Question involving more chemistry than physics (it seems)

In summary, the question asks for the mass of sand grains that would have the same total surface area as a cube with an edge length of 0.8 m. To solve this problem, you need to use the equations for the volume and surface area of spheres, as well as the density of silicon dioxide. By calculating the volume and surface area of one sand grain, you can then find the mass. To find the mass of all the sand grains with the same total surface area as the cube, you need to equate the two surface areas and solve for the number of grains. Finally, you can find the mass of all the sand grains by multiplying the mass of one grain by the number of grains.
  • #1
tigerlili
62
0

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
 
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  • #2
tigerlili said:

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!
 
  • #3
berkeman said:
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
 
  • #4
tigerlili said:
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.
 
  • #5
oh.. of course! thanks again :P
 
  • #6
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

:/
 
  • #7
tigerlili said:
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.
 
  • #8
sorry.. do you think you could sort of spell it out for me? I'm feeling sort of dense at the moment :/
 
  • #9
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.
 
  • #10
i finally got it, thanks so much!
 

FAQ: Question involving more chemistry than physics (it seems)

1. What is the difference between chemistry and physics?

Chemistry is the study of matter and its interactions, while physics is the study of matter and energy and how they interact with each other. Chemistry focuses on the composition, structure, and properties of substances, while physics focuses on the fundamental laws and principles that govern the behavior of matter and energy.

2. How do chemistry and physics overlap?

Chemistry and physics are closely related and often overlap in their study of matter and energy. For example, the principles of thermodynamics are applicable in both chemistry and physics, as they describe the transfer of heat and energy. Additionally, the laws of motion and forces are important in both fields.

3. What are some examples of chemical reactions and physical changes?

Chemical reactions involve the breaking and forming of chemical bonds, resulting in the creation of new substances with different properties. For example, burning wood is a chemical reaction that produces ash and smoke. Physical changes, on the other hand, involve a change in the physical state or appearance of a substance, without any change in its chemical composition. An example of a physical change is melting ice into water.

4. How are chemistry and physics used in everyday life?

Chemistry and physics have many practical applications in our daily lives. Chemistry is used in the production of medicines, food, and household products, while physics is used in the design of buildings, vehicles, and electronic devices. Both fields also play a crucial role in understanding and addressing environmental issues.

5. Can you give an example of how chemistry and physics work together in a specific scientific study?

One example of how chemistry and physics work together is in the field of materials science. Researchers use principles from both fields to study the properties and behavior of various materials, such as metals, ceramics, and polymers. This interdisciplinary approach allows them to develop new materials with specific properties for different applications.

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