Problem 106 - Chemistry The Molecular Science

Question

Imagine yourself to be the size of ions and molecules inside a beaker containing this equilibrium mixture with a \(K_{\mathrm{c}}\) greater than \(1 .\) $$ \mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}(\mathrm{aq})+4 \mathrm{Cl}^{-}(\mathrm{aq}) \rightleftharpoons \mathrm{CoCl}_{4}^{2-}(\mathrm{aq})+6 \mathrm{H}_{2} \mathrm{O}(\ell)$$ pink blue Write a brief description of what you observe around you before and after additional water is added to the mixture.

Step-by-Step Solution

Answer

Initially, more blue ions are present. Adding water shifts the equilibrium to form more pink ions.

Step 1: Understand the Reaction

The given reaction is an equilibrium reaction: \[ \text{Co(H}_2\text{O)}_{6}^{2+} (\text{aq}) + 4 \text{Cl}^- (\text{aq}) \rightleftharpoons \text{CoCl}_4^{2-} (\text{aq}) + 6 \text{H}_2\text{O} (\ell) \]This involves cobalt complexes, changing from a pink complex to a blue one. A high \( K_c \) value indicates that the forward reaction is favored, meaning more of the blue \( \text{CoCl}_4^{2-} \) will be present at equilibrium.

Step 2: Describe Initial Equilibrium

Initially, in equilibrium, there is a mix of pink \( \text{Co(H}_2\text{O)}_{6}^{2+} \) ions and blue \( \text{CoCl}_4^{2-} \) ions. Given the \( K_c \) is greater than \( 1 \), there will be more blue \( \text{CoCl}_4^{2-} \) ions compared to pink \( \text{Co(H}_2\text{O)}_{6}^{2+} \) ions. Water molecules are abundant, mostly floating around.

Step 3: Predict Changes upon Adding Water

When additional water is added, Le Chatelier's principle suggests the equilibrium will shift to counteract this change. Since water is a product, the equilibrium will shift to the left to produce more reactants, resulting in more pink \( \text{Co(H}_2\text{O)}_{6}^{2+} \) ions and fewer blue \( \text{CoCl}_4^{2-} \) ions.

Step 4: Describe Observations after Adding Water

After adding water, the color of the solution would change towards pink as the concentration of \( \text{Co(H}_2\text{O)}_{6}^{2+} \) increases. You would observe many \( \text{Cl}^- \) ions being released back into the solution, while water molecules remain the most abundant component around you.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry. It explains how equilibrium shifts when a system experiences a change in concentration, temperature, or pressure. In our exercise, we see this principle in action.

• Understanding the shift: When additional water is added to our equilibrium system, we observe a shift in the reaction.
• Reaction Direction: Adding water increases the concentration of a product (water itself), so according to Le Chatelier's Principle, the system will adjust by favoring the reverse reaction to reduce water concentration.
• Outcome: This results in more pink \ \( \text{Co(H}_2\text{O)}_{6}^{2+} \ \) and fewer blue \ \( \text{CoCl}_4^{2-} \ \).

This principle provides a predictive framework, allowing chemists to understand how changes impact a chemical system. It's crucial for controlling reactions in industrial and laboratory settings.

Cobalt Complexes

Cobalt complexes are fascinating examples of transition metal chemistry. The exercise features two such complexes, each with distinct colors:

• Cobalt Hexaaqua Complex: The pink \ \( \text{Co(H}_2\text{O)}_{6}^{2+} \ \) ion is formed when cobalt is surrounded by six water molecules. It's stable in aqueous solutions and exhibits a lovely pink hue.
• Tetrachlorocobaltate Complex: The blue \ \( \text{CoCl}_4^{2-} \ \) ion arises when cobalt coordinates with four chloride ions. Its blue color provides a stark contrast to the pink complex.
• Color Changes: The observable color change from pink to blue (or vice versa) is an indicator of the predominant complex present in the solution.

These complexes exemplify how metal ions can form different structures with varied properties depending on the surrounding ligands.

Equilibrium Constant

The equilibrium constant, \( K_c \), is a critical parameter in chemical reactions. It quantifies the ratio of products to reactants at equilibrium. In our specific reaction:

• High \( K_c \) Value: A \( K_c \) greater than 1 indicates a reaction that favors product formation. For our equilibrium, this means more \ \( \text{CoCl}_4^{2-} \ \) is present at equilibrium than \ \( \text{Co(H}_2\text{O)}_{6}^{2+} \ \).
• Equilibrium Expressions: The \( K_c \) expression for our reaction is formulated as \ \( K_c = \frac{[\text{CoCl}_4^{2-}]}{[\text{Co(H}_2\text{O)}_{6}^{2+}][\text{Cl}^-]^4} \).
• Interpretation: The larger the \( K_c \), the more extensively the forward reaction proceeds, confirming that, under normal conditions, the blue complex dominates.

The equilibrium constant is a powerful tool for predicting the position of equilibrium and the extent of reactions under various conditions.