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Hydrogen bonds are a bit weaker than covalent bonds. Because they are fairly strong, it takes more energy to break these bonds when heating, thus increasing the boiling point of the substance, in your case, water. Hydrogen bonding doesn't occur in H2S (only weak bonds like dispersion forces, etc.), so its boiling point will be lower than water.

Electronegativity:

H = 2.1, O = 3.5, S = 2.5,
All of these molecules have dispersion forces (weakest force)
All these molecules are bent
Polarity of each bond:
H – O : 3.5 – 2.1 = 1.4 > 0 polar
H – S : 2.5 – 2.1 = 0.4 > 0 weak polar (less polar than O – H)
Dipole – dipole forces:

H2O > H2S

Strength of hydrogen bonding:

H2O >> H2S

Therefore boiling point of H2O > H2S

When the boiling point is reached, a lot of particles gain enough enery to overcome the interaction to the other particles and break away from the bulk liquid. In the case of H2O and H2S molecules, hydrogen bond is the interaction among H2O molecules and is much stronger than the Van de Waal Force among H2S so the boiling point of H2O should be higher than that of H2S.

Usually, when the atom is getting bigger, due to the increase of the number of electron and so as the Van der Waal force, the intermolecular force will increase. The boiling point will accordingly increase since more energy is required to break the intermolecular bonds. However, it is not applicable in comparing H2O and H2S. It is no doubt that H2S is bigger than H2O. However, in H2O, due to the high electronegativity of the oxygen atom, it can form strong hydrogen bonds between the hydrogen and oxygen. This is much stronger than the normal Van Der Waal force. Therefore higher energy is required to break the hydrogen bond and a boiling point is found in H2O.