Why do nonpolar molecules usually have a much lower surface tension than polar ones?
Non-polar molecules have a lower surface tension because they have lower intermolecular forces of attraction.
Surface tension is the force required to stretch the surface of a liquid against the intermolecular forces.
The molecules below the surface of a liquid are attracted to the molecules all around them.
The molecules at the surface do not have other molecules above them, so they are attracted more strongly to their neighbours on the surface.
This forms a surface "film" or "stretched membrane" that makes it more difficult to move an object through the surface than to move it when it is under the surface.
That's why small insects can walk on water.
The stronger the attractive forces, the greater the surface tension, and the tougher the "membrane" across the surface.
Benzene, for example, is a nonpolar molecule with only weak London dispersion forces. Its surface tension is only 29 mN/m.
Water is a polar molecule with strong hydrogen bonds. Its surface tension is 73 mN/m.
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Surface tension is the result of cohesive forces between molecules at a liquid's surface; polar molecules, with their dipole-dipole interactions or hydrogen bonding, have stronger cohesive forces than nonpolar molecules, which results in higher surface tension. Nonpolar molecules typically have lower surface tension than polar ones because they lack strong intermolecular forces like hydrogen bonding.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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