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Consider SiF4. Si-F bond would be ionic (and polar, and have dipoles) because the electronegativity difference is greater than 2. However, since SiF4 is tetrahedral, this same force is exerted in four directions opposite to each other. The vectors would thus cancel out and the molecule would be nonpolar.
A good example of a nonpolar molecule with polar bonds is CO2. The central carbon will have a net positive charge and the two outer electrons will have a net negative charge. Since the shape of the molecule is linear, these two bond dipoles will cancel each other and the overall molecule will have zero dipole moment (nonpolar).
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