The standard potential for the reduction of AgSCN(s) is +0.09 V. AgSCN(s) + e⁻ → Ag(s) + SCN⁻(aq). Using this value and the electrode potential for Ag⁺(aq), calculate the Ksp for AgSCN.

Verified step by step guidance

Step 1: Write the half-reaction for the reduction of AgSCN(s) to Ag(s) and SCN⁻(aq) and note its standard reduction potential, E° = +0.09 V.

Step 2: Write the half-reaction for the reduction of Ag⁺(aq) to Ag(s) and note its standard reduction potential, E° = +0.80 V.

Step 3: Use the Nernst equation to relate the standard reduction potentials to the equilibrium constant (K) for the overall reaction. The Nernst equation is: E°cell = (RT/nF)lnK, where E°cell is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, and F is Faraday's constant.

Step 4: Calculate the standard cell potential (E°cell) for the dissolution of AgSCN(s) by subtracting the standard reduction potential of Ag⁺(aq) from that of AgSCN(s): E°cell = E°(AgSCN) - E°(Ag⁺).

Step 5: Rearrange the Nernst equation to solve for the solubility product constant (Ksp) of AgSCN: Ksp = exp((nF * E°cell) / (RT)).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Standard Electrode Potential

The standard electrode potential (E°) is a measure of the tendency of a chemical species to be reduced, measured under standard conditions. It is expressed in volts and is crucial for predicting the direction of redox reactions. In this case, the given potential for the reduction of AgSCN indicates how readily AgSCN can gain electrons to form Ag and SCN⁻.

Nernst Equation

The Nernst equation relates the electrode potential of a half-cell to the concentrations of the reactants and products involved in the redox reaction. It allows for the calculation of the cell potential under non-standard conditions and is essential for determining the solubility product constant (Ksp) from the standard potential and concentrations of ions in solution.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that quantifies the solubility of a sparingly soluble ionic compound. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced dissolution equation. For AgSCN, Ksp can be calculated using the concentrations of Ag⁺ and SCN⁻ ions at equilibrium, which are influenced by the standard electrode potential.

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Related Practice

Textbook Question

Cytochrome, a complicated molecule that we will represent as CyFe2+, reacts with the air we breathe to supply energy required to synthesize adenosine triphosphate (ATP). The body uses ATP as an energy source to drive other reactions (Section 19.7). At pH 7.0 the following reduction potentials pertain to this oxidation of CyFe2+: O21g2 + 4 H+1aq2 + 4 e- ¡ 2 H2O1l2 Ered ° = +0.82 V CyFe3+1aq2 + e- ¡ CyFe2+1aq2 E°red = +0.22 V (a) What is ∆G for the oxidation of CyFe2+ by air? (b) If the synthesis of 1.00 mol of ATP from adenosine diphosphate (ADP) requires a ∆G of 37.7 kJ, how many moles of ATP are synthesized per mole of O2?

Textbook Question

Cytochrome, a complicated molecule that we will represent as CyFe2+, reacts with the air we breathe to supply energy required to synthesize adenosine triphosphate (ATP). The body uses ATP as an energy source to drive other reactions (Section 19.7). At pH 7.0 the following reduction potentials pertain to this oxidation of CyFe2+: O21g2 + 4 H+1aq2 + 4 e- ¡ 2 H2O1l2 Ered ° = +0.8 (b) If the synthesis of 1.00 mol of ATP from adenosine diphosphate (ADP) requires a ∆G of 37.7 kJ, how many moles of ATP are synthesized per mole of O2?

Textbook Question

A student designs an ammeter (a device that measures electrical current) that is based on the electrolysis of water into hydrogen and oxygen gases. When electrical current of unknown magnitude is run through the device for 2.00 min, 12.3 mL of water-saturated H21g2 is collected. The temperature of the system is 25.5 °C, and the atmospheric pressure is 768 torr. What is the magnitude of the current in amperes?