Which one of the following bonds would you expect to be the most polar? a) B–H b) N–H c) P–H d) Al–H e) C–H

The answer is b) N - H.

The quick answer - right from the get-go, since nitrogen is one of the most electronegative elements in the periodic table, the bond it forms with hydrogen will be the most polar out of all those listed.

The polarity of a bond is given by the difference in electronegativity between the two atoms that form said bond.

According to the Pauling scale, hydrogen has an electronegativity (EN) value of 2.20. To get a polar covalent bond, the difference in EN between hydrogen and the other atom it bonds with must be greater than 0.5 and smaller than 1.7 - 1.8 .

So, the EN difference between hydrogen and each of those elements listed is

#"B-H" -> Delta_(EN) = 2.20 - 1.57 = 0.63#
#"N-H" -> Delta_(EN) = 3.04 - 2.20 = color(green)(0.84)#
#"P-H" -> Delta_(EN) = 2.20 -2.19 = 0.01#
#"Al-H" -> Delta_(EN) = 2.2 - 1.61 = 0.59#
#"C-H" -> Delta_(EN) = 2.55 - 2.20 = 0.35#