The solubility product of \(\mathrm{Co}(\mathrm{OH})_{3}\) is \(2.7 \times 10^{-43}\). The pH of saturated solution of \(\mathrm{Co}(\mathrm{OH})_{3}\) is about (a) \(7.0\) (b) \(11.0\) (c) \(3.0\) (d) \(3.48\)

When a solid compound, like Co(OH)₃, dissolves in water, it undergoes a process called the dissolution reaction. This type of reaction is fundamental in understanding solubility and involves the breaking apart of the compound into its constituent ions. In our case, the Co(OH)₃ dissociates into one Co³⁺ ion and three OH^- ions, forming an equilibrium between the solid phase and its dissolved ions in solution.

The dissolution reaction can be influenced by various factors like temperature, the presence of other ions in the solution, and the common ion effect, which occurs when one of the ions produced by the dissolution is already present in the solution. Understanding the dissolution reaction is crucial for predicting solubility and for calculating the concentrations of ions in a solution, which has many practical applications, including those in environmental science, medicine, and engineering.

The pH calculation is a critical aspect when dealing with solutions in chemistry, especially in the context of solubility products. pH is a measure of the acidity or basicity of an aqueous solution, and it is directly related to the concentration of hydrogen ions (H⁺) in the solution. The pH of a solution is calculated as the negative logarithm (base 10) of the H⁺ ion concentration, typically expressed in moles per liter (M).

In our exercise, we don't directly calculate the pH from H⁺, but instead, we focus on the hydroxide ions (OH^-) concentration to first find the pOH, which is similarly defined as the negative logarithm of the OH^- ion concentration. The pH is then found by subtracting the pOH from 14, which is based on the relationship between pH and pOH at room temperature. Knowing how to correctly perform pH calculations is essential for scientists and students, impacting other areas of study like titrations, buffer solutions, and the biological relevance of pH in body fluids.

Equilibrium concentration refers to the concentrations of reactants and products in a reaction mixture at the state of equilibrium. At equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction, leading to constant concentrations of all species involved. In our exercise with Co(OH)₃, the equilibrium concentrations of Co³⁺ and OH^- are directly tied to the solubility product constant, K_sp.

The concept of equilibrium concentration is not limited to solubility reactions; it's also applicable in various chemical systems, including gaseous reactions, acid-base equilibria, and complexation reactions. The calculation of equilibrium concentrations often involves a combination of equilibrium constants, such as K_sp, and stoichiometric relationships from the balanced chemical equation. Mastery of this concept is crucial for chemists when predicting reaction extents, optimizing product yields, and designing chemical processes.