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Chapter 21: Problem 7

Figure 21.17 shows that the cis isomer of $\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}^{+}$ is optically active while the trans isomer is not optically active. Is the same true for \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}+?\) Explain.

Short Answer

Expert verified
The same is true for Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\), as the cis isomer is optically active due to its chirality, while the trans isomer is not optically active due to its symmetry. This is similar to the optical activity observed for the Co(en)\(_{2}\mathrm{Cl}_{2}^{+}\) isomers.

Step by step solution

01

Understanding optical activity

Optical activity is the ability of a substance to rotate the plane of polarized light. A molecule is considered to be optically active if it exists in a chiral form, meaning it cannot be superimposed with its mirror image. A molecule is considered chiral if it has at least one chiral center, which is usually a carbon atom with four different groups or substituents attached to it. In these given coordination compounds, the chiral center would be the central metal ion (Co) with different adjacent ligands.
02

Determine the structure of cis and trans isomers of Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\)

Both isomers have the same chemical formula, but they differ in the positions of the ligands around the coordination sphere of the Co atom. In the cis isomer, the two Cl ligands are adjacent to each other, while in the trans isomer, they are opposite to each other. To better visualize these structures, consider the following representations: cis-Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\): ``` NH3 | Cl-Co-Cl | NH3 ``` trans-Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\): ``` NH3 | Cl-Co-NH3 | Cl ```
03

Examine the cis isomer of Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\) for chirality

With the cis-isomer, the Co atom is connected to: 1. Two Cl atoms next to each other 2. Four NH3 groups around it Because the Co atom has two Cl and four NH\(_{3}\) groups in a specific arrangement around it, we can conclude that there is chirality in the cis isomer, resulting in optical activity.
04

Examine the trans isomer of Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\) for chirality

With the trans-isomer, the Co atom is connected to: 1. Two Cl atoms opposite to each other 2. Four NH3 groups around it In this case, the trans isomer has a plane of symmetry that divides the molecule into two mirror images that can be superimposed onto each other. Due to this symmetry, the trans isomer does not display chirality, and therefore, it is not optically active. In conclusion, the cis isomer of Co(NH\(_{3}\))\(_{4}\mathrm{Cl}_{2}^{+}\) is optically active while the trans isomer is not, which is the same as observed for the Co(en)\(_{2}\mathrm{Cl}_{2}^{+}\) isomers.

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Most popular questions from this chapter

Which of the following molecules exhibit(s) optical isomerism? a. \(c i s-P t\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\) b. trans-Ni(en) \(_{2} \mathrm{Br}_{2}\) (en is ethylenediamine) c. $c i s-\mathrm{Ni}(\mathrm{en})_{2} \mathrm{Br}_{2}(\text { en is ethylenediamine })$

Silver is sometimes found in nature as large nuggets; more often it is found mixed with other metals and their ores. Cyanide ion is often used to extract the silver by the following reaction that occurs in basic solution: $$\mathrm{Ag}(s)+\mathrm{CN}^{-}(a q)+\mathrm{O}_{2}(g) \stackrel{\mathrm{Basic}}{\longrightarrow} \mathrm{Ag}(\mathrm{CN})_{2}^{-}(a q)$$ Balance this equation by using the half-reaction method.

The compound $\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6} \mathrm{Cl}_{2}$ is green, whereas \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{2}\) is violet. Predict the predominant color of light absorbed by each compound. Which compound absorbs light with the shorter wavelength? Predict in which compound \(\Delta\) is greater and whether \(\mathrm{H}_{2} \mathrm{O}\) or \(\mathrm{NH}_{3}\) is the stronger field ligand. Do your conclusions agree with the spectrochemical series?

Consider the complex ions $\mathrm{Co}\left(\mathrm{NH}_{3}\right) 6^{3+}, \mathrm{Co}(\mathrm{CN})_{6}^{3-},\( and \)\mathrm{CoF}_{6}^{3-} .$ The wavelengths of absorbed electromagnetic radiation for these compounds (in no specific order) are \(770 \mathrm{nm},\) \(440 \mathrm{nm},\) and 290 $\mathrm{nm} .$ Match the complex ion to the wave- length of absorbed electromagnetic radiation.

a. In the absorption spectrum of the complex ion \(\mathrm{Cr}(\mathrm{NCS})_{6}^{3-}\) there is a band corresponding to the absorption of a photon of light with an energy of $1.75 \times 10^{4} \mathrm{cm}^{-1} .\( Given \)1 \mathrm{cm}^{-1}=1.986 \times 10^{-23} \mathrm{J},$ what is the wavelength of this photon? b. The \(\mathrm{Cr}-\mathrm{N}-\mathrm{C}\) bond angle in \(\mathrm{Cr}(\mathrm{NCS})_{6}^{3-}\) is predicted to be \(180^{\circ} .\) What is the hybridization of the N atom in the \(\mathrm{NCS}^{-}\) ligand when a Lewis acid-base reaction occurs between \(\mathrm{Cr}^{3+}\) and \(\mathrm{NCS}^{-}\) that would give a $180^{\circ} \mathrm{Cr}-\mathrm{N}-\mathrm{C}$ bond angle? \(\mathrm{Cr}(\mathrm{NCS})_{6}^{3-}\) undergoes substitution by ethylenediamine (en) according to the equation $$\mathrm{Cr}(\mathrm{NCS})_{6}^{3-}+2 \mathrm{en} \longrightarrow \mathrm{Cr}(\mathrm{NCS})_{2}(\mathrm{en})_{2}^{+}+4 \mathrm{NCS}^{-}$$ Does \(\mathrm{Cr}(\mathrm{NCS})_{2}(\mathrm{en})_{2}^{+}\) exhibit geometric isomerism? Does \(\mathrm{Cr}(\mathrm{NCS})_{2}(\mathrm{en})_{2}^{+}\) exhibit optical isomerism?
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