What is electrode potential?

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Q. What is electrode potential?

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Concept understanding — Cell Representation Nernst Equation

Cell Representation and the Nernst Equation: From Intuition to Precision

Imagine you have a Daniell cell — a zinc rod in zinc sulphate solution connected by a salt bridge to a copper rod in copper sulphate solution. You know it produces a voltage. But what happens if you dilute the copper sulphate solution? Or if you change the temperature? The voltage changes. The Nernst equation is the tool that tells you exactly how much it changes.

The Intuition First

A battery works because the two half-cells "want" to react — zinc wants to lose electrons, copper ions want to gain them. This "want" is measured as a tendency, or potential. But the strength of that tendency depends on how crowded the ions are.

Think of it like this: If you have a room full of people who all want to leave (like zinc ions wanting to form), the push to get out is stronger when the room is packed. If the room is nearly empty, the push is weaker. Similarly, for copper ions wanting to enter the metal (gain electrons), the pull is stronger when there are many copper ions around, and weaker when there are few.

The Nernst equation quantifies this: the actual cell potential depends on the concentrations (or activities) of the ions involved.

The Precise Statement

For a general cell reaction:

aA + bB \rightarrow cC + dD

The cell potential $E$ under non-standard conditions is given by:

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

Where:

$E$ = cell potential under the given conditions (in volts)
$E^\circ$ = standard cell potential (when all reactants/products are at 1 M, 1 atm, 25°C)
$R$ = universal gas constant (8.314 J/mol·K)
$T$ = temperature in Kelvin
$n$ = number of moles of electrons transferred in the balanced half-reactions
$F$ = Faraday constant (96,485 C/mol)
$Q$ = reaction quotient = $\frac{[C]^c [D]^d}{[A]^a [B]^b}$ (using concentrations for dilute solutions)

At 25°C (298 K), the equation simplifies to a very practical form:

E = E^\circ - \frac{0.0591}{n} \log_{10} Q

The 0.0591 comes from $\frac{2.303RT}{F}$ at 298 K. Notice it uses $\log_{10}$ (common log), not natural log.

Cell Representation: How We Write It

In electrochemistry, we represent a cell with a shorthand notation. For the Daniell cell:

\text{Zn(s)} \mid \text{Zn}^{2+}(\text{aq}) \parallel \text{Cu}^{2+}(\text{aq}) \mid \text{Cu(s)}

The single vertical line $\mid$ represents a phase boundary (solid electrode | solution). The double line $\parallel$ represents the salt bridge.

The anode (oxidation) is written on the left, the cathode (reduction) on the right. Electrons flow from left to right in the external circuit.

Applying the Nernst Equation to a Cell Representation

For the Daniell cell, the half-reactions are:

Anode (oxidation): $\text{Zn(s)} \rightarrow \text{Zn}^{2+}(\text{aq}) + 2e^-$
Cathode (reduction): $\text{Cu}^{2+}(\text{aq}) + 2e^- \rightarrow \text{Cu(s)}$

Overall: $\text{Zn(s)} + \text{Cu}^{2+}(\text{aq}) \rightarrow \text{Zn}^{2+}(\text{aq}) + \text{Cu(s)}$

Here $n = 2$ (two electrons transferred). The reaction quotient is:

Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]}

So the Nernst equation becomes:

E = E^\circ - \frac{0.0591}{2} \log_{10} \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]}

Note

Solids (Zn, Cu) do not appear in $Q$ because their concentrations are constant (activity = 1).

A Worked Example

Suppose you have a Daniell cell where $[\text{Zn}^{2+}] = 0.1$ M and $[\text{Cu}^{2+}] = 1.0$ M at 25°C. $E^\circ$ for the cell is 1.10 V.

$E = 1.10 - \frac{0.0591}{2} \log_{10} \frac{0.1}{1.0}$ …

Why this formula?

