I am a Sophomore taking chemistry for the first time, and our teacher assigned us some homework problems. Even though it's for a completion grade, I want to try to figure out the right answers, but I need some hints on some of them, particularly this one:

"To the alchemists, gold was the material representation of purity. It is a very soft metal that can be hammered into extremely thin sheets. If a 2g piece of gold is hammered into a sheet whose area is 42.8 sq. ft., what is the average thickness of the sheet? (The density of gold is 19.32 g/cm^3.)"

Okay, so I know that volume = base * height; and I know that density = mass/volume... but the area of the sheet of gold is in feet and the unit for density involves centimeters. How do I do dimensional analysis when one unit is squared and the other is cubed?

Hikari wrote:volume = area of base * height

the area of base is in squared units, times height, adds the third unit and you end up with length cubed.

From the mass (2g) and the density (19.32 g/cm

^{3}) find the volume in cm^{3}so now you know the volume and the area of the base, solve for height.

2.54 cm = 1 in and 12 in = 1 ft

cube both sides on both equalitites to find the conversions from cm

^{3}-> in^{3}-> ft^{3}you can also convert the area to square inches and then to square cm and work everything in cm

Oh, I see. I guess I was just over-thinking it. Thank you!

Actually, I still don't think I'm getting the right answer. Please check my work.

v = d/m, so:

v = (2 g) / (19.32 g/cm^3) = 1.035196687 -> 1.035 cm^3

1.035 cm^3 * (2.54^3 in^3 / 1cm^3) * (1^3 ft^3 / 12^3 in^3) =

1.035 cm^3 * (16.39 in^3 / 1cm^3) * (1 ft^3/ 1728 in^3) = .0098169271 -> .0098 ft^3

v = b*h

h = v/b

h = .0098ft^3/42.8ft^2 = 2.29e-4 ft

I feel like I'm doing something wrong.

almost

V = m/d you have d/m

however, your math is correct in that part because you placed the mass on the numerator

Thus v = 1.035 cm

^{3}is correctHikari wrote:that part is backwards it should be (1

^{3}in^{3}/ 2.54^{3}cm^{3})When you correct for that part v = 3.6596 x 10

^{-6}ft^{3}v = b*h

h = v/b

h = 3.6596 x 10

^{-6}ft^{3}/42.8ft^{2}= 8.71 x 10^{-8}ftin inches = 1.05 x 10

^{-6}thus about 1 micro inch very thin sheet indeed, but in order for 2g to cover over 42 ft^{2}it would have to be very thin.Oops! I see now. Thank you so much for the help!