A. Give the number of total electron groups, the number of bonding groups, and the number of lone pairs for (a)'s geometry. B. Give the...

To begin with, this question is focusing on VSEPR theory or Valence Shell Electron Pair Repulsion theory.  In short, electrons around an atom, be them electrons involved in bonding or as a lone pair on an atom, repel one another and spread as far as possible in 3-dimensional space.

When determining the number electron groups, you are looking for 4 different possibilities:

1. Single bonds


2. Double bonds


3. Triple bonds


4. Lone pairs

The number of bonding groups can be determined by looking for single, double, and triple bonds (1-3 above).  Lone pairs (number 4 above) should be fairly obvious, but are a group of electrons that belong solely to a single atom.  The combined number of bonding groups and lone pairs gives you the number of electron groups.

For image A, you have an octahedral molecule or a central atom with 6 bonding groups around it (all single bonds) and no lone pairs.  6 electron groups of which 6 are bonding groups and 0 are lone pairs.

For image B, you are looking at a square planar molecule.  The central atom has 4 atoms bonded to it (4 bonding groups) and 2 lone pairs (1 above and 1 below) on the central atom.  6 electron groups of which 4 are bonding groups and 2 are lone pairs.

For image C, the image doesn't clearly depict what the molecular shape is.  It appears that image C is identical to image A, but missing two of the atoms along the horizontal plane.  If that truly is what is being shown, then the missing atoms have been replaced with 2 lone pairs to create the distortion seen.  Without the lone pairs, the shape would be tetrahedral instead.  6 electron groups of which 4 are bonding pairs and 2 are lone pairs.

**My personal opinion as a chemist: image C is not a proper image.  If it truly shows 2 lone pairs on the central atom, the bond angle between the remaining two atoms along with horizontal plane would be less.  This is because lone pairs create more repulsion than a pair of bonding electrons.  It is quite possible that image C is showing not two but one lone pair of electrons on the central atom.  This would create a bond angle greater than 90 but less than 120.  This would result in a molecule with 5 electron groups of which 4 are bonding and 1 is a lone pair.

What would make this question easier to analyze would be the presence of lone pairs on the central atom.