Cell Representation & the Nernst Equation: Why It Works

The Core Question

Why does a cell's voltage change when concentrations change? The Nernst equation answers this — but the reason lies in the link between chemical free energy and electrical work.

1. The Fundamental Link: Gibbs Free Energy & Cell Potential

A galvanic cell does electrical work. The maximum useful work a cell can do equals the change in Gibbs free energy ( $\Delta G$ ):

\Delta G = -nFE_{\text{cell}}

Where:

$n$ = moles of electrons transferred
$F$ = Faraday constant ( $96,485 \, \text{C mol}^{-1}$ )
$E_{\text{cell}}$ = cell potential (volts)

Why negative? A spontaneous reaction has $\Delta G < 0$ and $E_{\text{cell}} > 0$ — the negative sign makes this consistent.

2. The Chemical Side: $\Delta G$ Depends on Concentration

For a general redox reaction:

aA + bB \rightarrow cC + dD

The Gibbs free energy under non-standard conditions is:

\Delta G = \Delta G^\circ + RT \ln Q

Where $Q$ is the reaction quotient:

Q = \frac{[C]^c [D]^d}{[A]^a [B]^b}

Why this form? It comes from the relationship between chemical potential and concentration — the entropy of mixing drives concentration dependence.

3. Combining Both Sides: The Derivation

Set the electrical work equal to the chemical free energy change:

-nFE_{\text{cell}} = -nFE^\circ_{\text{cell}} + RT \ln Q

Divide both sides by $-nF$ :

E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q

This is the Nernst equation.

4. The "Why" in Plain Terms

Concept	Physical Meaning
$E^\circ_{\text{cell}}$	Voltage when all species are at 1 M (standard state)
$-\frac{RT}{nF} \ln Q$	Correction factor — adjusts voltage for real concentrations
$Q$	Tells you how far the reaction is from equilibrium

Key insight: When $Q = K$ (equilibrium), $E_{\text{cell}} = 0$ — the battery is dead because no net reaction occurs.

5. The Common Form (log base 10)

At $25^\circ \text{C}$ ( $298 \, \text{K}$ ):

\frac{RT}{F} \ln 10 \approx 0.0592 \, \text{V}

So:

E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0592}{n} \log_{10} Q

Why convert to log? Exam convenience — most concentration values are powers of 10.

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Electrode potential is the voltage difference between a metal electrode and its surrounding electrolyte solution, measured relative to a standard reference electrode. It quantifies the tendency of an electrode to gain or lose electrons.

Electrode potential is one of those concepts that seems abstract at first, but it’s really just a measure of how badly a metal wants to be an ion (or vice versa). Think of it like a tug-of-war between the metal atoms and their ions in solution.

When you dip a metal rod into a solution of its own ions, two things can happen:

The metal atoms can lose electrons and go into solution as positive ions (oxidation).
The metal ions in solution can gain electrons and deposit onto the rod as metal atoms (reduction).

Which direction wins depends on the metal’s nature. Zinc, for example, readily gives up electrons — it has a strong tendency to oxidise. Copper, on the other hand, prefers to stay as metal or even pull ions out of solution.

The electrode potential is the voltage that builds up at the metal-solution interface because of this charge separation. It’s a direct measure of that tendency.

Important

You can never measure the absolute potential of a single electrode. You always measure the potential difference between two electrodes. That’s why we use a standard reference electrode (usually the Standard Hydrogen Electrode, SHE) as a zero point.

1. The standard hydrogen electrode (SHE) — our reference point

To give electrode potentials a numerical value, we define the SHE as exactly 0.00 V at all temperatures. It consists of:

A platinum electrode (inert, just conducts electrons)
Hydrogen gas at 1 bar pressure bubbled over it
An acidic solution with $H^+$ ions at 1 M concentration

The half-reaction is:

2H^+(aq) + 2e^- \rightleftharpoons H_2(g)

When we connect any other electrode to the SHE and measure the voltage, that reading is the standard electrode potential ( $E^\ominus$ ) of that electrode.

