F3.3 Relate half-cell voltages to overall cell potential

Ontario Grade 12 Chemistry

Electrochemistry

SCH4U study topic F3.3: relating two reduction potentials to the voltage of a galvanic cell

When two different half-cells are connected, a voltmeter can show a voltage across the electrodes. The reading belongs to the complete cell: it depends on both half-cells. To understand that reading, first recall that oxidation is the loss of electrons and reduction is the gain of electrons. In a galvanic cell, one half-cell supplies electrons while the other accepts them. Comparing the half-cell reduction potentials lets us identify which process occurs at each electrode and calculate the overall cell potential.

What you will learn

Explain what a half-cell reduction potential represents.
Identify the cathode and anode by comparing reduction potentials.
Calculate cell potential from the two half-cell reduction potentials.
Explain why balancing a half-reaction does not change its potential.

1. From electron transfer to half-cells

A redox reaction transfers electrons between reacting particles. Oxidation releases electrons, while reduction accepts them. These processes occur together: electrons released by one substance are accepted by another.

In a galvanic cell, the oxidation and reduction processes occur in separate half-cells. A half-cell consists of an electrode and the solution containing the particles involved in its reaction. Electrons move through the external wire from the electrode where oxidation occurs to the electrode where reduction occurs. A voltmeter connected across the electrodes measures the cell’s potential difference, also called its voltage.

At the particle level, the two half-cells have different tendencies to gain electrons. Their difference is what gives the connected cell its voltage. Neither half-cell’s listed potential, on its own, is the voltage of the complete cell.

Oxidation releases electrons; reduction accepts electrons.
Cell potential depends on both half-cells.

2. Read and compare reduction potentials

A reduction potential is a voltage assigned to a half-reaction written in the reduction direction. Reference tables give reduction potentials for half-reactions. The values share a reference, which allows them to be compared. The standard cell potential is the cell voltage calculated from standard reduction potentials.

A more positive reduction potential means that reduction is more favourable relative to the shared reference. When two half-cells form a galvanic cell, the half-reaction with the more positive reduction potential occurs as reduction at the cathode. The cathode is the electrode where reduction occurs. The other half-cell operates as oxidation at the anode, the electrode where oxidation occurs.

The reference table still lists the anode half-reaction as a reduction. For the cell reaction, that half-reaction is reversed to show oxidation. A useful calculation rule avoids changing the table value’s sign by keeping both values as reduction potentials: subtract the anode’s reduction potential from the cathode’s reduction potential.

A positive result is consistent with the chosen direction of a galvanic cell. It means the cell potential calculated from the supplied standard reduction potentials is positive for that direction.

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

The more positive reduction potential identifies the cathode reduction.
The anode reaction is oxidation, but use its tabulated reduction potential in the subtraction.
Calculate cathode reduction potential minus anode reduction potential.

3. Balance the reaction without scaling voltages

To write the overall reaction, use the more positive half-reaction as the reduction. Reverse the other half-reaction to show oxidation. Then balance the electrons lost and gained so the electron count cancels when the half-reactions are added. The resulting overall reaction must conserve atoms and net charge.

Balancing can require multiplying a half-reaction by a number. That changes the number of particles represented in the reaction, not the half-cell voltage. Do not multiply a reduction potential by the balancing number. Use the original table values in the cell-potential calculation.

Keep the units in the calculation. Half-cell and cell potentials are measured in volts, abbreviated V. Report the result to a sensible precision based on the values provided. Check the reaction and the voltage independently: electrons must cancel in the reaction, and the potential calculation must use cathode minus anode.

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

Balance electron counts to form the overall reaction.
Do not multiply a half-cell potential when balancing a half-reaction.
Use volts for the potentials and check the subtraction order.

4. Interpret the result

The cell potential is a difference between the two tabulated reduction potentials. It is not their sum. Subtracting the anode reduction potential accounts for that half-reaction running in reverse as oxidation in the cell.

A common sign pattern is a positive cathode reduction potential and a negative anode reduction potential. Subtracting a negative value increases the result. Keep the parentheses when substituting values; this makes the signs easier to track.

The voltage is not a count of electrons or a measure of how much material reacts. Balancing the overall reaction and finding the cell potential answer different questions: one gives the particle proportions, and the other gives the voltage difference between the half-cells.

The overall cell potential is a difference, not a sum.
Parentheses help prevent sign errors.
Reaction coefficients and cell potential have different meanings.

