# 2: Galvanic Cells (Worksheet)

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- 80443

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Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.

The batteries in your remote and the engine in your car are only a couple of examples of how chemical reactions create power through the flow of electrons. The cell potential is the way in which we can measure how much voltage exists between the two half cells of a battery. We will explain how this is done and what components allow us to find the voltage that exists in an electrochemical cell.

## Q1: A Redox Reaction

Balance the redox reaction

\[ \ce{Cu^{2+} (aq) + Al (s) -> Cu (s) + Al^{3+} (aq) } \nonumber\]

## Q2: The Activity Series

Use the activity series to determine if the balanced redox reaction in Q1 is spontaneous or not as written. If not, rewrite the reaction so that it is spontaneous.

## Q3: A Cell Picture

Draw (graphically) a galvanic cell that takes advantage of the spontaneous redox reaction indicated in Q2. Make you indicate all of the following components and aspects in your cell drawing:

- Anode
- Cathode
- Electrode Salt Bridge
- Wire
- Voltmeter
- Oxidation half reaction
- Reduction half reaction
- flow of electrons (when the cell is operational)
- Flow of ion (indicate which one you select and where they go when the cell is operational)

## Q4: Importance

For each of the components you drew in Q3 explain what its contribution is to your cell and what would happen if it were removed.

- Anode
- Cathode
- Electrode Salt Bridge
- Voltmeter
- Wire

## Q5: Cell Diagram under Standard Conditions

Assuming your cell is operating under standard conditions, write the corresponding cell notation (sometimes called "Cell Diagram") for your cell.

## Q6: Cell Diagram under Non-Standard Conditions

What would your cell notation look like if your cell operated under non-standard conditions?

## Q7: Cell Diagram under Equilibrium Conditions

What would your cell notation look like if your cell operated under equilibrium conditions? How would you know what these conditions are?

## Q8: Cell Potential under Standard Conditions

The standard cell potential (\(E^o_{cell}\)) is the difference electric potential of the two electrodes of that cell. To find the difference of the two half cells, the following equation is used:

\[E^o_{cell}= E^o_{SRP}(Cathode) - E^o_{SRP} (Anode) \nonumber \]

with

- \(E^o_{cell}\) is the standard cell potential (under 1M, 1 Barr and 298 K).
- \(E^o_{Red,\, Cathode}\) is the
**standard reduction potential**for the reduction half reaction occurring at the cathode - \(E^o_{Red,\, Anode}\) is the
**standard reduction potential**for the oxidation half reaction occurring at the anode

Tables P1 (or P2) on the Libretexts site tabulates the standard reduction potential for many reduction half reactions, including those for your constructed cell.

What is the cell potential of your constructed cell under standard conditions?

## Q9: Cell Potential under Equilibrium Conditions

What is the cell potential of your constructed cell under Equilibrium Conditions?

## Q10: \(\Delta{G}\) and \(E_{cell}\)

The relationship between the cell potential (under any conditions) and \(\Delta{G}\) is:

\[\Delta{G} = −nFE_{cell} \label{20.5.4}\]

where \(n\) is the number of electrons transferred in your BALANCED equations of Q2 and \(F\) is Faraday's constant (96,485 C/mole; that is Coulombs/mole)

- What is \(\Delta{G}^o\) for your cell (that is under standard conditions)?
- What is \(\Delta{G}\) for your cell under equilibrium conditions?

## Q11: Equilibrium Constant

We can use the relationship between \(\Delta{G^°}\) and the equilibrium constant \(K\), to obtain a relationship between \(E^°_{cell}\) and \(K\). The standard free-energy change and the equilibrium constant are related by the following equation:

\[\Delta{G°} = −RT \ln K \nonumber\]

Given the relationship between the standard free-energy change and the standard cell potential (Equation \(\ref{20.5.4}\)), we can write

\[−nFE^°_{cell} = −RT \ln K \label{20.5.12}\]

Rearranging this equation,

\[E^\circ_{\textrm{cell}}= \left( \dfrac{RT}{nF} \right) \ln K \label{20.5.12B}\]

At \(T = 298\, K\), Equation \(\ref{20.5.12}\) can be simplified as follows:

\[ \begin{align} E^\circ_{\textrm{cell}} &=\left(\dfrac{RT}{nF}\right)\ln K \nonumber \\[4pt] &\approx \left(\dfrac{\textrm{0.0591 V}}{n}\right)\log_{10} K \label{20.5.13} \end{align}\]

What is the equilibrium constant for the balance and spontaneous redox reaction that drives your cell?

## Q12: Reaction Quotients (Q)

The reaction quotient (\(Q\)) measures the relative amounts of products and reactants present during a reaction at a particular point in time. The reaction quotient aids in figuring out which direction a reaction is likely to proceed, given either the pressures or the concentrations of the reactants and the products.

- What is the value of \(Q\) for your cell under standard conditions?
- What is the value of \(Q\) for your cell under equilibrium conditions?
- What is the value of \(Q\) for your cell under non-standard (and non-equilibrium) conditions?

## Q13: \(\Delta{G}\) under Nonstandard Conditions (The Nernst Equation)

The Nernst Equation (\(\ref{Eq3}\)) can be used to determine the value of Ecell, and thus the direction of spontaneous reaction, for any redox reaction under any conditions.

\[E_\textrm{cell}=E^\circ_\textrm{cell}-\left(\dfrac{RT}{nF}\right)\ln Q \label{Eq3}\]

The *Nernst Equation* enables the determination of cell potential **under non-standard conditions** and relates the measured cell potential to the reaction quotient and allows the accurate determination of equilibrium constants (including solubility constants).

- What is the cell potential of your cell when the concentration of all aqueous solutions are halved?
- What is the cell potential of your cell when the concentration of all aqueous solutions are doubled?

(Hint: You can simplify the calculations if you use a similar approximation used in Q11).