electrode potential is a cornerstone of electrochemistry. An electrode potential ($E$) is the potential difference that develops at the interface between a metal electrode and its surrounding electrolyte solution.

This potential arises from the dynamic equilibrium between the metal atoms and their ions, involving both oxidation and reduction processes. Crucially, the absolute potential of a single electrode cannot be measured directly; it must always be measured relative to a reference electrode.

The universally accepted primary reference is the Standard Hydrogen Electrode (SHE). Its standard electrode potential ($E^circ_{\text{SHE}}$) is defined as exactly $0.00,\text{V}$ under standard conditions.

These standard conditions are: $298,\text{K}$ ($25^circ\text{C}$) temperature, $1,\text{M}$ concentration for all ionic species, and $1,\text{atm}$ partial pressure for any gases involved. The SHE consists of a platinum electrode immersed in $1,\text{M H}^+$ solution, with $ext{H}_2$ gas at $1,\text{atm}$ bubbling over it.

Platinum acts as an inert surface for the redox reaction $2\text{H}^+(\text{aq}) + 2\text{e}^- \rightleftharpoons \text{H}_2(\text{g})$.

To measure the standard electrode potential of an unknown half-cell, it is coupled with the SHE to form a galvanic cell. The voltmeter reading then directly gives the standard potential of the unknown half-cell.

By convention, these potentials are reported as standard reduction potentials. For example, if a zinc half-cell ($1,\text{M Zn}^{2+}$) is connected to SHE, and the cell potential is $0.76,\text{V}$ with electrons flowing from Zn to SHE, then $E^circ_{ ext{Zn}^{2+}/ ext{Zn}} = -0.

76, ext{V}$. A more negative reduction potential indicates a greater tendency for oxidation (stronger reducing agent), while a more positive reduction potential indicates a greater tendency for reduction (stronger oxidizing agent).

For a complete galvanic cell, the standard cell potential ($E^circ_{\text{cell}}$) is calculated using the formula $E^circ_{\text{cell}} = E^circ_{\text{cathode}} - E^circ_{\text{anode}}$. The cathode is the half-cell with the more positive (or less negative) standard reduction potential, where reduction occurs. The anode is the half-cell with the less positive (or more negative) standard reduction potential, where oxidation occurs. A positive $E^circ_{\text{cell}}$ indicates a spontaneous reaction.

When conditions deviate from standard, the electrode potential ($E$) changes. The Nernst equation quantifies this change:

$$E = E^circ - \frac{RT}{nF} ln Q$$

At $298,\text{K}$, this simplifies to: $$ E = E^circ - \frac{0.

0592}{n} log Q $$Here,$n$is the number of electrons transferred in the half-reaction (or overall cell reaction), and$Q$is the reaction quotient. For a reduction half-reaction$ ext{M}^{n+}( ext{aq}) + n ext{e}^- ightarrow ext{M}( ext{s})$,$Q = \frac{1}{[ ext{M}^{n+}]}$.

The Nernst equation is vital for calculating potentials under varying concentrations and pressures, and for understanding how cell voltage responds to changes in conditions.

Worked Example: Calculate the cell potential of a galvanic cell at $298,\text{K}$ consisting of a $ext{Zn}/\text{Zn}^{2+}$ electrode ($[\text{Zn}^{2+}] = 0.01,\text{M}$) and a $ext{Cu}/\text{Cu}^{2+}$ electrode ($[\text{Cu}^{2+}] = 0.1,\text{M}$). Given $E^circ_{\text{Zn}^{2+}/\text{Zn}} = -0.76,\text{V}$ and $E^circ_{\text{Cu}^{2+}/\text{Cu}} = +0.34,\text{V}$.

1
Identify Cathode/Anode and $E^circ_{ ext{cell}}$: — $ext{Cu}^{2+}/\text{Cu}$ has higher $E^circ$ ($+0.34,\text{V}$), so it's the cathode. $ext{Zn}^{2+}/\text{Zn}$ has lower $E^circ$ ($-0.76,\text{V}$), so it's the anode.

$E^circ_{\text{cell}} = E^circ_{\text{cathode}} - E^circ_{\text{anode}} = (+0.34,\text{V}) - (-0.76,\text{V}) = +1.10,\text{V}$.

1
**Write Overall Reaction and find $n$:**

Anode (oxidation): $ext{Zn}(\text{s}) \rightarrow \text{Zn}^{2+}(\text{aq}) + 2\text{e}^-$ Cathode (reduction): $ext{Cu}^{2+}(\text{aq}) + 2\text{e}^- \rightarrow \text{Cu}(\text{s})$ Overall: $ext{Zn}(\text{s}) + \text{Cu}^{2+}(\text{aq}) \rightarrow \text{Zn}^{2+}(\text{aq}) + \text{Cu}(\text{s})$ Number of electrons transferred, $n=2$.