Worked example

Finding the potential of a zinc–copper cell

A zinc half-cell and a copper half-cell are connected as a galvanic cell. The standard reduction potentials are

\mathrm{Zn^{2+}(aq)+2e^-\rightarrow Zn(s)}

,

-0.76\,\mathrm{V}

, and

\mathrm{Cu^{2+}(aq)+2e^-\rightarrow Cu(s)}

,

+0.34\,\mathrm{V}

. Identify the cathode and anode, write the balanced overall reaction, and calculate the standard cell potential.

Identify the cathode
Copper has the more positive reduction potential. Its half-reaction remains a reduction, so the copper electrode is the cathode. Zinc is the anode, where oxidation occurs.
$+0.34\,\mathrm{V}>-0.76\,\mathrm{V}$
Combine the half-reactions
Reverse the zinc reduction half-reaction to show oxidation. Each half-reaction involves two electrons, so they cancel when the reactions are added. The resulting equation conserves atoms and net charge.
$\mathrm{Zn(s)+Cu^{2+}(aq)\rightarrow Zn^{2+}(aq)+Cu(s)}$
Calculate the cell potential
Use the tabulated reduction potential for each half-cell. Subtract the anode value from the cathode value. Subtracting the negative zinc value gives a positive cell potential.
$E^\circ_{\text{cell}}=(+0.34\,\mathrm{V})-(-0.76\,\mathrm{V})=+1.10\,\mathrm{V}$

Answer: The cathode is the copper electrode, and the anode is the zinc electrode. The balanced overall reaction is

\mathrm{Zn(s)+Cu^{2+}(aq)\rightarrow Zn^{2+}(aq)+Cu(s)}

. The standard cell potential is

+1.10\,\mathrm{V}

.

Check: The equation has one zinc atom and one copper atom on each side, and its net charge is

+2

on each side. The electrons cancel when the half-reactions are added. The positive cell potential matches the chosen galvanic-cell direction.

Common mistakes and how to avoid them

Adding the two tabulated reduction potentials.

Correction: Subtract the anode reduction potential from the cathode reduction potential.

Reversing the anode half-reaction, changing its potential’s sign, and then subtracting it as if it were still the tabulated reduction potential.

Correction: Use the stated rule consistently: keep both tabulated values as reduction potentials and calculate cathode minus anode.

Multiplying a half-cell potential when multiplying a half-reaction to balance electrons.

Correction: Change reaction coefficients as needed, but leave the half-cell potentials unchanged.

Choosing the cathode from the more negative reduction potential.

Correction: The more positive reduction potential identifies the reduction at the cathode.

Lesson summary

A reduction potential is assigned to a half-reaction written as reduction.
In a galvanic cell, the more positive reduction potential identifies the cathode; the other half-cell is the anode, where oxidation occurs.
Calculate standard cell potential as cathode reduction potential minus anode reduction potential.
Balance electrons to write the overall reaction, but do not scale the half-cell potentials.

Check your understanding

Question 1

Half-cell A has a reduction potential of

+0.52\,\mathrm{V}

, and half-cell B has a reduction potential of

-0.18\,\mathrm{V}

. Which is the cathode in a galvanic cell?

A, because its reduction potential is more positive.
B, because its reduction potential is more negative.
A, because its reduction potential must be reversed.
Neither; first add the two potentials.

Show answer and explanation

A, because its reduction potential is more positive.

The half-cell with the more positive reduction potential is the site of reduction and is the cathode.

Question 2

Using the same two values, what is the standard cell potential?

$+0.34\,\mathrm{V}$
$-0.34\,\mathrm{V}$
$+0.70\,\mathrm{V}$
$-0.70\,\mathrm{V}$

Show answer and explanation

+0.70\,\mathrm{V}

A is the cathode and B is the anode. Subtract the anode reduction potential from the cathode reduction potential:

(+0.52\,\mathrm{V})-(-0.18\,\mathrm{V})=+0.70\,\mathrm{V}

.

Key terms

Half-cell: One electrode and the solution containing the particles involved in its half-reaction.
Reduction potential: A voltage assigned to a half-reaction written as a reduction.
Cathode: The electrode where reduction occurs in a galvanic cell.
Anode: The electrode where oxidation occurs in a galvanic cell.
Cell potential: The voltage difference between the two half-cells.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 12 Chemistry (SCH4U), expectation F3.3. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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F3.3 · Relate half-cell voltages to overall cell potential