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Question: If the %-s-character in one Sb-H bond in SbH$_{3}$ is 1.0%. What is % p-character is the orbital occ...

If the %-s-character in one Sb-H bond in SbH3_{3} is 1.0%. What is % p-character is the orbital occupied by its lone pair -

A

99.0

B

97

C

90

D

None

Answer

None

Explanation

Solution

To determine the percentage of p-character in the orbital occupied by the lone pair in SbH₃, we use the principle of conservation of s and p character in hybrid orbitals.

  1. Identify the central atom and its hybridization:
    The central atom is Antimony (Sb), which belongs to Group 15. It forms three bonds with hydrogen atoms (Sb-H bonds) and has one lone pair of electrons. In a molecule like SbH₃, the central atom's valence orbitals (one s and three p) participate in hybridization to form the bonding orbitals and accommodate the lone pair.

  2. Conservation of s and p character:
    For a central atom undergoing hybridization, the sum of the s-character of all hybrid orbitals must be equal to 1 (since only one s-orbital is involved in hybridization). Similarly, the sum of the p-character of all hybrid orbitals must be equal to 3 (since three p-orbitals are involved).

    Let:

    • s_b be the s-character in each Sb-H bond orbital.
    • p_b be the p-character in each Sb-H bond orbital.
    • s_lp be the s-character in the lone pair orbital.
    • p_lp be the p-character in the lone pair orbital.

    There are 3 Sb-H bond orbitals and 1 lone pair orbital.

    • Total s-character: 3 * s_b + 1 * s_lp = 1
    • Total p-character: 3 * p_b + 1 * p_lp = 3

  3. Use the given information:
    We are given that the %-s-character in one Sb-H bond is 1.0%.
    So, s_b = 0.01.

  4. Calculate s_lp:
    Substitute s_b into the total s-character equation:
    3 * (0.01) + s_lp = 1
    0.03 + s_lp = 1
    s_lp = 1 - 0.03 = 0.97

  5. Calculate p_lp:
    For any hybrid orbital, the sum of its s-character and p-character is 1 (or 100%).
    So, for the lone pair orbital: s_lp + p_lp = 1
    0.97 + p_lp = 1
    p_lp = 1 - 0.97 = 0.03

  6. Convert to percentage:
    The percentage p-character in the orbital occupied by the lone pair is 0.03 * 100 = 3.0%.

  7. Compare with options:
    The calculated value is 3.0%.
    The given options are (A) 99.0, (B) 97, (C) 90, (D) None.
    Since 3.0% is not among options A, B, or C, the correct choice is (D) None.

The final answer is None\boxed{\text{None}}

Explanation of the solution: The problem involves calculating the percentage p-character of the lone pair orbital in SbH₃ given the s-character of the Sb-H bond. We use the principle of conservation of s and p character. For a central atom, the sum of s-character in all hybrid orbitals equals 1, and the sum of p-character equals 3. Given 1% s-character in each of the three Sb-H bonds (s_b = 0.01), we calculate the s-character of the lone pair (s_lp) using 3 * s_b + s_lp = 1. This yields s_lp = 0.97. Since s_lp + p_lp = 1, the p-character of the lone pair (p_lp) is 1 - 0.97 = 0.03. As a percentage, this is 3.0%. Since this value is not among the given options, the answer is None.