Electrochemical Cells Notes

Electrochemical Cells

• There are two categories of electrochemical cells:
  • Galvanic/Voltaic: A spontaneous reaction occurs, generating electricity.
  • Electrolytic: Electricity is supplied to the cell, causing a non-spontaneous reaction to occur.

Galvanic Cells

• The most common type of galvanic cell is the "Daniell cell."
• The reaction is: $Zn(s) + Cu^{2+}(aq) \leftrightarrow Zn^{2+}(aq) + Cu(s)$
• Shorthand cell notation is used to represent galvanic cells.

Daniell Cell

• Anode Electrode (Zn): Oxidation occurs; has a negative charge.
• Cathode Electrode (Cu): Reduction occurs; has a positive charge.
• The Daniell cell's theoretical voltage is 1.1 volts, and the chemical reaction is: $Zn(s) + Cu^{2+}(aq) \leftrightarrow Zn^{2+}(aq) + Cu(s)$

Cell-Potential

• The total cell-potential can be expressed as follows: $E°<em>{cell} = E°</em>{cathode} - E°_{anode}$
• Example: $Zn(s) + Cu^{2+}(aq) \leftrightarrow Zn^{2+}(aq) + Cu(s)$
• $E°_{Zn^{2+}(aq) + 2e^- \rightarrow Zn(s)} = -0.76V$
• $E°_{Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)} = +0.34V$
• Thus: $E°_{cell} = 0.34 - (-0.76)V = 1.10V$

Cell-Potential Example: Zinc Chlorine Battery

• A new battery system under study for possible use in electric vehicles is the zinc-chlorine battery.
• The overall reaction producing electricity in this cell is $Zn(s) + Cl<em>2(g) \rightarrow ZnCl</em>2(aq)$.
• The question is to determine the $E°_{cell}$ of this voltaic cell.

The Relationship between $E°$ and Spontaneity

• At standard concentration, temperature, and pressure: $\Delta G = -nFE°_{cell}$
  • Where:
    • $n$ is the number of moles of electrons transferred.
    • $F$ is Faraday’s Constant = 96,500 Cmol^{-1}.
  • A positive $E°$ value means the reaction is spontaneous as $\Delta G$ is negative.
  • A negative $E°$ value means the reaction is non-spontaneous as $\Delta G$ is positive.

Calculating $\Delta G°$

• Calculate $\Delta G°$ for the following reaction: $Zn(s) + Cl<em>2(g, 1 atm) \rightarrow ZnCl</em>2(aq, 1 M)$

Standard Reduction Potentials

• A table of standard reduction potentials is provided, listing various half-reactions and their corresponding $E°$ values.
• The table also indicates the relative strengths of oxidizing and reducing agents.

Nernst Equation

• The previous relationships apply to cells under standard conditions.
• For a cell under non-standard conditions, we use the Nernst Equation:
  • $E = E°_{cell} - (\frac{RT}{nF}) \ln Q$
  • $E = E°_{cell} - (\frac{0.0592}{n}) \log Q$

Nernst Equation Example

• Will the cell reaction proceed spontaneously as written for the following cell?
• $Ag(s)|Ag^+ (0.075 M)||Hg^{2+}(0.85 M)|Hg(l)$
• To determine:
  • Half-reactions
  • $E°$
  • $E_{cell}$
  • Spontaneity

Aluminum and Copper(II) Ions

• Will aluminum metal displace $Cu^{2+}$ ion from aqueous solution? That is, will a spontaneous reaction occur in the forward direction for the following reaction?
• $2Al(s) + 3Cu^{2+}(1 M) \rightarrow 3Cu(s) + 2Al^{3+}(1 M)$