Question

In $PO_4^{3-}$ ion, the average charge on the oxygen atoms is [NCERT Pg. 105]

• A. +1
• B. -1
• C. -0.75
• D. +0.75

Answer 1

Answer: (C)

-0.75

Answer 2

To find the average charge on the oxygen atoms in the $PO_4^{3-}$ ion, we need to consider the concept of resonance and formal charge distribution.

1. Determine the total valence electrons:

   • Phosphorus (P) is in Group 15, so it has 5 valence electrons.
   • Oxygen (O) is in Group 16, so it has 6 valence electrons.
   • For $PO_4^{3-}$: 1 (P atom) × 5 electrons + 4 (O atoms) × 6 electrons + 3 (for the -3 charge) = 5 + 24 + 3 = 32 valence electrons.

2. Draw the Lewis structure and assign formal charges:

   • Phosphorus is the central atom, bonded to four oxygen atoms.
   • A common and more stable Lewis structure for phosphate involves phosphorus expanding its octet to minimize formal charges. This structure has one P=O double bond and three P-O single bonds.
   • Let's calculate the formal charges for this structure:
     • For Phosphorus (P):
       • Valence electrons = 5
       • Non-bonding electrons = 0
       • Bonding electrons = 4 (1 double bond) + 6 (3 single bonds) = 10 electrons
       • Formal Charge (P) = 5 - 0 - (1/2 × 10) = 5 - 5 = 0
     • For the Oxygen atom with a double bond (P=O):
       • Valence electrons = 6
       • Non-bonding electrons = 4 (2 lone pairs)
       • Bonding electrons = 4 (1 double bond)
       • Formal Charge (O=P) = 6 - 4 - (1/2 × 4) = 6 - 4 - 2 = 0
     • For the Oxygen atoms with single bonds (P-O): (There are three such oxygen atoms)
       • Valence electrons = 6
       • Non-bonding electrons = 6 (3 lone pairs)
       • Bonding electrons = 2 (1 single bond)
       • Formal Charge (O-P) = 6 - 6 - (1/2 × 2) = 6 - 6 - 1 = -1

3. Consider Resonance:

   • The $PO_4^{3-}$ ion exhibits resonance. The double bond can be formed with any of the four oxygen atoms.
   • This means there are four equivalent resonance structures.
   • In each resonance structure, three oxygen atoms carry a formal charge of -1, and one oxygen atom carries a formal charge of 0. The phosphorus atom carries a formal charge of 0.
   • The total charge of the ion (-3) is distributed among these four oxygen atoms.

4. Calculate the average charge:

   • Since all four P-O bonds are equivalent due to resonance, the total negative charge of -3 is delocalized equally over all four oxygen atoms.
   • Average charge on each oxygen atom = (Total charge on the ion) / (Number of oxygen atoms)
   • Average charge = (-3) / 4 = -0.75

Therefore, the average charge on the oxygen atoms in the $PO_4^{3-}$ ion is -0.75.

Explanation: The $PO_4^{3-}$ ion exhibits resonance, with the total negative charge of -3 being delocalized over all four equivalent oxygen atoms. In the most stable resonance structures, three oxygen atoms carry a formal charge of -1, and one oxygen atom carries a formal charge of 0. Due to the rapid interconversion of these structures, each oxygen atom effectively shares the three negative charges. Thus, the average charge on each oxygen atom is the total charge of the ion divided by the number of oxygen atoms: $-3 / 4 = -0.75$.