Problem 88 - General Chemistry: Principles and Modern Applications

Question

A common reference electrode consists of a silver wire coated with \(\mathrm{AgCl}(\mathrm{s})\) and immersed in \(1 \mathrm{M} \mathrm{KCl}\) $$\mathrm{AgCl}(\mathrm{s})+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(\mathrm{s})+\mathrm{Cl}^{-}(1 \mathrm{M}) E^{\circ}=0.2223 \mathrm{V}$$ (a) What is \(E_{\text {cell }}^{\circ}\) when this electrode is a cathode in combination with a standard zinc electrode as an anode? (b) Cite several reasons why this electrode should be easier to use than a standard hydrogen electrode. (c) By comparing the potential of this silver-silver chloride electrode with that of the silver-silver ion electrode, determine \(K_{\mathrm{sp}}\) for \(\mathrm{AgCl}\).

Step-by-Step Solution

Answer

a) The standard cell potential (\(E_{\text {cell }}^{\circ}\)) of the Ag/AgCl and Zn/Zn++ cell is \(0.9823 V\).\nb) The Ag/AgCl electrode is easier to use than a standard hydrogen electrode due to its safety (no dangerous gases involved), stability of potential, consistency in various temperatures, and wide application range.\nc) To calculate \(K_{\mathrm{sp}}\), we could use the Nernst equation with the cell and standard electrode potentials of the Ag/Ag+ and Ag/AgCl half-cells. However, without those specific experimental values, the exact \(K_{\mathrm{sp}}\) can't be computed in this case.

Step 1: Calculating Standard Cell Potential, \(E_{\text {cell }}^{\circ}\)

The standard cell potential (\(E_{\text {cell }}^{\circ}\)) of a galvanic cell can be calculated using the equation: \(E_{\text {cell }}^{\circ} = E_{\text {cathode }}^{\circ}- E_{\text {anode }}^{\circ}\). Given that the standard reduction potential (\(E^{\circ}\)) of AgCl is 0.2223 V and that of Zn/Zn++ is -0.76 V, we can substitute these values into the formula to find \(E_{\text {cell }}^{\circ}\).

Step 2: Identifying Advantages of Ag/AgCl Electrode Over Standard Hydrogen Electrode

There are multiple reasons why the Ag/AgCl electrode is easier to use than a standard hydrogen electrode. First, it is much easier to handle physically, as it doesn't involve the handling of a dangerous gas such as hydrogen. Additionally, it maintains a stable potential over an extended period and is consistent in various temperatures. It also has a wide range of applications, as it can be used in both laboratory and industrial settings.

Step 3: Calculating the Solubility Product Constant (\(K_{\mathrm{sp}}\)) for AgCl

The solubility product constant, \(K_{\mathrm{sp}}\), can be found using the Nernst equation, which relates the reduction potential of a redox reaction to the standard electrode potential, the temperature, and the reaction quotient. We'll need to know the standard electrode potential for the Ag/Ag+ half-cell and the experimental cell potential. Once we have these, we can rearrange the Nernst equation and solve for \(K_{\mathrm{sp}}\).

Key Concepts

Silver-Silver Chloride Electrode

The Silver-Silver Chloride (Ag/AgCl) electrode is a common reference electrode used in electrochemistry. It consists of a silver wire coated with solid silver chloride (AgCl), immersed in a solution of potassium chloride (KCl). This setup creates a stable environment where the electrode potential remains constant. Typically, the standard electrode potential (\(E^{\circ}\)) for the Ag/AgCl electrode is 0.2223 V.

The Ag/AgCl electrode is preferred over other reference electrodes, such as the standard hydrogen electrode, because it is safer and more convenient. No handling of gases like hydrogen is necessary, which simplifies experimental setups and improves safety. Additionally, the Ag/AgCl electrode provides a stable reference potential, making it useful for various electrochemical measurements in both research and industry. Its durability and ease of use further solidify its status as a reliable tool in many applications.

Standard Cell Potential

The Standard Cell Potential is a critical concept in electrochemistry. It is used to determine how much voltage a galvanic cell can produce under standard conditions when all reactants and products are at their standard states, often at 1 M concentration and 1 atm pressure. To find this potential, you use the equation: \(E_{\text{cell}}^{\circ} = E_{\text{cathode}}^{\circ} - E_{\text{anode}}^{\circ}\).

For example, in a cell with a Silver-Silver Chloride electrode as the cathode and a zinc electrode as the anode, the standard potentials are given for each: 0.2223 V for the Ag/AgCl electrode and -0.76 V for the Zn/Zn++ electrode, respectively. By substituting these values into the equation, you can calculate the standard cell potential for the entire electrochemical cell. This potential is an essential factor for determining the feasibility and direction of a chemical reaction within the cell.

Solubility Product Constant (Ksp)

The Solubility Product Constant, often abbreviated as \(K_{\text{sp}}\), is a crucial parameter in chemistry, especially when dealing with sparingly soluble compounds like silver chloride (AgCl). It quantifies the extent to which a compound dissociates into its constituent ions in solution. For a compound like AgCl, which dissociates into Ag+ and Cl- ions, the formula for \(K_{\text{sp}}\) is: \[K_{\text{sp}} = [Ag^+][Cl^-]\]

To find \(K_{\text{sp}}\) for AgCl, you can use the Nernst equation, which connects the cell potential with the activities of the reactants and products. When comparing the potential of the Ag/AgCl electrode with a silver-silver ion electrode, the Nernst equation reveals the relationship between the electrode potential and \(K_{\text{sp}}\). Through this approach, you can calculate the solubility product, thereby gaining insight into the solubility characteristics of AgCl under specific conditions. Understanding \(K_{\text{sp}}\) is critical for applications in qualitative analysis, and predicting the formation of precipitates in chemical reactions.