Using molecular orbital theory, explain why the removal of one electron in o2 strengthens bonding, while the removal of one electron in n2 weakens bonding?

First you have a knowledge of bond order which is
 B.O=(no. of electrons in bonding orbital - no. of electrons in non-bonding orbital)÷2  
Note:
bond strength is directly proportional to bond order.
For oxygen:
B.O=(6-2)/2= 2; after the removal of two electrons(removal occur from non-bonding orbital)
B.O=(6-0)/2= 3 (As B.O increased bond strength increased)
For Nitrogen:
B.O=(6-0)/2= 3; after the removal of two electrons(removal occur from bonding orbital)
B.O=(4-0)/2= 2 (As B.O decreased bond strength decreased)

Solubility would be your answer.

Here is the link to the all information u need i mean answer key