Easy Cell Potential Calculations Practice Questions

Concept Explanation

Cell potential, often denoted as Ecell, is the measure of the potential difference between two half-cells in an electrochemical cell, representing the driving force behind the flow of electrons. It is calculated by taking the difference between the reduction potential of the cathode and the reduction potential of the anode under standard conditions (25°C, 1 atm, and 1 M concentrations). Understanding these calculations is essential for mastering redox reaction practice questions and predicting whether a chemical reaction will occur spontaneously.

To calculate the standard cell potential (E°cell), we use the standard reduction potentials found in a standard reduction potential table. The fundamental formula is:

E°cell = E°cathode - E°anode

Key concepts to remember include:

• Cathode: The electrode where reduction occurs (gain of electrons). It has the more positive reduction potential.

• Anode: The electrode where oxidation occurs (loss of electrons). It has the more negative reduction potential.

• Spontaneity: If E°cell is positive, the reaction is spontaneous (a galvanic or voltaic cell). If E°cell is negative, the reaction is non-spontaneous and requires an external power source (an electrolytic cell).

• Stoichiometry: Unlike many other thermodynamic values, you do not multiply the E° value by the coefficients in the balanced equation. The potential is an intensive property.

For more advanced scenarios involving non-standard conditions, students typically progress to Nernst equation practice questions.

Solved Examples

Review these worked examples to understand the step-by-step process of identifying electrodes and calculating voltage.

Example 1: Zinc-Copper Cell
Calculate the standard cell potential for a cell involving Zn/Zn²⁺ (E° = -0.76 V) and Cu/Cu²⁺ (E° = +0.34 V).

1. Identify the cathode and anode. Since +0.34 V is more positive than -0.76 V, Copper is the cathode and Zinc is the anode.

2. Apply the formula: E°cell = E°cathode - E°anode.

3. E°cell = (+0.34 V) - (-0.76 V).

4. E°cell = 0.34 V + 0.76 V = +1.10 V.

Example 2: Silver-Magnesium Cell
Given E°(Ag⁺/Ag) = +0.80 V and E°(Mg²⁺/Mg) = -2.37 V, determine the E°cell.

1. Compare potentials: Ag⁺ has a higher reduction potential (+0.80 V), so it is the cathode. Mg²⁺ is the anode.

2. Set up the calculation: E°cell = 0.80 V - (-2.37 V).

3. Solve: E°cell = 0.80 + 2.37 = +3.17 V.

Example 3: Lead-Tin Cell
Calculate E°cell for Pb²⁺ + 2e⁻ → Pb (E° = -0.13 V) and Sn²⁺ + 2e⁻ → Sn (E° = -0.14 V).

1. Identify the cathode: -0.13 V is slightly more positive than -0.14 V, so Lead (Pb) is the cathode.

2. Identify the anode: Tin (Sn) is the anode.

3. Calculation: E°cell = (-0.13 V) - (-0.14 V).

4. Result: E°cell = +0.01 V.

Practice Questions

Test your knowledge with these easy cell potential calculations practice questions.

1. Calculate E°cell for a cell with a Nickel electrode (E° = -0.25 V) and a Gold electrode (E° = +1.50 V).

2. A galvanic cell consists of Al/Al³⁺ (E° = -1.66 V) and Fe/Fe²⁺ (E° = -0.44 V). What is the standard cell potential?

3. Determine the spontaneous cell potential for the reaction between Chlorine gas (E° = +1.36 V) and Bromine liquid (E° = +1.07 V)

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4. If a cell uses the half-reactions Li⁺/Li (E° = -3.05 V) and F₂/F⁻ (E° = +2.87 V), calculate the total voltage.

