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### (a) Electronic Configuration of [tex]\( \text{Cu}^{2+} \)[/tex]
Copper ([tex]\( \text{Cu} \)[/tex]) has an atomic number of 29. This means a neutral copper atom has 29 electrons. The electronic configuration of a neutral copper atom is:
[tex]\[ [\text{Ar}] 3d^{10} 4s^1 \][/tex]
When copper loses two electrons to form [tex]\( \text{Cu}^{2+} \)[/tex], it loses those electrons from the 4s and 3d orbitals. Therefore, the electronic configuration of [tex]\( \text{Cu}^{2+} \)[/tex] is:
[tex]\[ [\text{Ar}] 3d^9 \][/tex]
### (c) Explanation for Cr having the Configuration [tex]\( [\text{Ar}] 4s^1 3d^5 \)[/tex] rather than [tex]\( [\text{Ar}] 4s^2 3d^4 \)[/tex]
Chromium (Cr) has an atomic number of 24. For a neutral Cr atom, the expected electronic configuration might be:
[tex]\[ [\text{Ar}] 4s^2 3d^4 \][/tex]
However, the actual configuration is:
[tex]\[ [\text{Ar}] 4s^1 3d^5 \][/tex]
This occurs because having a half-filled [tex]\( 3d \)[/tex]-subshell (i.e., [tex]\( 3d^5 \)[/tex]) provides extra stability. Electrons in a half-filled [tex]\( d \)[/tex]-orbital experience less repulsion and more exchange energy. Exchange energy is a quantum mechanical effect where the parallel spins of the [tex]\( d \)[/tex]-electrons result in a more stable arrangement. Therefore, to achieve this stable configuration, one electron from the 4s orbital is promoted to the 3d orbital, resulting in [tex]\( [\text{Ar}] 4s^1 3d^5 \)[/tex].
### (d) Boiling Points of HF and H[tex]\(_2\)[/tex]O
- Boiling Point of HF: [tex]\(19^\circ \text{C}\)[/tex]
- Boiling Point of H[tex]\(_2\)[/tex]O: [tex]\(100^\circ \text{C}\)[/tex]
The significant difference in the boiling points of hydrogen fluoride (HF) and water (H[tex]\(_2\)[/tex]O) can be explained by the nature and strength of hydrogen bonding in these compounds.
1. Hydrogen Bonding in HF:
- HF has hydrogen bonding, but it is not as extensive as in water. Each HF molecule forms hydrogen bonds with only one other HF molecule on average, leading to a more linear structure.
- Because of these less extensive hydrogen bonds, HF has a lower boiling point ([tex]\(19^\circ \text{C}\)[/tex]) as less energy is required to break the intermolecular interactions.
2. Hydrogen Bonding in H[tex]\(_2\)[/tex]O:
- Water (H[tex]\(_2\)[/tex]O) can form up to four hydrogen bonds per molecule. On average, each water molecule forms hydrogen bonds with approximately four neighboring water molecules, leading to a three-dimensional network.
- This extensive hydrogen bonding network requires significantly more energy to break, resulting in a much higher boiling point ([tex]\(100^\circ \text{C}\)[/tex]) for water.
Thus, the greater hydrogen bonding capability of water compared to HF leads to its significantly higher boiling point.
### (a) Electronic Configuration of [tex]\( \text{Cu}^{2+} \)[/tex]
Copper ([tex]\( \text{Cu} \)[/tex]) has an atomic number of 29. This means a neutral copper atom has 29 electrons. The electronic configuration of a neutral copper atom is:
[tex]\[ [\text{Ar}] 3d^{10} 4s^1 \][/tex]
When copper loses two electrons to form [tex]\( \text{Cu}^{2+} \)[/tex], it loses those electrons from the 4s and 3d orbitals. Therefore, the electronic configuration of [tex]\( \text{Cu}^{2+} \)[/tex] is:
[tex]\[ [\text{Ar}] 3d^9 \][/tex]
### (c) Explanation for Cr having the Configuration [tex]\( [\text{Ar}] 4s^1 3d^5 \)[/tex] rather than [tex]\( [\text{Ar}] 4s^2 3d^4 \)[/tex]
Chromium (Cr) has an atomic number of 24. For a neutral Cr atom, the expected electronic configuration might be:
[tex]\[ [\text{Ar}] 4s^2 3d^4 \][/tex]
However, the actual configuration is:
[tex]\[ [\text{Ar}] 4s^1 3d^5 \][/tex]
This occurs because having a half-filled [tex]\( 3d \)[/tex]-subshell (i.e., [tex]\( 3d^5 \)[/tex]) provides extra stability. Electrons in a half-filled [tex]\( d \)[/tex]-orbital experience less repulsion and more exchange energy. Exchange energy is a quantum mechanical effect where the parallel spins of the [tex]\( d \)[/tex]-electrons result in a more stable arrangement. Therefore, to achieve this stable configuration, one electron from the 4s orbital is promoted to the 3d orbital, resulting in [tex]\( [\text{Ar}] 4s^1 3d^5 \)[/tex].
### (d) Boiling Points of HF and H[tex]\(_2\)[/tex]O
- Boiling Point of HF: [tex]\(19^\circ \text{C}\)[/tex]
- Boiling Point of H[tex]\(_2\)[/tex]O: [tex]\(100^\circ \text{C}\)[/tex]
The significant difference in the boiling points of hydrogen fluoride (HF) and water (H[tex]\(_2\)[/tex]O) can be explained by the nature and strength of hydrogen bonding in these compounds.
1. Hydrogen Bonding in HF:
- HF has hydrogen bonding, but it is not as extensive as in water. Each HF molecule forms hydrogen bonds with only one other HF molecule on average, leading to a more linear structure.
- Because of these less extensive hydrogen bonds, HF has a lower boiling point ([tex]\(19^\circ \text{C}\)[/tex]) as less energy is required to break the intermolecular interactions.
2. Hydrogen Bonding in H[tex]\(_2\)[/tex]O:
- Water (H[tex]\(_2\)[/tex]O) can form up to four hydrogen bonds per molecule. On average, each water molecule forms hydrogen bonds with approximately four neighboring water molecules, leading to a three-dimensional network.
- This extensive hydrogen bonding network requires significantly more energy to break, resulting in a much higher boiling point ([tex]\(100^\circ \text{C}\)[/tex]) for water.
Thus, the greater hydrogen bonding capability of water compared to HF leads to its significantly higher boiling point.
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