Chapter 22: Problem 68
How many geometric isomers of the complex ion \(\left[\mathrm{Cr}(\text { dmen })_{3}\right]^{3+}\) can exist? (dmen is the bidentate ligand \(1,1-\) dimethylethy-lenediamine. $$\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}$$
Short Answer
Expert verified
Only one geometric isomer exists for \([\text{Cr}(\text{dmen})_3 ]^{3+}\).
Step by step solution
01
Understanding the Complex Ion
The complex ion is \([ \text{Cr} ( \text{dmen})_3 ]^{3+}\). Here, Cr is a metal that forms octahedral complexes, and dmen is a bidentate ligand, connecting to the metal at two coordination sites. Each dmen ligand forms a ring in the structure due to its bidentate nature.
02
Counting the Coordination Sites
In an octahedral complex, the metal ion (Cr) is surrounded by 6 coordination sites. Since dmen is a bidentate ligand, each dmen occupies two coordination sites. Therefore, \(3\) dmen ligands completely utilize the 6 available coordination sites around the chromium atom.
03
Determining Possible Geometric Isomers
For the complex \([\text{Cr} ( \text{dmen})_3 ]^{3+}\) with three identical bidentate ligands, geometric isomerism occurs due to the arrangement around the metal center. With three identical bidentate ligands in an octahedral geometry, only one arrangement is possible because all the ligands are identical. They will form a symmetrical structure which does not lead to different isomers.
04
Conclusion on Geometric Isomers
Since all three bidentate ligands (dmen) are identical and occupy the entire coordination sphere symmetrically in an octahedral complex, no geometric isomerism occurs. Therefore, there is only one possible geometric arrangement of the complex ion \([\text{Cr} (\text{dmen})_3 ]^{3+}\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Octahedral Complexes
In coordination chemistry, octahedral complexes are one of the most common types of molecular geometries seen in metal complexes. An octahedral structure consists of a central metal atom surrounded by six ligands at the corners of an octahedron. The term "octahedral" comes from the eight faces that make up this three-dimensional shape.
When a central metal ion is bonded to six atoms or groups of atoms (ligands), it forms a highly symmetrical structure. The geometry provides a unique environment because of its specific spatial arrangement. Understanding this structure helps in determining the physical and chemical properties of the complex.
Given that octahedral structures are symmetric, they tend to be very stable. The arrangement allows the formation of multiple isomers, especially in larger ligands or mixed-ligand complexes. However, when all ligands are identical and occupy equivalent positions, like the complex described, geometric isomerism is minimized.
When a central metal ion is bonded to six atoms or groups of atoms (ligands), it forms a highly symmetrical structure. The geometry provides a unique environment because of its specific spatial arrangement. Understanding this structure helps in determining the physical and chemical properties of the complex.
Given that octahedral structures are symmetric, they tend to be very stable. The arrangement allows the formation of multiple isomers, especially in larger ligands or mixed-ligand complexes. However, when all ligands are identical and occupy equivalent positions, like the complex described, geometric isomerism is minimized.
Bidentate Ligands
Bidentate ligands are special types of ligands that can bind to a metal atom at two distinct points, effectively forming a ring structure with the metal center. The term "bidentate" translates to "two teeth," indicating the ligand's ability to latch onto the metal ion twice.
This two-point attachment can increase the stability of a complex due to the chelate effect. This effect occurs because rings formed by bidentate ligands lower the energy of the system, making the entire complex more stable than if monodentate ligands were used.
In the complex \([\text{Cr} (\text{dmen})_3 ]^{3+}\), each dmen ligand serves as a bidentate ligand. This means it occupies two coordination sites, effectively forming a three-ring organic structure around the central chromium ion. The formation of these rings plays a crucial role in determining the arrangement of the entire complex, contributing to its stability and symmetry.
This two-point attachment can increase the stability of a complex due to the chelate effect. This effect occurs because rings formed by bidentate ligands lower the energy of the system, making the entire complex more stable than if monodentate ligands were used.
In the complex \([\text{Cr} (\text{dmen})_3 ]^{3+}\), each dmen ligand serves as a bidentate ligand. This means it occupies two coordination sites, effectively forming a three-ring organic structure around the central chromium ion. The formation of these rings plays a crucial role in determining the arrangement of the entire complex, contributing to its stability and symmetry.
Coordination Chemistry
Coordination chemistry is a fascinating area of inorganic chemistry focused on the study of complex compounds and their interactions. In these complexes, a central metal atom is surrounded by molecules or ions known as ligands. The metal-ligand interactions are key to understanding the properties and behaviors of these compounds.
In octahedral complexes, coordination chemistry often involves exploring how different ligand arrangements can lead to various isomers with distinctive chemical and physical properties. With different ligands or mixed types, multiple geometric isomers could potentially form.
However, in the example of \([\text{Cr} (\text{dmen})_3 ]^{3+}\), since the ligands are all identical, the configuration results in a highly symmetric and singular structure, eliminating isomers. This aspect of coordination chemistry illuminates the relationship between ligand identity and spatial arrangement, crucial for predicting the formation of geometric isomers or lack thereof."}]}}]} 40+11 tundra-crossing 頇╆笀 氍 58 歆勳爼頃 韮愱惮 韼胳潣 瓴氍 雼れ嫓 鞓り皝歆 項れ澊肟 甑“ 臧滊厫鞚 攵臁表暅 於旍姢毳 齑 觳 瓿摐雼 鞎 鞏检柎攵 氙检瓿糰ders: 40+12 something like this 氇厰 靾滉皠鞚 靾橃啞 鞓娂 animacji-animated blind execution 電ル牓鞛堧姅 頉堧牗霐 頃橃毎 nama animatorboxDress 鞛愳偘 氚濎晞鞖 鞎堨爠鞐 ac岷 芒y毽棎瓴",
In octahedral complexes, coordination chemistry often involves exploring how different ligand arrangements can lead to various isomers with distinctive chemical and physical properties. With different ligands or mixed types, multiple geometric isomers could potentially form.
However, in the example of \([\text{Cr} (\text{dmen})_3 ]^{3+}\), since the ligands are all identical, the configuration results in a highly symmetric and singular structure, eliminating isomers. This aspect of coordination chemistry illuminates the relationship between ligand identity and spatial arrangement, crucial for predicting the formation of geometric isomers or lack thereof."}]}}]} 40+11 tundra-crossing 頇╆笀 氍 58 歆勳爼頃 韮愱惮 韼胳潣 瓴氍 雼れ嫓 鞓り皝歆 項れ澊肟 甑“ 臧滊厫鞚 攵臁表暅 於旍姢毳 齑 觳 瓿摐雼 鞎 鞏检柎攵 氙检瓿糰ders: 40+12 something like this 氇厰 靾滉皠鞚 靾橃啞 鞓娂 animacji-animated blind execution 電ル牓鞛堧姅 頉堧牗霐 頃橃毎 nama animatorboxDress 鞛愳偘 氚濎晞鞖 鞎堨爠鞐 ac岷 芒y毽棎瓴",