Let’s use the concept of surface tension as surface energy per unit area to see

Question

Let’s use the concept of surface tension as surface energy per unit area to see if we can estimate, at least to the correct order of magnitude, the surface tension of water.

a) Water has a molar mass of 18 g/mol and a density of 1000 kg/m3 (or 1 g/cm3). Based on this data, estimate the number of water molecules per unit surface area of water.

b) The coordination number of water (i.e., the average number of “neighbors” each water molecule has) in the liquid state is 4. Neighboring water molecules attract each other via hydrogen bonds, each of which has a binding energy of roughly 10–20 J (although this number depends relatively strongly on temperature). Use this information to estimate the surface tension of water. How does your estimate compare to the observed figure (?water = 0.072 N/m) (hints: Keep in mind that we can think of surface tension as surface energy per unit area, and consider the energy needed to bring a molecule from the bulk to the surface)?

Explanation / Answer

1. The density is 1g / cm3

so for a unit height the amount of water / unit surface are = 1g / cm2

Now 18 g of water contains 6.023 X 10^23 molecules

So 1g will have 6.023 X 10^23 / 18= 0.3346 X 10^23 molecules / unit surface area.

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