E^\ominus = \text{potential difference when the electrode is connected to SHE under standard conditions (1 M, 1 bar, 298 K)}

2. How the Nernst equation connects concentration to potential

The standard potential $E^\ominus$ only applies when all species are at 1 M concentration and 1 bar pressure. In real cells, concentrations vary — and so does the potential. The Nernst equation tells us exactly how.

For a general reduction half-reaction:

aA + bB + ne^- \rightarrow cC + dD

The Nernst equation is:

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

Where:

$E$ = electrode potential under non-standard conditions
$E^\ominus$ = standard electrode potential
$R$ = gas constant (8.314 J mol⁻¹ K⁻¹)
$T$ = temperature in Kelvin
$n$ = number of electrons transferred
$F$ = Faraday constant (96485 C mol⁻¹)
$Q$ = reaction quotient (products over reactants, raised to stoichiometric coefficients)

At 298 K, using log₁₀, this simplifies to:

E = E^\ominus - \frac{0.0591}{n} \log_{10} Q

Tip

The 0.0591 comes from $(2.303RT)/F$ at 298 K. It’s a constant you’ll use so often in electrochemistry that it becomes second nature. For quick calculations, remember: 0.059 V per decade of concentration change per electron transferred.

3. What the sign of electrode potential tells you

The sign convention is crucial for exams:

Positive $E^\ominus$ → The reduction half-reaction is spontaneous compared to SHE. The electrode tends to gain electrons (act as a cathode in a galvanic cell).
Negative $E^\ominus$ → The oxidation half-reaction is spontaneous compared to SHE. The electrode tends to lose electrons (act as an anode).

For example:

$Cu^{2+}/Cu$ : $E^\ominus = +0.34$ V → Copper ions readily reduce to copper metal.
$Zn^{2+}/Zn$ : $E^\ominus = -0.76$ V → Zinc metal readily oxidises to zinc ions. …

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Common Mistakes on "Electrode Potential" (and How to Avoid Them)

Electrode potential is a fundamental concept in electrochemistry. Here are the most frequent errors students make, along with clear strategies to avoid them.

Mistake 1: Confusing Electrode Potential with Cell Potential

The error: Students often use "electrode potential" and "cell potential" interchangeably. They think the potential of a single electrode is the same as the voltage of a full electrochemical cell.

Why it happens: Both involve voltage differences, but the context is different.

How to avoid:

Remember: Electrode potential is the potential difference between a metal electrode and the solution it is immersed in (measured relative to a standard reference, usually the Standard Hydrogen Electrode).
Cell potential ( $E_{\text{cell}}$ ) is the difference between two electrode potentials:

E_{\text{cell}} = E_{\text{cathode}} - E_{\text{anode}}

Mnemonic: "Single electrode → single potential; two electrodes → cell potential."

Mistake 2: Forgetting the Standard Conditions

The error: Students quote electrode potential values without specifying that they are standard electrode potentials ( $E^\ominus$ ), measured under standard conditions.

Why it happens: Many textbooks list $E^\ominus$ values as if they are absolute, leading to casual usage.

How to avoid:

Always state: Standard electrode potential is measured at:
- 1 M concentration for all ions
- 1 atm pressure for gases
- 298 K (25°C)
Write correctly: $E^\ominus_{\text{Zn}^{2+}/\text{Zn}} = -0.76\ \text{V}$ (not just $-0.76\ \text{V}$ )
Exam tip: If conditions change, the potential changes (use the Nernst equation).

Mistake 3: Misinterpreting the Sign Convention

The error: Students think a negative electrode potential means the electrode is "bad" or "weak." They confuse the sign with reactivity.

Why it happens: Everyday language associates "negative" with "less" or "worse."

