You know the following about a coordination compound: (1) The partial empirical formula is \(\mathrm{KM}\left(\mathrm{CrO}_{4}\right) \mathrm{Cl}_{2}\left(\mathrm{NH}_{3}\right)_{4}\) (2) It has A (red) and B (blue) crystal forms. (3) When \(1.0 \mathrm{~mol}\) of \(\mathrm{A}\) or \(\mathrm{B}\) reacts with \(1.0 \mathrm{~mol}\) of \(\mathrm{AgNO}_{3}, 0.50 \mathrm{~mol}\) of a red precipitate forms immediately. (4) After the reaction in ( 3 ), \(1.0 \mathrm{~mol}\) of A reacts very slowly with \(1.0 \mathrm{~mol}\) of silver oxalate \(\left(\mathrm{Ag}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) to form \(2.0 \mathrm{~mol}\) of a white precipitate. (Oxalate can displace other ligands.) (5) After the reaction in ( 3 ), \(1.0 \mathrm{~mol}\) of \(\mathrm{B}\) does not react further with \(1.0 \mathrm{~mol}\) of \(\mathrm{AgNO}_{3}\). From this information, determine the following: (a) The coordination number of \(\mathrm{M}\) (b) The group(s) bonded to \(\mathrm{M}\) ionically and covalently (c) The stereochemistry of the red and blue forms

Step by step solution

01

- Analyze the empirical formula

The given empirical formula is \(\text{KM(CrO}_4)\text{Cl}_2(\text{NH}_3)_4\). This suggests the compound contains potassium (\text{K}), a metal (\text{M}), chromate (\text{CrO}_4), chloride (\text{Cl}), and ammonia (\text{NH}_3).

02

- Identify reacting species with AgNO3

From point (3), 1.0 mol of \(\text{A}\) or \(\text{B}\) reacts with 1.0 mol of \(\text{AgNO}_3\) to form 0.50 mol of red precipitate. The red precipitate is due to the precipitation of silver chromate (\text{Ag}_2\text{CrO}_4). Thus, \(\text{CrO}_4^2-\) group forms a red precipitate with \(\text{Ag}^+\).

03

- Investigate further reactions with silver oxalate

From point (4), after the initial reaction in step 2, 1.0 mol of \(\text{A}\) reacts very slowly with 1.0 mol \(\text{Ag}_2\text{C}_2\text{O}_4\) to form 2.0 mol of white precipitate. Silver chloride (\text{AgCl}) is known to be white. Thus, chloride (\text{Cl}^-) is ionically bonded as it forms \(\text{AgCl}\) white precipitate.

04

- Recognize non-reactivity of \(\text{B}\) after the initial reaction

From point (5), 1.0 mol of \(\text{B}\) does not react further with additional \(\text{AgNO}_3\) after the initial reaction. This indicates that all the chloride ions in \(\text{B}\) have precipitated out already in Step 2. Thus chloride ions must be outside the coordination sphere in \(\text{A}\).

05

- Determine the coordination number

From the empirical formula \(\text{KM(CrO}_4)\text{Cl}_2(\text{NH}_3)_4\), the metal \(\text{M}\) is coordinated with four \(\text{NH}_3\) and two \(\text{Cl}^-\). Thus, coordination number of \(\text{M}\) is 6.

06

- Identify bonds to ion \(\text{M}\)

From previous steps, \(\text{CrO}_4^2-\) is ionically bonded, \(\text{NH}_3\) and \(\text{Cl}^-\) are covalently bonded to metal ion \(\text{M}\).

07

- Determine the stereochemistry

From points (2) and (5), the two forms of crystallization A (red) and B (blue), likely represent linkage isomerism where the orientation of ligands are different around \(\text{M}\). Red form A indicates trans- isomer (relative cis \(\text{CrO}_4^2-\) and two axial \(\text{NH}_3\) ), Blue form B indicates cis isomer (relative trans forms).

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Key Concepts

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

Coordination Compounds

Coordination compounds are fascinating chemical structures where central metal atoms or ions are surrounded by molecules or ions known as ligands. The intriguing nature of these compounds often lies in their complex bonding and varied applications.
Coordination compounds form when ligands donate electron pairs to a central metal ion to form coordinate bonds. These can create diverse and geometrically rich structures, influencing their physical and chemical properties. A central metal like M in our exercise typically binds multiple ligands, leading to unique molecular configurations.

Empirical Formula Analysis

Analyzing empirical formulas help us understand the composition and structure of coordination compounds. The given formula, K[M(CrO_4)Cl_2(NH_3)_4] , reveals key insights. It suggests the presence of potassium (K), a central metal (M), chromate (CrO_4), chloride (Cl), and ammonia (NH_3) in the structure.
This analysis allows us to ascertain the central metal's coordination environment and the roles of different ligands. In our exercise, recognizing the presence of these components helps predict reactivity and interactions with other substances, especially in subsequent reactions with AgNO_3 and Ag_2C_2O_4.

Ligand Interactions

Ligands are vital to the function and structure of coordination compounds. They can be neutral molecules like NH_3 or charged ions like Cl^- and CrO_4^2-. These ligands donate pairs of electrons to the central metal, forming complex structures.
In the given compound K[M(CrO_4)Cl_2(NH_3)_4], , the ligands NH_3 and Cl^- form coordinate covalent bonds with the metal, impacting its spatial arrangement. The behavior of each ligand, such as CrO_4 forming a red precipitate with AgNO_3, , informs us about their ionic or covalent nature within the complex.
The intricate bonding of ligands establishes the coordination number of the metal, which is 6 in the exercise, suggesting an octahedral geometry.

Stereochemistry

Stereochemistry in coordination chemistry involves the spatial arrangement of ligands around the central metal. It determines the compound's optical and physical properties. Our coordination compound showcases two crystalline forms, red (A) and blue (B), highlighting different ligand arrangements.
Linkage IsomerismLinkage isomerism is when ligands can attach to the central metal in different ways, influencing compound properties. In our exercise, the red form (A) represents one isomer (likely trans-), while the blue form (B) represents another isomer (likely cis-).
Understanding these isomers and their reactions ensures a thorough grasp of their structures and behaviors in various chemical environments.