Are bonds between Carbon and Hydrogen polar?
They tend not to be but it depends on the nature of the carbon atom. If the carbon is acetylene, the proton is considered to be somewhat acidic. sp3 carbon-hydrogen bond isn't really polar. sp carbon-hydrogen bond is much more polar but not really what I would use as an example of polar. pKa of acetylene is around 25.
in the case of ch4. would the individual c-h bonds be counted as polar bonding?
There's no strict distinction between 'polar' and 'non-polar' bonds (or ionic and covalent, either). Any bond between two different elements will invariably have some degree of polarization.
But a C-H bond is fairly non-polar in any circumstance, and yes, it's quite non-polar in CH4.
As the difference in electro negativities of Carbon and hydrogen comes out to be less than 7(I guess) its sufficiently non-polar.
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