Calculate the "surface energy" of succesively smaller cubes

[Jacob Daniel]

Homework Statement

NaCl has a density of 2.16 g/cm³ and a surface energy of 2x10^-5 J/cm². Calculate the surface energy of 1 g of NaCl. Initially the complete 1 g is in the form of a single cube (of mass 1 g) and progressively broken into smaller cubes with sides of 0.1 cm, 0.01 cm, 10 μm, 1 μm, 100 nm and finally 1 nm.

Make a plot of surface energy vs size of the cube.

Homework Equations

The surface energy of a new surface can be calculated based on the equation discussed in class:

γ = (1/2)N_bερ_a

Where N_b is the number of bonds broken to create the surface, ρ_a is the number of atoms per unit area of the new surface and ε is the bond strength.

The Attempt at a Solution

This question makes absolutely zero sense to me. 1st of all, it asks me to calculate the surface energy of 1 g of NaCl that gets broken into smaller and smaller cubes, but it gives a surface energy at the start. So am I supposed to assume that 2e-5 J/cm² is the surface energy of the single cube before it gets broken up?

Also, note how it wants me to make a plot but the scale of the x-axis is way out of wack. I'm going to have to plot a point at 1 nm and plot another at 0.1 cm which is equivalent to 1,000,000 nm!

I had to edit out grammar mistakes from this question. Another thing that pissed me off was that the prof wrote the shorthand for gram as gm instead of g. I know this is irrelevant but I had to vent a little bit.

I don't see how the formula for surface energy comes in handy because it assumes we are cutting into a unit cell on the molecular level, however the question clearly indicates that we are dealing with relatively big cubes of salt.

I don't even really know where to start. I'm not expecting anyone to make the plot for me. I just want to know how to calculate the surface energy with the variables I have been given. Thank you all very much.

 

[Borek]

You are asked to find a total surface energy, not specific (per cm²).

 

[Jacob Daniel]

You are asked to find a total surface energy, not specific (per cm²).

Oh ok. So the mass will always be 1 g but at 1st it will be one big cube, then an increasing number of smaller cubes. And the question is asking me to find the total surface energy.

My only question now is what is the formula for total surface energy. If I know which formula to use, then the rest is easy. I looked through my notes but I can't find a formula to use. Am I supposed to use the density and/or the mass in some kind of conversion pathway to arrive at the solution? Which will be in units of joules, not joules per cm²?

 

[Jacob Daniel]

Thanks to your help, I was able to solve the problem. Thank you.