chapter 19 cont

Standard Potential Calculation

• To find the standard potential for the cell, use the formula:
  $E_{standard} = E_{cathode} - E_{anode}$
    - The formula calculates the cell potential by subtracting the standard potential of the anode from that of the cathode.

Nernst Equation

• The second term in the calculation of cell potential is given by the Nernst equation:
  $E = E_{standard} - \frac{0.0592}{n} imes ext{log}(Q)$
    - Here, (n) is the number of electrons transferred in the half-reaction, and (Q) is the reaction quotient.

Copper Electrode and Reaction Balancing

• Determine how many electrons are transferred for the copper electrode.
• The electrode potential for the copper electrode under non-standard conditions is the potential used when conditions differ from standard (1 M concentration, 25°C).

Utilization of Nernst Equation

• The Nernst equation can determine electrochemical potentials for half-cells, as well as for the complete cell.
• Important to note the difference between the half-cell reactions:
    - Half-column potential for copper.
    - Half-column potential for zinc or other materials (like water) under non-standard conditions.

Concentration Cells

• Understand concentration cells, which consist of two electrodes in the same electrolyte at different concentrations.
• Example:
    - Left tube: copper metal placed in a copper sulfate solution at concentration 1.0 M.
    - Right tube: identical metal and solution but with a concentration of 2.1 M.
• The potential difference (cell potential) when both electrodes have the same concentration will be zero (no current flow).

Reaction Dynamics in Concentration Cells

• When concentrations are different, the potential differs and induces electron flow, establishing current.
• Over time, concentrations equalize, driving the cell to a state with reduced cell potential.

Application in Batteries

• The most common application of electrochemical cells involves various types of batteries, like dry cells.
• Dry Cell Construction:
    - Uses a zinc case as an anode and a graphite rod as the cathode.
    - The electrolyte often contains manganese dioxide (MnO2) and other salts.
  

Current Flow

• Electrons move from anode to cathode during a reaction.
• Example: at the anode, zinc (Zn) oxidizes to Zn²⁺:
    Zn
  ightarrow Zn^{2+} + 2e^{-}
    - The lead electrode experiences the opposite reaction, reducing lead ions.

Battery Drainage and Recharge

• When used continuously without recharging, batteries eventually drain as the electrodes become identical in composition, leading to failure ("dead battery").
• Rechargeable batteries can reverse the flow of electrons by applying an external voltage.

Electrolytic Process Explanation

• When recharging an electrolytic cell, connect an external voltage source—this reverses electron flow and replenishes the battery's energy.
• Cations (positive ions) and anions (negative ions) are attracted to the respective electrodes in the electrolytic process.

Metal Plating Process

• During metal plating, the surface of a target metal is coated with a thin layer of another metal through electrolysis.
• The species at the electrode undergo reduction reactions, depositing a layer of metal on the substrate.

Quantitative Analysis of Electrolysis

• To analyze the quantity of substances produced during electrolysis, use the formula relating electric current (I), time (t), and charge (Q):
  $Q = I imes t$
    - Where (I) is in amperes, and (t) is in seconds.

Faraday’s Law

• The Total charge passed can be related to the number of moles of electrons using Faraday's constant:
  $n = \frac{Q}{F}$
    - Where (F) is the Faraday constant (approximately 96485 C/mol).

Example Calculation

• Consider a gold plating process requiring knowledge of charge and current:
    - If you run an electroplating process for 25 minutes at a current of 5.5 A, measure total charge:
  $Q = I imes t = 5.5 A imes 1500 s = 8250 C$
    - Use Faraday’s constant to find moles of electrons transferred.
  $ext{Moles of electrons} = \frac{8250 ext{ C}}{96485 ext{ C/mol}} = 0.0856 ext{ moles}$
    - If gold requires 3 moles of electrons per mole plated, the amount of gold deposited is:
  $ext{Moles of gold} = \frac{0.0856}{3} = 0.0285 ext{ moles}$
    - Using the molar mass of gold (197 g/mol):
    $$ ext{Mass of gold deposited} = 0.0285 ext{ moles} imes 197 ext{ g/mol} = 5.61 ext{ g}
    - Thus, approximately 5.61 g of gold is plated on the metal surface.