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Quote from Wikipedia:

Another way to view surface tension is in terms of energy. A molecule in contact with a neighbor is in a lower state of energy than if it were alone (not in contact with a neighbor).

As I understand the above statement, is that if two molecules (of the same liquid) are separated, then they have a larger energy as when they are together. Can you please explain a bit why this happens? Is there a physical/chemical reason? Thank you.

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This is probably referring to the intermolecular forces operating between individual molecules of the same liquid. In the case of water, this could be hydrogen-bonding or general dispersion forces. These forces typically act as 'stabilising' forces which can be viewed as a lower energy state.

When the molecules are separated, these close-range forces can no longer operate, so the molecules are considered to be at a higher energy state. The Wikipedia article is quite helpful on the subject.