The short version: Sulfur is more electronegative than hydrogen, so the H-S bond is polar with electron higher on the sulfur atom

The short version: Sulfur is more electronegative than hydrogen, so the H-S bond is polar with electron higher on the sulfur atom. This leads to ##H_2S## being a polar molecule. However, the difference in polarity between H and S is very small, so neither the bond nor the molecule are very polar.

The longer version: There is some controversy about this. The difference in electronegativities of hydrogen (2.20) and sulfur(2.58) is almost exactly the same as that between hydrogen and carbon (2.55). The C-H bond is viewed as non-polar and so, therefore, should the H-S bond. However, there is some polar character to a C-H bond. Its dipole moment is only 0.3 D, compared with 5.04 D for an OH bond. We should therefore expect an H-S bond to have about the same dipole moment. Yet the measured molecular dipole moment of H?S is 0.95 D. If this were due entirely to the polar S-H bonds, the S-H bond dipole must be about 0.8 D, with the negative end pointing to the S atom. However, there is another explanation. Methane has a tetrahedral electron geometry, with two C-H bonds pointing to the lower left in the diagram and two C H bonds pointing to the upper left. Hydrogen sulfide has two S-H bonds pointing to the lower left. But, instead of two H atoms, there are now two lone pairs at the upper left. Lone pairs contribute to the molecule's dipole moment even though they do not constitute a 'bond'. Clearly the sulfur 'end' of the lone pair is positive, and the electron 'end' is negative so one might think of a 'lone pair dipole' contributing to the polarity of the molecule in analogy to a bond dipole. Thus, it may be the lone pairs that make the major contribution to the polarity of the molecule.