How Do You Calculate the Area of a Gold Leaf and the Length of a Gold Fiber?

[P.O.L.A.R]

Homework Statement

Gold, which has a density of 19.32 g/cm^3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold, witha mass of 27.63g, is pressed into a leaf 1.000 µm thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.500 µm, what is the length of the fiber?

Homework Equations

ρ=m/V (density)

The Attempt at a Solution

Im having trouble finding a direction to go in. I think converting to density is the way to go but I am having trouble using the density formula as well.

 

[rootX]

Homework Statement

Gold, which has a density of 19.32 g/cm^3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold, witha mass of 27.63g, is pressed into a leaf 1.000 µm thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.500 µm, what is the length of the fiber?

Homework Equations

ρ=m/V (density)

The Attempt at a Solution

Im having trouble finding a direction to go in. I think converting to density is the way to go but I am having trouble using the density formula as well.

But aren't you given the density: 19.32?
Hint: You need to know volume of a cylinder, and that other thing (cube ?) in order to solve this.

So, I guess both require two steps.

 

[P.O.L.A.R]

But aren't you given the density: 19.32?
Hint: You need to know volume of a cylinder, and that other thing (cube ?) in order to solve this.

So, I guess both require two steps.

Ok so my intial direction was right but the problem I am having now the area. It just doesn't make sense how I can take the density and find the area. The set-up is not making sense.

 

[rootX]

first find the relationship between area and volume
and then between volume and density/mass

and you will get the area

 

[P.O.L.A.R]

I got it. Thanks for the help the relationship is what I was confusing but all I had to do was divde the density by the mass to get rid of the grams and then convert the cm^3 to µm^3 and relate the area and volume as you said and then the volume with the area.

Thanks

 

[dhago07]

How to solve this problem after finding volume using density and mass

 

[chemisttree]

How to solve this problem after finding volume using density and mass

You need to find a relationship between area and volume for the shape you are considering. For gold leaf, assume that you are using the equation for 2 faces of a cube of material and for a rod assume the area is limited to that of a rod minus the ends.

 

[dhago07]

You need to find a relationship between area and volume for the shape you are considering. For gold leaf, assume that you are using the equation for 2 faces of a cube of material and for a rod assume the area is limited to that of a rod minus the ends.

But what kind of formula should i use for 2 face cube and also for the rod

Thanks for replaying back.

 

[chemisttree]

Using the example of the gold leaf, assume you have a collection of finite elements, each of which is a cube of the same dimension as the thickness (w= 1.000 µm) of the foil. The area of each face of the cube will be w² and you need two of 'em. Next, you need to understand that the total volume of the gold will be N*w³ where 'N' is equal to the number of elements of dimension w X w X w.

Can you get there from here?