Water molecules, surface tension and evaporation

[mkerikss]

Homework Statement

In this problem, the surface tension S represents the work done to the water when increasing the water's surface area. The vaporization temperature Q_vap represents the energy needed per volume unit to vaporize water at 100 degrees Celsius. We imagine that water molecules form a cubic lattice so that each molecule interacts weakly with its six closest neighbours. At the surface of the water there is naturally one neighbour and interaction less for each molecule.

a) What is the amount of water molecules N per square cm when Q_vap = 203*10⁹ J/m³ and S = 0.072 J/m²?
b) What is the diameter of one water molecule, if the molecules are as compressed as possible?
c) Use these results to estimate Avogadro's constant, when you know that the water's molar concentration is 56 M (moles/litre)
d) Estimate Avogadro's constant by using the density of water, the weight of a single water molecule and the molar concentration.

Homework Equations

The Attempt at a Solution

I don't really know where to start with this problem. I think if get some help getting started from you guys I will figure out the rest eventually, but I really don't know how to approach this problem, so I'd appreciate your help. Thanks!

 

[mkerikss]

The relevant equations I can think of are:

Q=Q_vap*V (heat used for vaporization of V)
W=S*A (work done to the water when increasing A)

But these equations come straight from Q_vap and S, (or they can be figured out) so that's why I didn't include them in my original post, but anyway, here they are for a complete picture of the problem.

Is there anyone who knows how to proceed?