3.5 - Measuring Cell Potential and Calculating Standard Cell Potentials
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Standard Cell Potential
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Welcome class! Let's discuss how we can calculate standard cell potentials. Do any of you recall the formula for this?
Is it EΒ°cell equals the difference between the reduction potentials of the cathode and the anode?
Correct, Student_1! The formula is EΒ°cell = EΒ°(cathode) β EΒ°(anode). Remember, the cathode is where reduction occurs.
What does it mean if the EΒ°cell value is positive?
Good question! A positive EΒ°cell indicates a spontaneous reaction. You can think of it as a sign that the reaction has enough 'push' to occur naturally. Can anyone come up with a mnemonic to remember the signs of the cathode and anode?
We could use 'Red Cat' for reduction at the cathode and 'Ox' for oxidation at the anode!
Excellent mnemonic, Student_3! To summarize, EΒ°cell is crucial as it tells us about the spontaneity of a redox reaction.
Example of Daniell Cell
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Now, let's look at a practical example, the Daniell Cell. Can anyone recall the half-reactions occurring in this cell?
I think zinc is oxidized to zinc ions and copper ions are reduced to copper metal.
Exactly! The half-reactions are: Zn(s) β Zn^2+(aq) + 2 eβ and Cu^2+(aq) + 2 eβ β Cu(s). So, how do we calculate EΒ°cell for this reaction?
We use EΒ°cell = EΒ°(cathode) β EΒ°(anode). So we should plug the values into the equation?
Correct! For Zn it is -0.76 V and for Cu it is +0.34 V. Overall, EΒ°cell = 0.34 V β (-0.76 V) yielding 1.10 V. Can anyone explain what this voltage indicates?
This means the reaction is spontaneous!
Well done, everyone! The spontaneity confirms that the Daniell cell can function as a power source.
Gibbs Free Energy and Cell Potential
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Let's connect Gibbs Free Energy with cell potential. Who can explain the relationship?
It's ΞGΒ° = -nF EΒ°cell, which shows how the cell potential affects the free energy change in the reaction.
Right! A negative ΞG signifies a spontaneous process. Can anyone tell me how to determine n in the equation?
n is the number of moles of electrons exchanged during the reaction!
Exactly! Understanding these relationships helps to predict the feasibility of reactions and the energetics involved. Does anyone have questions?
Can we use these equations in practical scenarios like batteries?
Absolutely! Each battery essentially operates on these principles. Great engagement today!
Nernst Equation in Non-Standard Conditions
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Finally, letβs discuss the Nernst equation. It helps us calculate cell potential under non-standard conditions. Who wants to share what the equation looks like?
Itβs Ecell = EΒ°cell β (RT/nF)ln(Q)!
Spot on! Remember R, T, n, and F represent universal gas constant, temperature, number of electrons transferred, and Faraday's constant, respectively. Who can explain what Q represents?
Q is the reaction quotient that compares the concentrations of products to reactants.
Exactly! It tells us how far along the reaction is. Using this equation allows us to see how changes in concentration affect potential. Can you explain how?
If products increase or reactants decrease, Q increases and Ecell decreases.
Excellent understanding! This is crucial for practical applications like batteries and biological systems!
Concentration Cells
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Last topic today is concentration cells. Who can give a brief rundown of what these are?
They're cells that have the same metal electrode but different ion concentrations!
Correct! They're designed to exploit concentration gradients to generate a potential. How does the cell potential relate to the concentrations?
We can use the Nernst equation, and Ecell depends on the concentration difference!
Great! These cells are used in measuring ion concentrations, and in biochemical applications. A wonderful discussion today, class.
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
In this section, students learn how to measure the cell potential of electrochemical cells through the formula EΒ°cell = EΒ°(cathode) β EΒ°(anode). They also explore the significance of standard electrode potentials in determining reaction spontaneity and the resulting cell voltage.
Detailed
Measuring Cell Potential and Calculating Standard Cell Potentials
This section elaborates on the measurement of cell potential in galvanic cells, showcasing how the difference in standard electrode potentials between oxidation and reduction half-reactions translates to overall cell voltage.
