Question

The correct statement about the geometries of $BH_2^+$ and $NH_2^+$ , based on valence shell electron pair repulsion (VSEPR) theory is

• A. both $BH_2^+$ and $NH_2^+$ are trigonal planar
• B. $BH_2^+$ is lincar and $NH_2^+$ is trigonal planar
• C. $BH_2^+$ is trigonal planar and $NH_2^+$ is linear
• D. both $BH_2^+$ and $NH_2^+$ are linear

Answer 1

The Correct Option is B

The question asks us to determine the geometries of \(BH_2^+\) and \(NH_2^+\) using the Valence Shell Electron Pair Repulsion (VSEPR) theory.

1. Understand the basic shapes predicted by VSEPR theory:
   • A molecule's geometry depends on the number of electron pairs (bonding and lone pairs) around the central atom.
   • Electron pairs repel each other and try to stay as far apart as possible.
2. Determine the geometry of \(BH_2^+\):
   • Boron (B) normally has three valence electrons (since it's in Group 13 of the periodic table).
   • In \(BH_2^+\), boron loses one electron due to the positive charge, leaving it with two valence electrons.
   • With 2 hydrogen atoms, there are two bonding electron pairs and no lone pairs.
   • According to VSEPR, the optimal geometry for two electron pairs is linear.
   • Therefore, \(BH_2^+\) is linear.
3. Determine the geometry of \(NH_2^+\):
   • Nitrogen (N) has five valence electrons (as it is in Group 15 on the periodic table).
   • In \(NH_2^+\), nitrogen loses one electron due to the positive charge, leaving it with four valence electrons.
   • With 2 hydrogen atoms, there are two bonding pairs, plus one lone pair from the nitrogen.
   • According to VSEPR, three electron pairs (2 bonding and 1 lone pair) result in a trigonal planar arrangement.
   • However, lone pairs repel more strongly than bonding pairs, leading to a bent structure typically around 120 degrees for the bonded atoms.
   • Since the question simplifies geometrical understanding, we accept "trigonal planar" as the correct description here.
4. Justification for the correct option:
   • The correct statement is "\(BH_2^+\) is linear and \(NH_2^+\) is trigonal planar".
   • This result matches the reasoning outlined above, based on the VSEPR theory.
   • Other options suggest incorrect geometries based on VSEPR predictions.