Intro to Chemistry Unit 17 Review: Electrochemistry

Key Concepts and Terminology

• Electrochemistry studies the interconversion of electrical and chemical energy through redox reactions
• Redox reactions involve the transfer of electrons between species
• Oxidation is the loss of electrons, while reduction is the gain of electrons
• Oxidizing agents are reduced in a redox reaction, while reducing agents are oxidized
• Anodes are the electrodes where oxidation occurs, while cathodes are the electrodes where reduction occurs
• Electrolytes are substances that conduct electricity when dissolved in water, typically ionic compounds or acids
• Electrochemical cells convert chemical energy into electrical energy, while electrolytic cells use electrical energy to drive non-spontaneous chemical reactions

Redox Reactions and Half-Cells

• Redox reactions can be split into two half-reactions: oxidation and reduction
• Oxidation half-reactions involve the loss of electrons and an increase in oxidation state
• Reduction half-reactions involve the gain of electrons and a decrease in oxidation state
• Half-cells are the separate compartments in an electrochemical cell where each half-reaction occurs
  • Each half-cell contains an electrode immersed in an electrolyte solution
  • The two half-cells are connected by a salt bridge or porous membrane to allow ion flow and maintain charge balance
• Electrons flow from the anode (oxidation) to the cathode (reduction) through an external circuit
• The overall cell reaction is the sum of the two half-reactions, with electrons canceling out

Electrochemical Cells and Batteries

• Electrochemical cells, also called galvanic or voltaic cells, generate electrical energy from spontaneous redox reactions
• A common example is the Daniell cell, which consists of a zinc electrode in a zinc sulfate solution and a copper electrode in a copper sulfate solution
  • At the anode, zinc is oxidized: $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$
  • At the cathode, copper is reduced: $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$
• Batteries are composed of one or more electrochemical cells connected in series or parallel
• Primary batteries (non-rechargeable) are single-use and irreversible, such as alkaline batteries
• Secondary batteries (rechargeable) can be recharged by applying an external voltage, such as lithium-ion batteries

Standard Electrode Potentials

• Standard electrode potentials ($E^0$) measure the tendency of a half-reaction to occur under standard conditions (1 M concentrations, 1 atm pressure, 25°C)
• The standard hydrogen electrode (SHE) is the reference electrode, assigned a potential of 0.00 V
• Half-cell potentials are measured relative to the SHE and tabulated as reduction potentials
• The standard cell potential ($E^0_{cell}$) is the difference between the reduction potentials of the cathode and anode: $E^0_{cell} = E^0_{cathode} - E^0_{anode}$
• A positive $E^0_{cell}$ indicates a spontaneous redox reaction, while a negative value indicates a non-spontaneous reaction
• The magnitude of $E^0_{cell}$ is related to the Gibbs free energy change ($\Delta G$) and the maximum electrical work the cell can perform: $\Delta G = -nFE^0_{cell}$

Nernst Equation and Non-Standard Conditions

• The Nernst equation relates the cell potential under non-standard conditions ($E_{cell}$) to the standard cell potential ($E^0_{cell}$) and the concentrations of reactants and products: $E_{cell} = E^0_{cell} - \frac{RT}{nF} \ln Q$
  • $R$ is the gas constant (8.314 J/mol·K), $T$ is the temperature (in Kelvin), $n$ is the number of electrons transferred, $F$ is Faraday's constant (96,485 C/mol), and $Q$ is the reaction quotient
• The Nernst equation allows for the calculation of cell potentials under various conditions, such as different concentrations or temperatures
• The concentration cell is an example of a cell that operates under non-standard conditions, where the same half-reaction occurs at both electrodes but with different concentrations
• The Nernst equation can also be used to determine the equilibrium constant ($K$) for a redox reaction: $\ln K = \frac{nFE^0_{cell}}{RT}$

Electrolysis and Faraday's Laws

• Electrolysis is the process of using electrical energy to drive a non-spontaneous redox reaction
• Electrolytic cells consist of two electrodes immersed in an electrolyte solution, connected to an external power source
• Common applications of electrolysis include the production of pure metals (aluminum, copper), the decomposition of water into hydrogen and oxygen, and electroplating
• Faraday's laws of electrolysis relate the amount of substance produced or consumed during electrolysis to the quantity of electricity passed through the cell
  • First law: The mass of a substance produced or consumed at an electrode is directly proportional to the quantity of electricity passed through the cell
  • Second law: The masses of different substances produced or consumed by the same quantity of electricity are proportional to their equivalent weights (molar mass divided by the number of electrons transferred)
• The quantity of electricity is measured in coulombs (C) and can be calculated as the product of the current (in amperes) and the time (in seconds): $Q = It$

Real-World Applications

• Batteries power numerous portable devices, such as smartphones, laptops, and electric vehicles
• Fuel cells generate electricity from the oxidation of fuels (hydrogen, methanol) and the reduction of oxygen, with applications in transportation and stationary power generation
• Corrosion is an electrochemical process that involves the oxidation of metals, leading to the deterioration of structures and equipment
  • Cathodic protection is a method of preventing corrosion by making the metal surface the cathode of an electrochemical cell
• Electrochemical sensors, such as pH meters and blood glucose monitors, use the principles of electrochemistry to measure the concentration of specific analytes
• Electrochemical water treatment, such as chlorine generation for disinfection and the removal of heavy metals, relies on redox reactions to purify water

Practice Problems and Review

1. Balance the following redox reaction in acidic solution: $MnO4^- + Fe^{2+} \rightarrow Mn^{2+} + Fe^{3+}$
2. Calculate the standard cell potential for a cell consisting of a nickel electrode in a $Ni^{2+}$ solution and a silver electrode in a $Ag^+$ solution. ($E^0_{Ni^{2+}/Ni} = -0.25 V$, $E^0_{Ag^+/Ag} = 0.80 V$)
3. Determine the cell potential at 25°C for a cell with $[Zn^{2+}] = 0.1 M$ and $[Cu^{2+}] = 0.01 M$. ($E^0_{Zn^{2+}/Zn} = -0.76 V$, $E^0_{Cu^{2+}/Cu} = 0.34 V$)
4. How many grams of copper can be produced by passing a current of 2.0 A through a $CuSO4$ solution for 1 hour? (Molar mass of Cu = 63.55 g/mol)
5. Explain the role of the salt bridge in an electrochemical cell and how it maintains charge balance.