Key Points:
- Standard Cell Potential: The standard cell potential (EΒ°cell) is calculated using the equation:
EΒ°cell = EΒ°(cathode) - EΒ°(anode). This formula infers that EΒ° values are always taken with respect to the more positive electrode being the cathode (site of reduction) and the less positive the anode (site of oxidation).
- Example (Daniell Cell): Through an example involving the Daniell Cell, where Zn is oxidized and Cu is reduced, the students can calculate the standard cell potential:
- Zinc half-reaction: Zn^2+ + 2 eβ β Zn(s) (EΒ° = -0.76 V)
- Copper half-reaction: Cu^2+ + 2 eβ β Cu(s) (EΒ° = +0.34 V)
- Therefore, EΒ°cell = 0.34 - (-0.76) = 1.10 V. This potential indicates a spontaneous redox reaction.
- Gibbs Free Energy Relationship: The section leads to a connection with Gibbs Free Energy via the formula:
ΞGΒ° = -nF EΒ°cell which determines the spontaneity of the reaction based on cell potential.
- Nernst Equation: It discusses the Nernst equation to calculate Ecell under non-standard conditions, incorporating reaction quotient Q, thus aiding in predicting how changes in concentration affect the potential of the cell.
- Concentration Cells: Lastly, concentration cells are highlighted as special galvanic cells where both compartments contain the same metal but differ in ion concentrations, thus demonstrating the basis for the generated cell potential relying solely on concentration gradients.
Audio Book
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Cell Potential Calculation
Chapter 1 of 3
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Chapter Content
A galvanic cell built from two halfβcells will have a cell potential (voltage) under standard conditions equal to the difference between the standard reduction potentials of the two halfβcells:
EΒ°cell = EΒ°(cathode) β EΒ°(anode)
where both EΒ° values are taken as standard reduction potentials. The cathode is the halfβcell where reduction occurs (the one with the higher EΒ°), and the anode is where oxidation occurs (the halfβcell with the lower EΒ°).
Detailed Explanation
In a galvanic cell, we can measure a voltage called the cell potential. This potential tells us how much energy can be drawn from the cell as it operates. The formula we use to calculate this potential is: EΒ°cell = EΒ°(cathode) β EΒ°(anode). This means that the cell potential is determined by subtracting the standard reduction potential of the anode (where oxidation occurs) from the standard reduction potential of the cathode (where reduction occurs). A higher electrode potential indicates that the reaction can happen more easily.
Examples & Analogies
Imagine a water slide where the height difference between the starting point and the end point determines how fast you can slide down. Similarly, in a galvanic cell, the difference in potential energy (voltage) between the cathode and anode determines how much electricity can be produced.
Example: Daniell Cell Standard Potential
Chapter 2 of 3
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Chapter Content
Example: Daniell Cell Standard Potential
Halfβreactions and standard potentials:
β Zinc half (written as reduction): Zn^2+ + 2 eβ β Zn(s) EΒ° = β0.76 V
β Copper half (reduction): Cu^2+ + 2 eβ β Cu(s) EΒ° = +0.34 V
In the Daniell cell, zinc metal is oxidized (written as the reverse of the reduction halfβreaction above):
Zn(s) β Zn^2+ + 2 eβ EΒ° (as oxidation) = +0.76 V (the negative of β0.76 V)
Copper(II) is reduced:
Cu^2+ + 2 eβ β Cu(s) EΒ° = +0.34 V (as reduction)
Cell potential (standard) = EΒ°(cathode) β EΒ°(anode). Because copper halfβcell has the higher reduction potential (+0.34 V) it is the cathode. Zinc halfβcellβs reduction potential (β0.76 V) is lower, so it is the anode if written as reduction. Therefore:
EΒ°cell = 0.34 V β (β0.76 V) = 1.10 V
Alternatively, thinking in terms of oxidation potential for zinc (+0.76 V) plus reduction potential for copper (+0.34 V) gives 1.10 V.
This 1.10βvolt cell potential is what would be measured with a voltmeter under standard conditions (1 M Zn2+, 1 M Cu2+, 25 Β°C, 1 atm H2 in SHE reference).
