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In order to answer this question, one must have an understanding of the types of forces that exist to hold atoms/ions in molecules. There are four principal chemical bonds, and they are: ionic, covalent, metallic, and van der Waals. All forces between atoms/ions exist to achieve the goal of a neutral state (no charge) for better stability.
Ionic bonds result from electrostatic attraction between two oppositely charged ions following the old adage that "opposites attract". In ionic bonds electrons are transferred from the negatively charged ion to the positively charged ion.
Covalent bonds result from the sharing of electrons between atoms of similar charge, and these types of bonds are the most common between atoms/ions of the same element.
Metallic bonds exist in the bonds between the same metallic elements, and result from the sharing of electrons. These are slightly different from covalent bonds in that the electrons are not shared between all of atoms 100% of the time.
Van der Waals bonds result from minor changes in polarities in molecules that are already bonded.
Knowing this, we can determine the type of chemical bonds in the three molecules: Br2 , NH3, PBr3.
Br2 - two Br ions of the same charge sharing electrons: covalent bond
NH3 - the bonds between N and H are also covalent.
PBr3 - P and Br are both negatively charged ions, therefore this bond is also covalent
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