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What is primarily responsible for the surface tension of water?

Answer
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Hint: There are two important properties of water, adhesion and cohesion. Cohesion is when water is attracted to water and adhesion is when water is attracted to other substances. The cohesive forces between the water molecules are responsible for its surface tension. The molecules on the surface do not have any other molecules surrounding them, the cohesion is therefore strong.

Complete Step By Step Answer:
The cohesive force between the molecules in the bulk liquid is shared by all the neighbouring molecules. But the molecules on the surface do not have any molecules to share this with. Thus, they exhibit stronger attractive force on their nearest neighbouring molecule, besides to them on the surface or below them. Thus, surface tension can also be given as the property to resist external force, due to the cohesion of molecules.
Within the bulk of the liquid, molecules do not have any net force, because the force of the molecules on each other gets cancelled in all the directions. But the molecules on the surface will experience an inward force since there will be no compensating force acting from above. This inward force causes the molecules to contract and resist itself from being stretched. Thus, we can say that the surface of the water in under tension, due to which it has the name ‘surface tension’
Objects tend to float on the surface because of this surface tension, as long as it doesn’t break the surface layer and breaks through. When the object is present on the surface of water, the surface will behave like an elastic membrane, resisting it from sinking.

Note:
The molecules of the surface don't form a ‘skin’ on the surface. The stronger the cohesion between the water molecules to that between the air and water molecules, makes it more difficult for an object to move on the surface than in the bulk of the fluid.
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