Question

Cupric hydroxide dissociates slightly in an aqueous solution as follows: $$\mathrm{Cu}(\mathrm{OH}{)}_2(s)\rightleftarrows {\mathrm{Cu}}^{2+}(aq)+2{\mathrm{OH}}^{-}(aq)$$ Teeth and bones are composed mainly of calcium phosphate, which dissociates slightly in an aqueous solution as follows: $${\mathrm{Ca}}_3{\left({\mathrm{PO}}_4\right)}_2(s)\rightleftarrows 3{\mathrm{Ca}}^{2+}(aq)+2{\mathrm{PO}}_4^{3-}(aq)$$ Predict the direction of equilibrium shift for each of the following stresses: (a) increase $\left[{\mathrm{Ca}}^{2+}\right]$ (b) increase $\left[{\mathrm{PO}}_4{}^{3-}\right]$ (c) decrease $\left[{\mathrm{Ca}}^{2+}\right]$ (d) decrease $\left[{\mathrm{PO}}_4{}^{3-}\right]$ (e) add solid ${\mathrm{Ca}}_3{\left({\mathrm{PO}}_4\right)}_2$ (f) add solid $\mathrm{Ca}{\left({\mathrm{NO}}_3\right)}_2$ (g) add solid ${\mathrm{KNO}}_3$ (h) decrease $\mathrm{pH}$

Short answer

Increasing [Ca²⁺] or [PO₄³⁻] shifts left; decreasing [Ca²⁺] or [PO₄³⁻] shifts right; adding a solid of Ca₃(PO₄)₂ or KNO₃ has no effect; adding Ca(NO₃)₂ shifts left; decreasing pH affects only cupric hydroxide.

Step-by-step solution

Le Chatelier's Principle Overview

Le Chatelier's Principle states that if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will adjust to partially counteract the imposed change.

Analyze Stress (a): Increase [Ca²⁺]

For reaction involving calcium phosphate, increasing $${\mathrm{Ca}}^{2+}$$ shifts the equilibrium to the left, towards the solid (reactants) side, to reduce the added calcium ions.

Analyze Stress (b): Increase [PO₄³⁻]

Adding more $${\mathrm{PO}}_4^{3-}$$ ions will also shift the equilibrium to the left, increasing the formation of the solid calcium phosphate to offset the increase.

Analyze Stress (c): Decrease [Ca²⁺]

Decreasing $${\mathrm{Ca}}^{2+}$$ will shift the equilibrium to the right, promoting the dissociation of more solid calcium phosphate to produce more calcium ions.

Analyze Stress (d): Decrease [PO₄³⁻]

A reduction in $${\mathrm{PO}}_4^{3-}$$ concentration causes the equilibrium to shift rightward, leading to more dissolution of the solid to produce additional phosphate ions.

Consider Stress (e): Add Solid Ca₃(PO₄)₂

Adding more solid calcium phosphate does not affect the equilibrium direction because it is a pure solid and does not change its concentration in the solution.

Consider Stress (f): Add Solid Ca(NO₃)₂

Introducing $$\mathrm{Ca}({\mathrm{NO}}_3{)}_2$$ increases $${\mathrm{Ca}}^{2+}$$ concentration, shifting the equilibrium to the left, similar to Stress (a).

Consider Stress (g): Add Solid KNO₃

Adding $${\mathrm{KNO}}_3$$ does not change the concentration of any species involved in the equilibrium, hence it has no effect on the position of equilibrium.

Consider Stress (h): Decrease pH

Decreasing the $$\text{pH}$$ (increasing $${\text{H}}^{+}$$ concentration) can affect the solubility equilibria by reacting with OH⁻ ions involved in the cupric hydroxide dissolution, which shifts that equilibrium to the right.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a fundamental concept in chemistry. It describes a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of products and reactants remain constant over time, but not necessarily equal. This dynamic balance means that reactions are still occurring, but there's no net change in the concentration of reactants and products.

• The equilibrium position is determined by the relative stabilities of the reactants and products.
• A system at equilibrium responds to changes in concentration, temperature, and pressure according to Le Chatelier's Principle.

Understanding chemical equilibrium is crucial for predicting how a system will respond to various stresses and is foundational for fields like enzymatic reaction kinetics and industrial chemical production. By mastering this concept, students can gain insight into a myriad of natural and synthetic processes.

Dissolution Reactions

Dissolution reactions involve solutes entering a solvent to form a solution, where the solute particles are well-dispersed down to the molecular or ionic level. In the context of chemical equilibrium, dissolution is a reversible process.

• The rate of dissolution and the rate of precipitation eventually balance out.
• This allows for a dynamic equilibrium state, where the solute re-dissolves as it crystallizes.

For example, the dissolution of calcium phosphate in water is a reversible reaction, meaning it can dissolve to form ions, but these ions can also recombine to form the solid, depending on the conditions of the system. Understanding dissolution reactions is crucial because they affect biological processes such as the bioavailability of minerals in the body and environmental processes like the weathering of rocks.

Effect of Concentration Changes

The concentration of reactants or products can significantly influence chemical equilibrium. According to Le Chatelier's Principle, if the concentration of a reactant or product changes, the equilibrium will shift to offset that change.

• Increasing the concentration of a reactant typically shifts the equilibrium to the right, forming more products.
• Conversely, increasing the concentration of a product shifts it to the left, forming more reactants.

For instance, adding more $${\text{Ca}}^{2+}$$ in the calcium phosphate equilibrium results in more solid calcium phosphate, as the reaction shifts to the left. This principle is essential for predicting the behavior of systems in response to stress, such as pollution in natural waters or drug concentrations in medical treatments.

Solubility Equilibria

Solubility equilibria refer to the equilibrium between a solid and its dissolved ions in a saturated solution. It describes how much of a solute can be dissolved in a solvent before the solution becomes saturated, and any additional solute will remain undissolved.

• This equilibrium is characterized by the solubility product constant, $K_{sp}.$
• It predicts the soluble nature of a compound under various conditions.

Understanding solubility equilibria is important for chemical processes such as designing pharmaceuticals that need to dissolve in the bloodstream efficiently, and environmental science where the solubility of minerals affects soil and water chemistry. Factors such as temperature, pressure, and the presence of common ions can all affect solubility equilibria. In specific cases, like decreasing the pH of a solution, the solubility of a compound like cupric hydroxide can be altered, affecting its equilibrium—favoring the dissolved state as hydrogen ions react with hydroxide ions.