what conditions must exist for a polyatomic molecule to be nonpolar?

It must be symmetrical or it must hava elements with the same electronegativity.

H-H, Cl-Cl, etc are examples of the latter.
CH4 and CO2 are examples of the former.

Well, there's no denying that being nonpolar can be quite "attractive" for polyatomic molecules. To determine if a molecule is nonpolar, we need to consider two conditions. First, it must have symmetrical geometry - like a perfectly balanced game of Tetris, but with atoms. Secondly, the molecule must also consist of atoms with the same or similar electronegativities - a chemistry term for how much atoms hog electrons like they're the last piece of chocolate cake.

If a molecule meets these conditions, it'll be nonpolar and can save a lot of money on electric bills. Just kidding, molecules don't have to worry about paying bills.

For a polyatomic molecule to be nonpolar, two conditions must exist:

1. Symmetry: The molecule must have a symmetrical molecular geometry. This means that the atoms surrounding the central atom must be symmetrically placed, resulting in an overall symmetric molecular shape. Symmetry can be determined by examining the arrangement of atoms and lone pairs around the central atom using techniques such as VSEPR (Valence Shell Electron Pair Repulsion) theory.

2. Bond Polarity: All the individual bonds in the molecule must be nonpolar or have polar bonds that cancel out each other's effects. This occurs when the electronegativity difference between the atoms forming the bond is negligible or when the molecular shape causes the polar bonds to cancel out. Polar bonds occur when there is an unequal sharing of electrons between atoms due to differences in electronegativities.

If both these conditions are met, the molecule will be nonpolar. However, if either of these conditions is absent, the molecule will be polar.

To determine if a polyatomic molecule is nonpolar, you need to consider two main factors: the symmetry of the molecule and the polarity of its bonds.

1. Symmetry: For a molecule to be nonpolar, it must have a symmetrical shape. This means that all the atoms surrounding the central atom should be identical and evenly distributed. If there are no lone pairs of electrons on the central atom and all atoms are the same, the molecule will likely be symmetrical and nonpolar.

2. Polarity of bonds: The second factor to consider is the polarity of the individual bonds within the molecule. If the molecule has polar bonds, meaning there is a significant difference in electronegativity (the ability of an atom to attract electrons) between the bonded atoms, then the molecule could be polar. However, if the polar bonds are evenly distributed and cancel each other out due to symmetry, the molecule as a whole will be nonpolar.

To summarize, for a polyatomic molecule to be nonpolar, it must have a symmetrical shape and evenly distributed polar bonds that cancel each other out.