1
**Calculate Reaction Quotient $Q$:**

$Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]} = \frac{0.01}{0.1} = 0.1$.

1
Apply Nernst Equation:

$E_{\text{cell}} = E^circ_{\text{cell}} - \frac{0.0592}{n} \log Q$ $E_{\text{cell}} = +1.10 - \frac{0.0592}{2} \log(0.1)$ $E_{\text{cell}} = +1.10 - 0.0296 \times (-1)$ (since $log(0.1) = -1$) $E_{\text{cell}} = +1.10 + 0.0296 = +1.1296,\text{V}$.

Prelims Revision Notes

Measurement of Electrode Potential (NEET Revision)

1. Electrode Potential ($E$):

Potential difference at electrode-electrolyte interface.
Arises from tendency of electrode to oxidize/reduce.
Cannot be measured absolutely; always relative.

2. Standard Electrode Potential ($E^circ$):

Electrode potential under specific standard conditions:

* Temperature: $298,\text{K}$ ($25^circ\text{C}$) * Concentration: $1,\text{M}$ for all ionic species. * Pressure: $1,\text{atm}$ (or $1,\text{bar}$) for all gases.

Conventionally reported as standard reduction potentials.

3. Standard Hydrogen Electrode (SHE):

Primary Reference Electrode.
Assigned $E^circ = 0.00, ext{V}$ — at all temperatures.
Construction: — Platinum electrode in $1,\text{M H}^+$ solution, with $ext{H}_2$ gas at $1,\text{atm}$ bubbling over it.
Half-reaction: — $2\text{H}^+(\text{aq}, 1,\text{M}) + 2\text{e}^- \rightleftharpoons \text{H}_2(\text{g}, 1,\text{atm})$.
Function: — Used to measure $E^circ$ of other half-cells by coupling them to SHE.
Practicality: — Difficult to construct and maintain precisely.

4. Cell Potential ($E_{ ext{cell}}$):

Potential difference between two half-cells in a galvanic cell.
Formula: — $E_{\text{cell}} = E_{\text{cathode}} - E_{\text{anode}}$.
Cathode: — Electrode where reduction occurs (higher $E^circ_{\text{red}}$).
Anode: — Electrode where oxidation occurs (lower $E^circ_{\text{red}}$).
Spontaneity: — If $E_{\text{cell}} > 0$, the reaction is spontaneous.

5. Nernst Equation (for Non-Standard Conditions):

Relates $E$ to $E^circ$, temperature, and concentrations/pressures.
General form: — $E = E^circ - \frac{RT}{nF} ln Q$
At $298, ext{K}$: — $E = E^circ - \frac{0.0592}{n} \log Q$
For a reduction half-reaction $ ext{M}^{n+}( ext{aq}) + n ext{e}^- ightarrow ext{M}( ext{s})$: — $Q = \frac{1}{[\text{M}^{n+}]}$.
For a cell reaction: — $Q = \frac{[\text{Products}]}{[\text{Reactants}]}$ (excluding pure solids/liquids).
$n$: Number of electrons transferred in the balanced half-reaction/cell reaction.

6. Electrochemical Series:

List of elements/ions arranged by increasing $E^circ_{\text{red}}$ values.
Interpretation:

* Higher (more positive) $E^circ_{\text{red}}$: Stronger oxidizing agent (species easily reduced). * Lower (more negative) $E^circ_{\text{red}}$: Stronger reducing agent (species easily oxidized).

7. Relationship with Thermodynamics:

$Delta G^circ = -nFE^circ_{\text{cell}}$ (Standard Gibbs Free Energy)
$Delta G^circ = -RT ln K$ (Equilibrium Constant)
$E^circ_{\text{cell}} = \frac{0.0592}{n} \log K$ (at $298,\text{K}$)

Key Points for NEET:

Always identify cathode/anode correctly.
Balance reactions to find 'n' for Nernst equation.
Correctly formulate 'Q' for Nernst equation (solids/liquids = 1).
Practice log calculations and sign conventions.

Vyyuha Quick Recall

SHE is ZERO for Standard conditions: Hydrogen, Electrode, Zero potential, Exact conditions (1M, 1atm, 298K).

Nernst Equation for Non-Standard: "Every Electrode Needs Reaction Temperature, Numerous Factors, and Log Quickly!" (E = E° - (RT/nF)lnQ)