I am trying to explain how to predict bond polarity to a student. A web- based revision testing question, states that the carbon-hydrogen bond is non- polar, yet the difference in electronegativity suggests that it should be polar. I have tried to show that the hydrogen atom becomes envelopped in the electron orbital, but that doesn't explain why it is non-polar and it doesn't explain why the oxygen-hydrogen bond is, except for the greater difference in electronegativity. I would like a more satisfactory answer that my student can understand please.

Part of the problem is that electronegativity values don't absolutely correspond to the way bonds form in every situation; they are calculated as a combination of a number of properties of an element. The best values for those data may not be represented in a particular set of electronegativities. (For example, Pauling electronegativities are most commonly quoted; but they are based on data 30 years out-of-date.) And worse, there are different ways of calculating electronegativity from the data! So electronegativity for most purposes is a somewhat fuzzy number.

Furthermore, in principle ALL bonds between different elements are polar, because no two elements have absolutely identical electronegativities*. So whether a bond is "polar" or "non-polar" is a matter of degree. The typical C-H bond has DEN = 0.45, while a typical O-H bond has DEN = 1.44. So the O-H bond is much more polar than the C-H bond, polar enough that most alcohols will dissolve in water. Hydrocarbons don't.

A good rule of thumb might be that most bonds with DEN ("delta-electronegativity") less than about 0.5 will be essentially non-polar, while bonds with DEN greater than 2.0 are often considered to be ionic. Of course there are exceptions there, as well, for covalent and ionic compounds are typically defined functionally. Two examples:

• Silicon tetrafluoride SiF₄ is a covalently-bonded, molecular gas, with a boiling point of -86°. Yet it has DEN=2.08 (Pauling).
  Boiling point from the Aldrich Catalog.
• Calcium sulfide CaS is an essentially ionic, cubic-crystalline mineral with a detailed structure similar to sodium chloride and a melting point of at least 2400°. Yet it has DEN=1.58 (Pauling).
  Melting point from WebElements

* Of course there are exceptions: carbon and sulfur have identical Pauling electronegativities to two decimal places.