Problem 113 - Chemistry The Molecular Science

Question

If \(1.00 \mathrm{~mol}\) of each compound is dissolved in a separate sample of water sufficient to dissolve the compound, how many moles of ions are present in each solution? (a) \(\left[\mathrm{Pt}(\mathrm{en}) \mathrm{Cl}_{2}\right]\) (b) \(\mathrm{Na}\left[\mathrm{Cr}(\mathrm{en})_{2}\left(\mathrm{SO}_{4}\right)_{2}\right]\) (c) \(\mathrm{K}_{3}\left[\mathrm{Au}(\mathrm{CN})_{4}\right]\) (d) \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\left(\mathrm{NH}_{3}\right)_{4}\right] \mathrm{Cl}_{2}\)

Step-by-Step Solution

Answer

(a) 0 moles, (b) 2 moles, (c) 4 moles, (d) 2 moles.

Step 1: Analyze Compound (a)

The compound is \( \left[\mathrm{Pt}(\mathrm{en}) \mathrm{Cl}_{2}\right] \). This is a neutral complex and consists of \( \mathrm{Pt} \) coordinated with \( \mathrm{en} \) (ethylenediamine) and 2 chloride ions. The compound dissolves without dissociation. Therefore, the solution has only 1 mole of the compound and 0 moles of ions.

Step 2: Analyze Compound (b)

The compound is \( \mathrm{Na}\left[\mathrm{Cr}(\mathrm{en})_{2}\left(\mathrm{SO}_{4}\right)_{2}\right] \). It contains 1 mole of \( \mathrm{Na}^+ \) and 1 mole of the complex anion \( \left[\mathrm{Cr}(\mathrm{en})_{2}\left(\mathrm{SO}_{4}\right)_{2}\right]^- \). Upon dissolving, it produces 1 mole of \( \mathrm{Na}^+ \) ions and 1 mole of the complex ion, making a total of 2 moles of ions.

Step 3: Analyze Compound (c)

The compound is \( \mathrm{K}_{3}\left[\mathrm{Au}(\mathrm{CN})_{4}\right] \). It dissociates in water to form 3 moles of \( \mathrm{K}^+ \) ions and 1 mole of the complex ion \( \left[\mathrm{Au}(\mathrm{CN})_{4}\right]^{3-} \). Thus, the solution contains a total of 4 moles of ions.

Step 4: Analyze Compound (d)

The compound is \( \left[\mathrm{Ni}\left(\mathrm{H}_{2}\mathrm{O}\right)_{2}\left(\mathrm{NH}_{3}\right)_{4}\right] \mathrm{Cl}_{2} \). It dissociates in water to release 2 moles of \( \mathrm{Cl}^- \) ions; the complex itself does not dissociate further. Thus, the solution contains a total of 2 moles of ions.

Key Concepts

Complex Ions

Complex ions are fascinating structures in chemistry that arise when a central metal ion binds to a group of surrounding ligands. These ligands can be simple ions or more complex molecules. In these ions, the metal atom is at the center, surrounded by molecules or ions that are bonded through coordinate covalent bonds.
Some key features of complex ions are:

• The metal atom (or ion) acts as a Lewis acid by accepting electrons from the ligands.
• Ligands, which are the surrounding species, act as Lewis bases and donate electron pairs.
• The entire structure oftentimes carries a charge, making it an ion.

When these complex ions dissolve in water, they may or may not dissociate further depending on their structure and the charge balance. Complex ions play critical roles in areas such as catalysis, biological systems, and industrial applications.

Moles of Ions

When calculating moles of ions in a solution, it's crucial to consider both the complex structure and the nature of dissociation of compounds. Let's explore this idea further:
1. **Completely undissociated complexes**: Some compounds, like like compound (a) , remain intact when dissolved, meaning zero moles of ions are formed.
2. **Partially dissociated complexes**: In other scenarios, part of the complex dissociates in water, releasing different ions in the solution. Compound (b), for instance, disassociates to produce 2 moles of ions: 1 mole of \( \mathrm{Na}^+ \) and 1 mole of the complex anion.3. **Fully dissociated complexes**: These are formed when all possible ions are released into the solution, such as with compound (c), which releases 3 moles of \( \mathrm{K}^+ \) and 1 mole of the complex ion, totaling 4 moles of ions.
Understanding these dissociation details is essential for correctly predicting or analyzing ionic strengths in chemical solutions.

Coordination Compounds

Coordination compounds are unique structures where transition metals or elements bond with multiple ligands to form complex crystals and solutions. These compounds form due to the specific ability of certain metal ions to coordinate with multiple donor atoms from the ligands, creating a special configuration.
Key aspects of coordination compounds include:

• **Central metal (or ion)**: Usually, a transition metal serves as the center, responsible for the overall properties of the compound.
• **Coordination number**: This defines the number of ligand atoms directly bonded to the central metal, influencing the geometry and stability of the compound.
• **Ligands**: Can be ions or neutral molecules, which affect the color, solubility, and reactivity of the complex.
• **Dissociative behavior**: As seen in compounds like (d), some coordination compounds may only partially dissociate, affecting the number of free ions in solution.

These compounds are pivotal in fields ranging from medicine and biochemistry to materials science, highlighting their importance in both biological and industrial processes.