Formation constants for the ammonia and ethylenediamine complexes of nickel(II) indicate that Ni(en)₃²⁺ is much more
stable than Ni(NH₃)₆²⁺:
(1) <REACTION>
(2) <REACTION>
The enthalpy changes for the two reactions, ΔH°₁ and ΔH°₂, should be about the same because both complexes have six Ni﹣N bonds.
(c) Assuming that ΔH°₂ - ΔH°₁ is zero, calculate the value of ΔS°₂ - ΔS°₁.

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Identify the reactions given for the formation of Ni(en)3^2+ and Ni(NH3)6^2+. Write down the balanced chemical equations for both reactions.

Understand that the enthalpy change (ΔH°) for both reactions is assumed to be the same, hence ΔH°2 - ΔH°1 = 0. This simplifies the calculation as it eliminates the enthalpy term from the Gibbs free energy equation.

Recall the Gibbs free energy equation for a reaction at constant temperature: ΔG° = ΔH° - TΔS°. Since ΔH°2 - ΔH°1 = 0, the equation simplifies to ΔG°2 - ΔG°1 = -T(ΔS°2 - ΔS°1).

Use the relationship between Gibbs free energy and the equilibrium constant, K, which is ΔG° = -RT ln K. Set up the equation for both reactions and find the difference ΔG°2 - ΔG°1 = -RT ln(K2/K1).

Combine the simplified Gibbs free energy equation with the equilibrium constant relationship to solve for ΔS°2 - ΔS°1. Rearrange to isolate ΔS°2 - ΔS°1 and solve using the known or given values of K1 and K2, and the temperature T.

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Key Concepts

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

Formation Constants

Formation constants (Kf) quantify the stability of complex ions in solution. A higher formation constant indicates a more stable complex, as it reflects the equilibrium between the free metal ion and the complex. In this context, the formation constants for Ni(en)3^2+ and Ni(NH3)6^2+ suggest that the ethylenediamine complex is significantly more stable than the ammonia complex.

Enthalpy and Entropy Changes

Enthalpy (ΔH) and entropy (ΔS) are thermodynamic properties that describe the heat content and disorder of a system, respectively. In the context of complex formation, ΔH reflects the energy change associated with bond formation, while ΔS indicates the change in disorder when reactants form products. The relationship between these changes is crucial for understanding the stability and spontaneity of the complexation reactions.

Gibbs Free Energy

Gibbs Free Energy (ΔG) is a thermodynamic potential that determines the spontaneity of a reaction at constant temperature and pressure. It is related to enthalpy and entropy by the equation ΔG = ΔH - TΔS. For the complexes in question, if ΔH°2 - ΔH°1 is zero, the difference in Gibbs Free Energy can be analyzed through the entropy changes, allowing for the calculation of ΔS°2 - ΔS°1 to assess the relative stability of the complexes.

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