Consider the following two ligand exchange reactions: \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}+6 \mathrm{NH}_{3} \rightleftharpoons\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}+6 \mathrm{H}_{2} \mathrm{O}\) $$\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}+3 \mathrm{en} \rightleftharpoons\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}+6 \mathrm{H}_{2} \mathrm{O}$$ (a) Which of the reactions should have a larger \(\Delta S^{\circ}\) ? (b) Given that the \(\mathrm{Co}-\mathrm{N}\) bond strength is approximately the same in both complexes, which reaction will have a larger equilibrium constant? Explain your choices.

Step by step solution

01

Comparing Entropy Change ΔS°

Entropy gauges the disorder or randomness in a system. In general, the side of the reaction with more particles often has higher entropy, as more particles lead to more disorder. In both reactions, there are the same number of reactants and products (2 reactants and 2 products). However, in the first reaction, the product side forms six molecules of water, while in the second, it also forms six molecules of water. Here, both produce the same number of particles, hence we cannot make an exact quantitative assessment based on this information. More in-depth analysis based on the type of ligand may be required to be entirely accurate.

02

Comparing Equilibrium Constant

The equilibrium constant for a reaction is influenced by the standard Gibbs free energy change (ΔG°). ΔG°, in turn, is related to the enthalpy change (ΔH°) and entropy change (ΔS°) by the equation ΔG° = ΔH° - TΔS°. Given that the Co-N bond strength is roughly the same in both complexes, we can infer that the enthalpy change ΔH° is likely to be similar, as bond breaking and making processes are the major contributors to enthalpy change. Entropy change ΔS° appears to be roughly the same for both reactions. Therefore, without more specific details, it could be assumed that both reactions may have a similar equilibrium constant.

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