Question

The standard potential for the reduction of AgSCN is \(0.0895 \mathrm{~V}\) $$\mathrm{AgSCN}(s)+e^{-} \longrightarrow \mathrm{Ag}(s)+\mathrm{SCN}^{-}(a q)$$ Find another electrode potential to use together with the above value and calculate \(K_{\mathrm{sp}}\) for \(\mathrm{AgSCN}\).

Short answer

Question: Calculate the solubility product constant (Ksp) for AgSCN, given that the standard potential for the reduction of AgSCN is 0.0895 V. Answer: The solubility product constant for AgSCN is Ksp ≈ 1.10 × 10⁻¹².

Step-by-step solution

Recall the Nernst equation and the relationship between electrode potential and equilibrium constant

The Nernst equation relates the cell potential (E) to the standard cell potential (E°) and the concentrations of species involved in an electrochemical reaction: \[ E = E° - \frac{RT}{nF} \ln Q\] Also, remember that for any reaction, \[ \Delta G° = -RT \ln K \] And since ΔG° is related to E° by the equation: \[ \Delta G° = -nFE° \] We can substitute and rearrange to find K for a reaction: \[ K = e^{-\frac{nFE°}{RT}}\]

Identify another half-cell reaction to use

We need another half-cell reaction to combine with the given reaction to form a complete redox reaction. We choose the silver ion reduction half-cell reaction because it involves silver like AgSCN: \[ \mathrm{Ag}^{+}(aq) + e^{-} \longrightarrow \mathrm{Ag}(s) \] Additionally, we should know that the standard potential for the reduction of silver ions, Ag⁺, to solid silver, Ag, is E°(Ag⁺/Ag) = +0.7996V.

Write the overall redox reaction

Combine the two half-reactions to form the overall redox reaction. Here, we will construct a cell in which the reduction of Ag ions occurs at the cathode and the reduction of AgSCN occurs at the anode. The overall redox reaction is: \[ \mathrm{AgSCN}(s) \longrightarrow \mathrm{Ag}^{+}(aq) + \mathrm{SCN}^{-}(aq) \]

Determine the standard potential for the overall redox reaction

Subtract the silver ion reduction potential from the AgSCN reduction potential to find the standard potential, E°, for the overall redox reaction: \[ E° = \left(\mathrm{E°_{AgSCN~reduction}} - \mathrm{E°_{\mathrm{Ag^{+}~reduction}}\right) = \left(0.0895 \mathrm{V} - 0.7996 \mathrm{V}\right) = -0.7101 \mathrm{~V} \]

Calculate the solubility product constant, Ksp

Use the relationship between K and E° to calculate the solubility product constant, Ksp, for AgSCN: \[ K_{sp} = e^{\frac{-nFE°}{RT}} \] Here, n = 1 (since there is only one electron exchanged in the redox reaction), F = 96485 C/mol (Faraday constant), R = 8.314 J/molK (gas constant), and T = 298.15 K (assuming the reaction takes place at standard temperature). Plug in the values to find Ksp: \[ K_{sp} = e^{\frac{-1 \times 96485 \times (-0.7101)}{8.314 \times 298.15}} \] \[ K_{sp} \approx 1.10 \times 10^{-12} \] So, the solubility product constant for AgSCN is Ksp ≈ 1.10 × 10⁻¹².

Key concepts

Understanding the Nernst Equation

The Nernst equation is a fundamental principle in electrochemistry connecting the concentrations of chemicals and the electric potential of a cell. It is expressed as:

\[ E = E° - \frac{RT}{nF} \ln Q \]
where \( E \) is the cell potential, \( E° \) is the standard cell potential, \( R \) is the universal gas constant, \( T \) is the temperature in Kelvin, \( n \) is the number of moles of electrons transferred in the electrochemical reaction, \( F \) is Faraday’s constant, and \( Q \) is the reaction quotient.

In simple terms, the Nernst equation helps predict the potential of an electrode in a given environment, taking into account the temperature and concentrations of reactants and products. For a spontaneous reaction, the potential \( E \) will be positive, and negative if non-spontaneous. Through the Nernst equation, we can also understand changes in electrode potential as the reaction progresses.

Electrode Potential: The Driving Force in Electrochemistry

Electrode potential, often denoted as \( E \) or \( E° \) for standard electrode potential, is a measure of the intrinsic ability of a species to gain or lose electrons in a redox reaction. Standard electrode potentials are measured under standard conditions, (25°C, 1 atm pressure, and 1 M concentration of ions).

Comparing electrode potentials can predict the direction of electron flow in an electrochemical cell. A higher electrode potential means a stronger tendency to gain electrons and be reduced, making it a better oxidizing agent. Vice versa, a lower electrode potential means a stronger tendency to lose electrons and be oxidized. When dealing with a full cell, the overall potential is calculated by taking the difference between the potentials of the cathode and the anode. This provides the electromotive force (emf) for the reaction, which is the potential difference driving the electron flow from anode to cathode.

Redox Reactions: The Transfer of Electrons

Redox reactions, short for reduction-oxidation reactions, are a type of chemical reaction that involves a transfer of electrons between two species. These reactions are characterized by changes in the oxidation states of atoms involved. An oxidation state is a measure of the degree of oxidation of an atom in a substance. It is often thought of in terms of the number of electrons lost or gained by an atom.

In a redox reaction, one substance undergoes oxidation (loses electrons) and another undergoes reduction (gains electrons). These two processes always occur simultaneously, as the electrons lost by one substance must be gained by another. Identifying the reducing and oxidizing agents — the species that donate and accept electrons, respectively — is important for understanding and balancing redox reactions. These reactions are not only key in electrochemical cells but are also fundamental to many biological systems and industrial processes.