How to avoid:

Understand the meaning: A negative $E^\ominus$ $E^{⊖}$ means the electrode has a greater tendency to lose electrons (i.e., it is a stronger reducing agent).
- Example: $E^\ominus_{\text{Zn}^{2+}/\text{Zn}} = -0.76\ \text{V}$ → Zn readily oxidises (loses electrons).
Positive $E^\ominus$ means the electrode has a greater tendency to gain electrons (stronger oxidising agent).
- Example: $E^\ominus_{\text{Cu}^{2+}/\text{Cu}} = +0.34\ \text{V}$ → Cu²⁺ readily reduces.
Rule: More negative → stronger reducing agent; more positive → stronger oxidising agent.

Mistake 4: Confusing Anode and Cathode Based on Sign

The error: Students assume the negative electrode is always the anode and the positive electrode is always the cathode — but this is only true for galvanic (voltaic) cells.

Why it happens: The sign convention is taught early, but it flips in electrolytic cells.

How to avoid:

Remember the definitions:
- Anode: Where oxidation occurs (loss of electrons).
- Cathode: Where reduction occurs (gain of electrons).
Sign depends on cell type:
- Galvanic cell: Anode is negative, cathode is positive.
- Electrolytic cell: Anode is positive, cathode is negative.
Mnemonic: "In a galvanic cell, the anode is negative (AN = AN: Anode Negative). In electrolytic, it flips."

Mistake 5: Using the Wrong Formula for Cell Potential

The error: Students write $E_{\text{cell}} = E_{\text{cathode}} + E_{\text{anode}}$ or reverse the subtraction.

Why it happens: Some textbooks present it differently, or students memorise without understanding.

How to avoid:

Always use:

E_{\text{cell}} = E_{\text{cathode}} - E_{\text{anode}}

Check with an example: For the Daniell cell:
- $E^\ominus_{\text{Cu}^{2+}/\text{Cu}} = +0.34\ \text{V}$ (cathode)
- $E^\ominus_{\text{Zn}^{2+}/\text{Zn}} = -0.76\ \text{V}$ (anode)
- $E^\ominus_{\text{cell}} = 0.34 - (-0.76) = +1.10\ \text{V}$ (positive, spontaneous)
If you get a negative value, you likely reversed the subtraction — swap the electrodes.

Mistake 6: Ignoring the Nernst Equation for Non-Standard Conditions

The error: Students use standard electrode potentials even when concentrations or pressures are not standard.

Why it happens: They memorise $E^\ominus$ values but forget that real conditions differ.

How to avoid:

Use the Nernst equation when conditions are non-standard: …

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Q.What is electrode potential?

Concept understanding — Cell Representation Nernst Equation

Cell Representation and the Nernst Equation: From Intuition to Precision

The Intuition First

The Precise Statement

Cell Representation: How We Write It

Applying the Nernst Equation to a Cell Representation

A Worked Example

Why this formula?

Cell Representation & the Nernst Equation: Why It Works

The Core Question

1. The Fundamental Link: Gibbs Free Energy & Cell Potential

2. The Chemical Side: $\Delta G$ Depends on Concentration

3. Combining Both Sides: The Derivation

4. The "Why" in Plain Terms

5. The Common Form (log base 10)

1. The standard hydrogen electrode (SHE) — our reference point

2. How the Nernst equation connects concentration to potential

3. What the sign of electrode potential tells you

Concept: Electrode Potential — Definition via the Standard Hydrogen Electrode (SHE)

Method: Defining and Interpreting Electrode Potential

Common Mistakes on "Electrode Potential" (and How to Avoid Them)

Mistake 1: Confusing Electrode Potential with Cell Potential

Mistake 2: Forgetting the Standard Conditions

Mistake 3: Misinterpreting the Sign Convention

Mistake 4: Confusing Anode and Cathode Based on Sign

Mistake 5: Using the Wrong Formula for Cell Potential

Mistake 6: Ignoring the Nernst Equation for Non-Standard Conditions

Q.What is electrode potential?

1. The standard hydrogen electrode (SHE) — our reference point

2. How the Nernst equation connects concentration to potential

3. What the sign of electrode potential tells you

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