Final answer:
The correct order of increasing polar character for the given molecules is H₂S < NH₃ < H₂O < HF, which corresponds to their increasing electronegativity and bond polarity.
Step-by-step explanation:
The polar character of molecules depends on the electronegativity of the atoms and the polarity of the bonds within the molecules. Comparing the electronegativity of the non-hydrogen atoms, we see that fluorine is the most electronegative, followed by oxygen, nitrogen, and then sulfur. Hence, the polarity of these molecules increases in the order of HF (most polar) > H₂O > NH₃ > H₂S (least polar). This order can also be seen in the context of acid strength, where more polar molecules generally have a greater tendency to dissociate into ions, making them stronger acids.