Chemistry help: THE MOLE?

Question

i have a chemistry question and i need some help, the question is,

a mole of B.B.'s would cover teh state of Ohio to what depth?

i all ready have the weight of a B.B. (.343 g) and the size of the state ohio 944,825 square miles) but i need to know what to do from there.

Answer 1

The weight of a BB will not help you. You need to know the volume. Find the volume of 1 BB,then multiply that by 6.02x10^23. Then divide that number by the size of Ohio and that will give you the depth.

Answer 2

Since there's 454 grams to a pound, that comes to 1324 BBs in a pound. Steel weighs 490 pounds a cubic foot, so that comes to 648,760 BBs in a cubic feet of steel, if it were 100% full. But spheres can't pack that tightly. The expected density of randomly packed spheres is 0.74048 (see link), so

(0.74048)(648,760) = 480,393

balls per cubic foot with typical packing. Now, a mole is 6.022 x 10^23, so we do the division:

(6.022 x 10^23) / (4.804 x 10^5) = 1.254 x 10^18 cubic feet of packed BBs
Now, the state of Ohio is about 44,825 square miles, or

(44,825)(5,280)^2 = 1.250 x 10^12 square feet. So we divide the two:

(1.254 x 10^18) / (1.250 x 10^12) = (roughly) 10^6, or a million feet deep, or about 190 miles out into space.