Calculating Square Meters of Gold Leaf from 28.35g of Gold

[ZackDT]

Hi. First time asking question here so sorry if format is wrong.

Question:

Gold leaf, which is used for many decorative purposes is made by hammering pure gold into very thin sheets. Assuming that a sheet of gold leaf is 1.27x10^-5 cm thick, how many square meters of gold leaf could be obtained from 28.35 g of gold.


I know Density equals M/V and Volume equals M/D

I've devised that 28.35 is the mass, but I don't know what the volume is, or what I'm even trying to find (Volume or Density? I'm guessing volume)

All help welcome. Thanks a lot.

 

[Gokul43201]

Look up the density of gold.

http://www.webelements.com/webelements/elements/text/Au/phys.html

Now you can determine the volume and hence the area of the sheet.

PS: Next time, post questions like this in the Other Sciences subforum under Homework & Coursework. This thread will soon be moved there.

 

[Blueshift5]

Hello,

Thank you for your question. I would be happy to provide a response to your inquiry.

To calculate the number of square meters of gold leaf that can be obtained from 28.35g of gold, we need to use the formula for density, which is mass divided by volume. In this case, the mass is given as 28.35g, and we need to find the volume.

To find the volume of the gold, we can use the formula for volume of a rectangular prism, which is length x width x height. In this case, the length and width are not given, but we can calculate the height using the given thickness of the gold leaf, which is 1.27x10^-5 cm.

To convert this thickness to meters, we need to divide it by 100, as there are 100 cm in 1 meter. This gives us a thickness of 1.27x10^-7 meters.

Now, we can plug in all the values into the formula for volume:

Volume = length x width x height

Volume = (length) x (width) x (1.27x10^-7 meters)

We do not know the length and width, but we do know that the gold leaf is in the shape of a rectangular prism. Therefore, we can assume that the length and width are equal, and we can use the formula for the area of a square to find the value of length and width.

Area = length x width

We know that the mass of the gold leaf is 28.35g, and we also know that the density of gold is 19.3 g/cm^3. Therefore, we can calculate the volume of the gold using the formula for density:

Volume = mass/density

Volume = 28.35g/19.3 g/cm^3

Volume = 1.47 cm^3

Now, we can plug this value into our original formula for volume:

1.47 cm^3 = (length) x (width) x (1.27x10^-7 meters)

Solving for (length) x (width), we get:

(length) x (width) = 1.47 cm^3/(1.27x10^-7 meters)

(length) x (width) = 1.16x10^10 cm^2

Now, we can use the formula for area to solve for length and width: