Question involving more chemistry than physics (it seems)

[tigerlili]

Homework Statement

Grains of fine California beach sand are approximately spheres with an average radius of 50 μm and are made of silicon dioxide, which has a density of 2.6 × 103 kg/m3. What mass of sand grains would have a total surface area (the total area of all the individual spheres) equal to the surface area of a cube 0.8 m on an edge?

Homework Equations

I'm really not sure. I am a chem major, but I have no recollection of how to do these types of problems. I have only had my first day of physics, and he just threw this homework at us :/

The Attempt at a Solution

I would think it is just a simple dimensional analysis.. but I'm not sure how to relate the cube edge part of the problem

 

[berkeman]

Homework Statement

Grains of fine California beach sand are approximately spheres with an average radius of 50 μm and are made of silicon dioxide, which has a density of 2.6 × 103 kg/m3. What mass of sand grains would have a total surface area (the total area of all the individual spheres) equal to the surface area of a cube 0.8 m on an edge?

Homework Equations

I'm really not sure. I am a chem major, but I have no recollection of how to do these types of problems. I have only had my first day of physics, and he just threw this homework at us :/

The Attempt at a Solution

I would think it is just a simple dimensional analysis.. but I'm not sure how to relate the cube edge part of the problem

You mainly need the equations for the volume and surface area of spheres. Do you have those? If not, a simple google search will turn them up.

Then you have the density of the material, and the radius of each sphere, so you can calculate the mass of each sand grain as well as its surface area. The rest should be straightforward...

EDIT -- Welcome to the PF, BTW!

 

[tigerlili]

You mainly need the equations for the volume and surface area of spheres. Do you have those? If not, a simple google search will turn them up.

Then you have the density of the material, and the radius of each sphere, so you can calculate the mass of each sand grain as well as its surface area. The rest should be straightforward...

EDIT -- Welcome to the PF, BTW!

Thank you very much :)!

I'm still just a little bit confused (forgive me- it's the 2nd day of the semester)
so, i found the volume and SA of the sphere.. and then i found the SA of the cube
how exactly does the volume come into play? I can imagine how to find the mass using the density and the radius.. but, after that i get lost

 

[berkeman]

Thank you very much :)!

I'm still just a little bit confused (forgive me- it's the 2nd day of the semester)
so, i found the volume and SA of the sphere.. and then i found the SA of the cube
how exactly does the volume come into play? I can imagine how to find the mass using the density and the radius.. but, after that i get lost

You find the mass using the volume and the density.

 

[tigerlili]

oh.. of course! thanks again :P

 

[tigerlili]

ugh, sorry to be such a pain, but i just tried it twice and the answer was wrong

i took the formula volume = 4/3 pi r^3 and used 50 μm and ended up getting ~ 5.236e-13 m^3

then i tried to multiply by the density of 2.6e3 kg/m^3 to get the mass.. and got 1.361e-9 kg, but that was wrong

:/

 

[berkeman]

ugh, sorry to be such a pain, but i just tried it twice and the answer was wrong

i took the formula volume = 4/3 pi r^3 and used 50 μm and ended up getting ~ 5.236e-13 m^3

then i tried to multiply by the density of 2.6e3 kg/m^3 to get the mass.. and got 1.361e-9 kg, but that was wrong

:/

But that's just for one grain of sand, isn't it? You need to do more calculating and equating to get the answer they are looking for, I believe.

 

[tigerlili]

sorry.. do you think you could sort of spell it out for me? I'm feeling sort of dense at the moment :/

 

[Jebus_Chris]

So you found surface area and mass of 1 grain of sand along with the surface area of the cube. You need x grains of sand for their total surface area to be equal to the surface area of the cube. Once you find x you can find the mass of all the sand grains.

 

[tigerlili]

i finally got it, thanks so much!