CHEMISTRY HELP! Can someone else work this problem out?

Question

A cube of gold that is 1.00 cm on a side has a mass of 19.3 g. A single gold atom has a mass of 197.0 amu.

(a) How many gold atoms are in the cube?

(b) From the information given, estimate the diameter in angstroms of a single gold atom. The answer is 2.6 angstroms - 6.8 angstroms.

Answer 1

for part (a):

Gold has an atomic weight of 197 g/mol.

1 mole is equivalent to 6.0 x 10^23 atoms (Avogadro's number).

So the weight of a single gold atom would be:

Weight of 1 gold atom = 197 g/mol / (6.0 x 10^23 atoms/mol)

You can then find the number of gold atoms in the sample by dividing the sample weight by the weight of a single atom:

#atoms = 19.3g/ (Weight of 1 gold atom).

I don't have a calculator handy so you'll have to do the actual math yourself.

for part (b):

for a rough estimate you can divide the volume of the cubic sample (1 cubic centimeter) by the number of atoms we just calculated to get the volume of a single gold atom:

volume of 1 gold atom = 1 cubic centimeter / (answer to part (a))

to find the diameter of a single atom, use the formula for the volume of a sphere:

Vol of Sphere = 4/3 x pi x (radius)^3

the radius would be:

radius = [3/4 x (volume)/ pi]^1/3

the diameter is then just 2 x radius.

Again, you'll have to do the actual math yourself.

Hope this helps