For the following half-reaction, E° = 1.103 V: Calculate the formation constant Kf for Cu(CN)2-.

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Identify the half-reaction and its standard reduction potential (E° = 1.103 V).

Understand that the formation constant (Kf) is related to the equilibrium constant for the formation of the complex ion Cu(CN)_2^- from Cu^+ and CN^- ions.

Use the Nernst equation to relate the standard reduction potential to the equilibrium constant: E° = (RT/nF) * ln(K), where 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.

Rearrange the Nernst equation to solve for the equilibrium constant K: K = e^(nFE°/RT).

Substitute the known values (E°, R, T, n, and F) into the equation to calculate the formation constant Kf for Cu(CN)_2^-.

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Key Concepts

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

Half-Reaction and Standard Electrode Potential (E°)

A half-reaction represents either the oxidation or reduction process in an electrochemical reaction. The standard electrode potential (E°) quantifies the tendency of a species to gain electrons, measured under standard conditions. A positive E° indicates a strong oxidizing agent, while a negative E° suggests a reducing agent. Understanding this concept is crucial for relating electrochemical data to equilibrium constants.

Nernst Equation

The Nernst equation relates the cell potential to the concentrations of the reactants and products in a redox reaction. It allows for the calculation of the equilibrium constant (K) from the standard electrode potential (E°) and the reaction quotient (Q). This equation is essential for determining the formation constant (Kf) of complex ions, as it connects thermodynamic properties with electrochemical measurements.

Formation Constant (Kf)

The formation constant (Kf) is a measure of the stability of a complex ion in solution, defined as the equilibrium constant for the formation of the complex from its constituent ions. A higher Kf value indicates a more stable complex. In the context of the given half-reaction, calculating Kf involves using the relationship between E° and Kf, which reflects the favorability of complex formation in terms of thermodynamic stability.

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