Detailed Explanation
In the Daniell cell, we examine two half-reactions: one involving zinc and the other involving copper. The standard potentials of these reactions tell us how readily each species will gain or lose electrons. For zinc, which has a more negative standard potential, it will oxidize and lose electrons, while copper gains electrons and is reduced. When calculating the total cell potential, we subtract the anodeβs potential from the cathodeβs. In our example, this results in a cell potential of +1.10 V, indicating that this galvanic cell can generate electrical energy efficiently under standard conditions.
Examples & Analogies
Think of a race where two athletes are competing. One athlete is faster (the copper), and the other is not (the zinc). By measuring the time difference or the potential between them, we can tell who will win. In our galvanic cell, the copper is the faster athlete (cathode), and by subtracting the slower time (anode, zinc), we find out how much faster the copper can complete the raceβthis is like finding the cell potential.
Spontaneity and Gibbs Free Energy Relationship
Chapter 3 of 3
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Chapter Content
A positive cell potential (Ecell > 0) under standard conditions indicates that the overall redox reaction is spontaneous as written. The relationship between the standard cell potential and the change in Gibbs free energy under standard conditions (ΞGΒ°) is:
ΞGΒ° = βn F EΒ°cell
where
β n is the number of electrons transferred in the balanced overall redox reaction,
β F is the Faraday constant (approximately 96,500 coulombs per mole of electrons),
β EΒ°cell is the standard cell potential in volts,
β ΞGΒ° is in joules per mole.
Hence, if EΒ°cell is positive, ΞGΒ° is negative, indicating a spontaneous reaction under standard conditions. If EΒ°cell is negative, ΞGΒ° is positive, indicating a nonspontaneous reaction under standard conditions (but which can proceed if an external voltage greater than |EΒ°cell| is applied, as in electrolysis).
Detailed Explanation
Here, we connect cell potential to the concept of spontaneity using Gibbs free energy (ΞGΒ°). When we have a positive EΒ°cell value, it signifies that the reaction can occur naturally (spontaneously). The equation ΞGΒ° = βn F EΒ°cell reveals this relationship, where n represents the number of electrons transferred. A positive standard cell potential leads to a negative Gibbs free energy, reinforcing that the reaction is favorable. Conversely, if the cell potential is negative, it means energy is needed to drive the reaction, making it nonspontaneous under standard conditions.
Examples & Analogies
Consider a ball at the top of a hill. If it starts rolling down, that's like a spontaneous process where energy is released (positive EΒ°cell). But if you want to roll it back up, you need to do work against gravity (nonspontaneous process)βrelated to a negative EΒ°cell. Just like itβs easy for the ball to roll down but hard to push it back up, reactions with positive cell potentials favor 'falling down' to completion spontaneously.
Key Concepts
-
Standard Cell Potential: The voltage difference between the reduction potential of the cathode and anode.
-
Nernst Equation: Used for calculating cell potentials under non-standard conditions.
-
Gibbs Free Energy: Related to the spontaneity of a reaction and is calculated through standard cell potential.
Examples & Applications
Example 1: For a Daniell Cell, Zn^2+ + 2 eβ β Zn(s) (EΒ° = -0.76 V) and Cu^2+ + 2 eβ β Cu(s) (EΒ° = +0.34 V). Thus, EΒ°cell = 1.10 V.
Example 2: A concentration cell where Zn is at 0.10 M and Cu is at 0.010 M will show how relative concentration impacts the Ecell.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
When E is positive, reactions will thrive, spontaneous steps make them come alive.
Stories
In the tale of the Daniell cell, Zinc and Copper played their roles well. With zinc losing its shine, the spontaneity was fine.
Memory Tools
Remember 'COR' - Cathode for Oxidation, Reduction at the anode!
Acronyms
Use 'FINE' for recognizing Gibbs Free Energy
= Free
= Indicator
= Negative
= Energy.
Flash Cards
Glossary
- Cell Potential
The electromotive force, or voltage, generated by an electrochemical cell.
- Standard Electrode Potential
The measure of the voltage (EΒ°) of a half-reaction under standard conditions.
- Galvanic Cell
A type of electrochemical cell that converts chemical energy into electrical energy spontaneously.
- Nernst Equation
An equation that relates the cell potential to the concentrations of the reactants and products.
- Reaction Quotient (Q)
A ratio of the concentrations of products over reactants for a reversible reaction at any point in time.
Reference links
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