Problem 116 - Chemistry The Molecular Science

Question

For the equilibrium $$ \mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}(\mathrm{aq})+4 \mathrm{Cl}^{-}(\mathrm{aq}) \rightleftharpoons \mathrm{CoCl}_{4}^{2-}(\mathrm{aq})+6 \mathrm{H}_{2} \mathrm{O}(\ell) $$ pink blue \(K_{\mathrm{c}}\) is somewhat greater than 1 . If water is added to a blue solution of \(\mathrm{CoCl}_{4}^{2-}(\mathrm{aq}),\) the color changes from blue to pink. (a) Does water appear in the equilibrium constant expression for this reaction? (b) How can adding water shift the equilibrium to the left? (c) Is this shift in the equilibrium in accord with Le Chatelier's principle? Why or why not?

Step-by-Step Solution

Answer

(a) No, water does not appear in the expression. (b) It dilutes ions, shifting equilibrium left. (c) Yes, this aligns with Le Chatelier's principle.

Step 1: Understanding Equilibrium Constant Expression

The equilibrium constant expression, \(K_c\), for a reaction is given as \(K_c = \frac{[products]}{[reactants]}\). Generally, only substances in the aqueous and gaseous states are included. Since water is a liquid in this reaction, it does not appear in the \(K_c\) expression.

Step 2: Investigating Effect of Adding Water

Adding water to the system will decrease the concentration of all aqueous ions due to dilution. This especially dilutes \(\mathrm{CoCl}_{4}^{2-}\), causing the reaction to shift left to produce more \(\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}^{2+}\). Consequently, the solution changes from blue to pink.

Step 3: Analyzing According to Le Chatelier's Principle

Le Chatelier's principle states that if a dynamic equilibrium is disturbed, the system will adjust to minimize the disturbance. Adding water reduces ion concentration, shifting the equilibrium to the left to counteract the change, thus aligning with Le Chatelier's principle.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that describes how a system at equilibrium responds to external changes. This principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will shift its position to counteract the change and re-establish equilibrium.

To put it simply, when a change occurs—such as a change in concentration, temperature, or pressure—the system will naturally adjust to minimize the effect of that change. In the case of our reaction, adding water causes a dilution of the reactants and products. According to Le Chatelier's Principle:

• The system will shift to the side that compensates for the diluted substances.
• In our reaction, this means producing more of the water-containing complex, resulting in a shift to the left.
• This shift is recognized as the solution changing from blue to pink.

This principle helps chemists predict the behavior of reactions under varying conditions, making it a valuable tool in controlling and optimizing chemical processes.

Equilibrium Constant

The equilibrium constant, denoted as \(K_c\), is a number that provides insight into the composition of a reaction at equilibrium. It is expressed using the concentrations of the products and reactants in the expression \(K_c = \frac{[\text{products}]}{[\text{reactants}]}\).

For reactions involving only aqueous and gaseous states, the concentrations of these species are used in the expression. However, it is important to note:

• Pure solids and liquids are not included in the equilibrium expression because their concentrations remain constant.
• In our specific reaction, water appears as a liquid, so it is excluded from the \(K_c\) expression.
• This exclusion simplifies the calculation and reflects only the aqueous reactants and products.

The value of \(K_c\) provides crucial information:

• If \(K_c\) is greater than 1, as in this reaction, it suggests that products are favored over reactants at equilibrium.
• Understanding \(K_c\) helps predict the direction in which a reaction will proceed to reach equilibrium.

Reaction Dynamics

Reaction dynamics involves studying how reactions proceed and how conditions affect the rates and mechanisms of these processes. In an equilibrium reaction, dynamics are particularly important because they determine how rapidly and effectively the reaction can respond to changes.

In the context of our reaction:

• When water is added, the dynamics of the reaction are altered as concentration changes occur.
• The system's response—to shift left—demonstrates the interplay between kinetics and equilibrium principles.
• The transition from blue to pink color indicates dynamic changes as new equilibrium is established.

Reaction dynamics also encompass the collision theory and transition states:

• The rate of reaction is influenced by the frequency and energy of collisions between particles.
• At equilibrium, forward and reverse reaction rates are equal, maintaining the balance of the dynamic system.

Consequently, reaction dynamics provide insight into how changes such as those invoked by Le Chatelier's principle are achieved in practical scenarios.