3.2 Standard States and Cell Potentials

Electrochemistry deals with the relationship between electrical and chemical energy. Standard states provide a consistent framework for measuring and comparing cell potentials, allowing us to predict the direction of electron flow and reaction spontaneity in electrochemical cells.

The Nernst equation extends our understanding beyond standard conditions. It lets us calculate cell potentials under various concentrations, helping predict how real-world factors affect electrochemical reactions and when they reach equilibrium.

Standard States and Cell Potentials

Standard states in electrochemistry

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• Standard state conditions for electrochemical systems require:
  • Temperature maintained at 25°C (298 K)
  • Gases at a pressure of 1 atm
  • Solutes in aqueous solutions at a concentration of 1 M
  • Pure substances in their most stable form at the specified temperature and pressure (25°C and 1 atm)
• Standard reduction potentials ($E^0$) measured under these well-defined standard state conditions
  • Reduction potentials expressed relative to the standard hydrogen electrode (SHE) which has an assigned potential of 0.00 V by convention
  • Examples of standard reduction potentials: $E^0_{\ce{Cu^2+/Cu}} = +0.34\text{ V}$, $E^0_{\ce{Zn^2+/Zn}} = -0.76\text{ V}$

Calculation of standard cell potentials

• Standard cell potential ($E^0_\text{cell}$) calculated as the difference between the standard reduction potentials of the cathode ($E^0_\text{cathode}$) and anode ($E^0_\text{anode}$)
  • Mathematical expression: $E^0_\text{cell} = E^0_\text{cathode} - E^0_\text{anode}$
• Standard reduction potentials typically listed in a table in order of increasing reduction potential
  • Species with the most positive $E^0$ acts as the strongest oxidizing agent and undergoes reduction at the cathode (gains electrons)
  • Species with the least positive (or most negative) $E^0$ acts as the strongest reducing agent and undergoes oxidation at the anode (loses electrons)
  • Example: In a cell with $\ce{Cu^2+/Cu}$ ($E^0 = +0.34\text{ V}$) and $\ce{Zn^2+/Zn}$ ($E^0 = -0.76\text{ V}$), $\ce{Cu^2+}$ reduces at the cathode while $\ce{Zn}$ oxidizes at the anode

Electron flow in electrochemical cells

• Electrons flow from the anode (site of oxidation) to the cathode (site of reduction) in an electrochemical cell
• Species with the least positive (or most negative) $E^0$ undergoes oxidation at the anode
  • Anode is the electrode where oxidation occurs and electrons are released
• Species with the most positive $E^0$ undergoes reduction at the cathode
  • Cathode is the electrode where reduction occurs and electrons are consumed
• Spontaneity of the cell reaction determined by the sign of $E^0_\text{cell}$
  • Positive $E^0_\text{cell}$ indicates a spontaneous cell reaction as written (galvanic cell)
  • Negative $E^0_\text{cell}$ indicates the reverse reaction is spontaneous (electrolytic cell)
  • Examples: In a $\ce{Zn/Cu}$ cell, $\ce{Zn}$ ($E^0 = -0.76\text{ V}$) oxidizes at the anode and $\ce{Cu^2+}$ ($E^0 = +0.34\text{ V}$) reduces at the cathode; $E^0_\text{cell} = +1.10\text{ V}$ (spontaneous)

Nernst Equation and Non-Standard Conditions

Nernst equation for non-standard conditions

• Nernst equation relates the cell potential ($E_\text{cell}$) to the standard cell potential ($E^0_\text{cell}$) and the concentrations (or partial pressures) of reactants and products
  • Mathematical expression: $E_\text{cell} = E^0_\text{cell} - \frac{RT}{nF} \ln Q$
    • $R$: universal gas constant (8.314 J/mol·K)
    • $T$: temperature in Kelvin (K)
    • $n$: number of electrons transferred in the balanced redox reaction
    • $F$: Faraday's constant (96,485 C/mol)
    • $Q$: reaction quotient (ratio of product concentrations to reactant concentrations, each raised to their stoichiometric coefficients)
• Nernst equation used to calculate cell potential at any given concentration (or partial pressure) of reactants and products
  • As reaction progresses, reactant concentrations decrease and product concentrations increase, causing cell potential to decrease
  • Example: For the cell reaction $\ce{Zn + Cu^2+ -> Zn^2+ + Cu}$, $E_\text{cell} = E^0_\text{cell} - \frac{RT}{2F} \ln \frac{[\ce{Zn^2+}]}{[\ce{Cu^2+}]}$
• Nernst equation also used to determine concentration (or partial pressure) of a reactant or product at equilibrium when $E_\text{cell} = 0$
  • Example: For the cell reaction $\ce{Zn + Cu^2+ -> Zn^2+ + Cu}$, at equilibrium $E_\text{cell} = 0$ and $\frac{[\ce{Zn^2+}]}{[\ce{Cu^2+}]} = e^{\frac{2FE^0_\text{cell}}{RT}}$