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Aside from the number of bonds (single, double, etc.), the overall length of a bond also determines how strong it is. When the bond length is larger, the bond is weaker because the atoms are further apart and therefore they can break apart easier. H2O has a bond length of about 1A and H2S has a bond length of about 2.8A. This is why H2O has a higher melting/boiling point, because its bond length is smaller than H2S's.
The electronegativity of oxygen causes water to be polar, leading to hydrogen bonding. Because of hydrogen bonding, H2O requires more energy needed to break the bonds, thus it has a much higher boiling point/melting point than that of H2S.
H2O has a higher melting and boiling point because the oxygen on one water molecule forms a hydrogen bond to the hydrogen onto another water molecule. These hydrogen bonds are the reason water has a higher melting and boiling point. A solid has many bonds between molecules so when changing phases to a liquid (where there are fewer bonds between the molecules), the bonds between the molecules (the inter molecular forces) must be broken. Because hydrogen bonds are stronger than regular dipole-dipole (which H2S has), it will take more energy (a higher temperature) to break the hydrogen bonds and melt water from solid to liquid and more energy to boil water from liquid to gas. The actual polar covalent bond of the water molecule is not broken; the water stays intact, it is just changing phases.
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