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Teeth and bones are composed mainly of calcium phosphate, which dissociates slightly in an aqueous solution as follows: $$\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s) \rightleftarrows 3 \mathrm{Ca}^{2+}(a q)+2 \mathrm{PO}_{4}^{3-}(a q)$$ 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 \(\mathrm{pH}\)

Step by step solution

01

Identify Reaction and Equilibrium

The dissociation reaction provided is: \(\mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2}(s) \rightleftarrows 3\mathrm{Ca}^{2+}(aq) + 2 \mathrm{PO}_{4}^{3-}(aq)\). At equilibrium, the forward and reverse reaction rates are equal.

02

Analyze Effect of Increasing [Ca虏鈦篯

(a) Increasing \([\mathrm{Ca}^{2+}]\) will cause the equilibrium to shift left towards \(\mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2}(s)\), according to Le Chatelier's Principle, to counter the increase in calcium ions.

03

Analyze Effect of Increasing [PO鈧劼斥伝]

(b) Increasing \([\mathrm{PO}_{4}^{3-}]\) will shift the equilibrium to the left, towards \(\mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2}(s)\), to reduce the concentration of phosphate ions.

04

Analyze Effect of Decreasing [Ca虏鈦篯

(c) Decreasing \([\mathrm{Ca}^{2+}]\) will shift the equilibrium to the right, favoring the formation of more \([\mathrm{Ca}^{2+}]\) by dissociating more \(\mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2}\).

05

Analyze Effect of Decreasing [PO鈧劼斥伝]

(d) Decreasing \([\mathrm{PO}_{4}^{3-}]\) will shift the equilibrium to the right, producing more phosphate ions from the dissociation of \(\mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2}\).

06

Effect of Adding Solid Ca鈧�(PO鈧�)鈧�

(e) Adding more solid \(\mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2}\) at equilibrium does not affect the reaction, as it is not involved in the equilibrium expression for solubility.

07

Effect of Adding Solid Ca(NO鈧�)鈧�

(f) Adding solid \(\mathrm{Ca(NO}_3)_2\) increases \([\mathrm{Ca}^{2+}]\), causing the equilibrium to shift left, towards \(\mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2}(s)\).

08

Effect of Adding Solid KNO鈧�

(g) Adding \(\mathrm{KNO}_3\) does not affect \([\mathrm{Ca}^{2+}]\) or \([\mathrm{PO}_{4}^{3-}]\), thus there is no significant change in equilibrium position.

09

Effect of Decreasing pH

(h) Decreasing pH increases \([\mathrm{H}^+]\), which reacts with \([\mathrm{PO}_{4}^{3-}]\) to form \(\mathrm{HPO}_{4}^{2-}, \) reducing \([\mathrm{PO}_{4}^{3-}]\). This shift causes the equilibrium to move right, increasing dissociation of \(\mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Equilibrium

Chemical equilibrium is a crucial concept in chemistry, representing a state where the forward and reverse reactions occur at the same rate. This means the concentrations of reactants and products remain constant over time. In the given dissociation reaction of calcium phosphate, this equilibrium state can be altered by changing conditions such as concentration, temperature, and pressure. Equilibrium is dynamic, meaning molecules continue to react, but without any net change in the concentrations of the substances involved. When equilibrium is disturbed, the system tries to counteract the change by shifting in a direction that restores balance, according to Le Chatelier's Principle.

Dissociation Reaction

A dissociation reaction occurs when a compound breaks down into its ions in solution. For calcium phosphate, the dissociation reaction is represented as:\[\mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2}(s) \rightleftarrows 3\mathrm{Ca}^{2+}(aq) + 2 \mathrm{PO}_{4}^{3-}(aq)\]This reaction describes how solid calcium phosphate dissociates into calcium ions and phosphate ions in water. Dissociation is influenced by factors such as concentration and temperature. In reactions like these, the initial solid doesn't directly appear in the equilibrium expression because its concentration doesn't change.

Effect of Concentration Changes

Concentration changes can significantly affect the position of equilibrium. If the concentration of a product or reactant is increased, the equilibrium will shift to oppose that change. For example, increasing \([\mathrm{Ca}^{2+}]\) would drive the reaction to the left to form more solid calcium phosphate, thus reducing the excess ions. Similarly, decreasing \([\mathrm{PO}_{4}^{3-}]\) would cause the equilibrium to shift to the right, increasing the dissociation of calcium phosphate to compensate. This behavior is consistent with Le Chatelier's Principle, which predicts that a system at equilibrium responds to a change in a way that counteracts the change.

Effect of pH on Equilibrium

pH changes can also influence equilibrium. In the system involving calcium phosphate, a decrease in pH means an increase in \([\mathrm{H}^{+}]\) ions. These hydrogen ions can react with phosphate ions to form \(\mathrm{HPO}_{4}^{2-}\), thereby reducing the concentration of \([\mathrm{PO}_{4}^{3-}]\). This drop in phosphate ion concentration shifts the reaction to the right, enhancing the dissociation of calcium phosphate into its ion components. Understanding how pH affects the equilibrium is crucial in biological systems, as many metabolic processes depend on maintaining specific pH levels.