Predict the sign of ΔS_sys for each of the following processes: (d) Calcium phosphate precipitates upon mixing Ca(NO₃)₂(aq) and (NH₄)₃PO₄(aq).

Verified step by step guidance

1. Identify the initial and final states of the system. Initially, you have two aqueous solutions: calcium nitrate, Ca(NO_3)_2(aq), and ammonium phosphate, (NH_4)_3PO_4(aq).
2. Recognize that the process involves the formation of a solid precipitate, calcium phosphate, Ca_3(PO_4)_2(s), from the aqueous ions in solution.
3. Understand that the formation of a solid from ions in solution generally leads to a decrease in the number of particles in the system, as ions are removed from the solution to form the solid.
4. Recall that entropy, S, is a measure of the disorder or randomness of a system. A decrease in the number of particles typically corresponds to a decrease in entropy.
5. Conclude that the sign of ΔS_sys, the change in entropy of the system, is likely negative because the process results in a more ordered state with fewer particles in the solution.

Key Concepts

Entropy (ΔS)

Entropy, denoted as ΔS, is a measure of the disorder or randomness in a system. In chemical processes, an increase in entropy typically indicates that the system is becoming more disordered, while a decrease suggests a more ordered state. Understanding how entropy changes during a reaction is crucial for predicting the spontaneity and direction of the process.

Precipitation Reactions

A precipitation reaction occurs when two aqueous solutions react to form an insoluble solid, known as a precipitate. In this case, calcium phosphate precipitates when calcium ions from Ca(NO3)2 and phosphate ions from (NH4)3PO4 combine. The formation of a solid from ions in solution generally leads to a decrease in entropy, as the solid structure is more ordered than the dispersed ions.

Factors Affecting Entropy Change

Several factors influence the change in entropy during a reaction, including the physical states of the reactants and products, the number of moles of gas produced or consumed, and the complexity of the molecules involved. In the case of the precipitation of calcium phosphate, the transition from ions in solution to a solid precipitate typically results in a negative ΔS, indicating a decrease in disorder.