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Chapter 20: Problem 30

Predict the number of unpaired electrons in these complex ions: (a) \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}(\mathrm{b})\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\)

Short Answer

Expert verified
The number of unpaired electrons in both \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\) and \(\left[\mathrm{Cr}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\) complexes are 4.

Step by step solution

01

Determine chromium oxidation state in the first complex

Considering the first complex \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{4-}\), each CN- ion provides a charge of -1, and there are six of them, which total to -6. However, the overall charge of the complex is -4. Thus, for the complex to neutralize, the chromium metal must be in the state of +2. So, the oxidation state of Cr in this complex is +2.
02

Determine the number of unpaired electrons in the first complex

Using the periodic table, Chromium (Cr) has atomic number 24, and its electron configuration can be written as [Ar] 3d5 4s1. When chromium is oxidized to the +2 state, the overall electron configuration becomes [Ar] 3d4. Therefore, there are 4 unpaired electrons.
03

Determine chromium oxidation state in the second complex

Now, considering the second complex \(\left[\mathrm{Cr}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\), the water molecule has no charge. Thus, the 2+ charge all arises from chromium. Therefore, the oxidation state of Cr in this complex is +2.
04

Determine the number of unpaired electrons in the second complex

Having Cr2+ in this complex as well, the electron configuration will be identical to the step above: [Ar] 3d4. Therefore, this complex also has 4 unpaired electrons.

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Most popular questions from this chapter

Without referring to the text, write the ground-state electron configurations of the first-row transition metals. Explain any irregularities.

The absorption maximum for the complex ion \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) occurs at \(470 \mathrm{nm}\). (a) Predict the color of the complex and (b) calculate the crystal field splitting in kilojoules per mole.

Define the terms (a) labile complex, (b) inert complex.

Give the oxidation numbers of the metals in these species: (a) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) (b) \(\mathrm{K}_{3}\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]\) (c) \(\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-}\)

Compounds containing the \(\mathrm{Sc}^{3+}\) ion are colorless, whereas those containing the \(\mathrm{Ti}^{3+}\) ion are colored. Explain.
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