5. Given the half-reactions: Cu²⁺ + 2e⁻ → Cu (E° = +0.34 V) and Ag⁺ + e⁻ → Ag (E° = +0.80 V), find E°cell.

6. Calculate the E°cell for a system using Cr³⁺/Cr (E° = -0.74 V) and Cd²⁺/Cd (E° = -0.40 V).

7. Identify the anode and calculate E°cell for a cell with Mn²⁺/Mn (E° = -1.18 V) and H⁺/H₂ (E° = 0.00 V).

8. What is the standard potential for a cell where Iodine (E° = +0.54 V) is reduced and Zinc (E° = -0.76 V) is oxidized?

9. A cell is constructed with Sn²⁺/Sn (E° = -0.14 V) and Mg²⁺/Mg (E° = -2.37 V). Calculate E°cell.

10. Determine if a cell with E°cathode = -0.40 V and E°anode = -0.80 V is spontaneous and calculate its potential.

Answers & Explanations

1. Answer: +1.75 V. Explanation: E°cell = E°cathode (Gold) - E°anode (Nickel) = 1.50 - (-0.25) = 1.75 V.

2. Answer: +1.22 V. Explanation: Iron is the cathode (-0.44 V) because it is more positive than Aluminum (-1.66 V). E°cell = -0.44 - (-1.66) = 1.22 V.

3. Answer: +0.29 V. Explanation: Chlorine is the cathode (+1.36 V) and Bromine is the anode (+1.07 V). E°cell = 1.36 - 1.07 = 0.29 V.

4. Answer: +5.92 V. Explanation: Fluorine is the cathode (+2.87 V) and Lithium is the anode (-3.05 V). E°cell = 2.87 - (-3.05) = 5.92 V.

5. Answer: +0.46 V. Explanation: Silver is the cathode (+0.80 V) and Copper is the anode (+0.34 V). E°cell = 0.80 - 0.34 = 0.46 V. Note: We do not multiply the Ag value by 2 even though the balanced equation requires 2 Ag⁺.

6. Answer: +0.34 V. Explanation: Cadmium is the cathode (-0.40 V) and Chromium is the anode (-0.74 V). E°cell = -0.40 - (-0.74) = 0.34 V.

7. Answer: +1.18 V; Anode is Mn. Explanation: The Standard Hydrogen Electrode (0.00 V) is the cathode. E°cell = 0.00 - (-1.18) = 1.18 V.

8. Answer: +1.30 V. Explanation: Iodine is the cathode and Zinc is the anode. E°cell = 0.54 - (-0.76) = 1.30 V.

9. Answer: +2.23 V. Explanation: Tin is the cathode (-0.14 V) and Magnesium is the anode (-2.37 V). E°cell = -0.14 - (-2.37) = 2.23 V.

10. Answer: Spontaneous; +0.40 V. Explanation: E°cell = -0.40 - (-0.80) = +0.40 V. Since the value is positive, the reaction is spontaneous.

Quick Quiz

Frequently Asked Questions

What is the difference between E and E°?

E° refers to the cell potential under standard conditions (1 M, 1 atm, 25°C), while E refers to the potential under any other non-standard conditions. You can find more details on adjusting for concentration in our cell potential calculations practice questions guide.

Why don't we multiply E° by coefficients?

Standard reduction potential is an intensive property, meaning it does not depend on the amount of substance present. According to LibreTexts Chemistry, cell potential measures the energy per unit charge, so scaling the reaction doesn't change the voltage.

What does a negative cell potential indicate?

A negative E°cell indicates that the reaction is non-spontaneous in the forward direction as written. This type of setup is characteristic of an electrolytic cell, which requires an external voltage to drive the reaction.

How do I identify the cathode from a list of reduction potentials?

The half-reaction with the more positive (or less negative) reduction potential will act as the cathode in a spontaneous cell. This is because the species with the higher potential has a greater tendency to gain electrons.

Can cell potential be used to find Gibbs Free Energy?

Yes, the relationship is defined by the equation ΔG° = -nFE°cell, where n is the moles of electrons and F is Faraday's constant. This link connects electrochemistry to chemical thermodynamics, which you can explore further in balancing redox practice questions.

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