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Question: How many of the following species obey Sidgwick's EAN rule? K₄[Fe(CN)₆], K₃[Fe(CN)₆], [Ni(CO)₄], [Cr...

How many of the following species obey Sidgwick's EAN rule? K₄[Fe(CN)₆], K₃[Fe(CN)₆], [Ni(CO)₄], [Cr(NH₃)₆]³⁺, [Cu(CN)₄]³⁻, [Co(NH₃)₆]³⁺, [Ni(NH₃)₆]²⁺

Answer

4

Explanation

Solution

The Effective Atomic Number (EAN) rule states that the total number of electrons around the central metal atom in a complex, including its own electrons and those donated by the ligands, should be equal to the atomic number of the next noble gas. The formula for EAN is:

EAN = Z - X + Y

Where:

Z = Atomic number of the central metal
X = Oxidation state of the central metal (number of electrons lost)
Y = Total number of electrons donated by the ligands (2 electrons per coordinate bond from each monodentate ligand)

Noble gas atomic numbers are 10 (Ne), 18 (Ar), 36 (Kr), 54 (Xe), 86 (Rn).

Let's calculate the EAN for each given species:

  1. K₄[Fe(CN)₆]

    • Metal: Fe (Z = 26)
    • Oxidation state of Fe: 4(+1) + x + 6(-1) = 0 ⇒ x = +2. So, X = 2.
    • Electrons from ligands: 6 CN⁻ ligands × 2 electrons/ligand = 12. So, Y = 12.
    • EAN = 26 - 2 + 12 = 36.
    • Since 36 is the atomic number of Krypton (Kr), this complex obeys the EAN rule.

  2. K₃[Fe(CN)₆]

    • Metal: Fe (Z = 26)
    • Oxidation state of Fe: 3(+1) + x + 6(-1) = 0 ⇒ x = +3. So, X = 3.
    • Electrons from ligands: 6 CN⁻ ligands × 2 electrons/ligand = 12. So, Y = 12.
    • EAN = 26 - 3 + 12 = 35.
    • 35 is not a noble gas atomic number, so this complex does not obey the EAN rule.

  3. [Ni(CO)₄]

    • Metal: Ni (Z = 28)
    • Oxidation state of Ni: x + 4(0) = 0 ⇒ x = 0. So, X = 0.
    • Electrons from ligands: 4 CO ligands × 2 electrons/ligand = 8. So, Y = 8.
    • EAN = 28 - 0 + 8 = 36.
    • Since 36 is the atomic number of Krypton (Kr), this complex obeys the EAN rule.

  4. [Cr(NH₃)₆]³⁺

    • Metal: Cr (Z = 24)
    • Oxidation state of Cr: x + 6(0) = +3 ⇒ x = +3. So, X = 3.
    • Electrons from ligands: 6 NH₃ ligands × 2 electrons/ligand = 12. So, Y = 12.
    • EAN = 24 - 3 + 12 = 33.
    • 33 is not a noble gas atomic number, so this complex does not obey the EAN rule.

  5. [Cu(CN)₄]³⁻

    • Metal: Cu (Z = 29)
    • Oxidation state of Cu: x + 4(-1) = -3 ⇒ x = +1. So, X = 1.
    • Electrons from ligands: 4 CN⁻ ligands × 2 electrons/ligand = 8. So, Y = 8.
    • EAN = 29 - 1 + 8 = 36.
    • Since 36 is the atomic number of Krypton (Kr), this complex obeys the EAN rule.

  6. [Co(NH₃)₆]³⁺

    • Metal: Co (Z = 27)
    • Oxidation state of Co: x + 6(0) = +3 ⇒ x = +3. So, X = 3.
    • Electrons from ligands: 6 NH₃ ligands × 2 electrons/ligand = 12. So, Y = 12.
    • EAN = 27 - 3 + 12 = 36.
    • Since 36 is the atomic number of Krypton (Kr), this complex obeys the EAN rule.

  7. [Ni(NH₃)₆]²⁺

    • Metal: Ni (Z = 28)
    • Oxidation state of Ni: x + 6(0) = +2 ⇒ x = +2. So, X = 2.
    • Electrons from ligands: 6 NH₃ ligands × 2 electrons/ligand = 12. So, Y = 12.
    • EAN = 28 - 2 + 12 = 38.
    • 38 is not a noble gas atomic number, so this complex does not obey the EAN rule.

The species that obey Sidgwick's EAN rule are: K₄[Fe(CN)₆] [Ni(CO)₄] [Cu(CN)₄]³⁻ [Co(NH₃)₆]³⁺

There are 4 such species.