Impossible AP chem question!?

Question

Calculate the average density of a single A1-27 atom by assuming that it is a sphere with a radius of .143 nm. The masses of a proton, electron, and neutron are 1.6726x10^ -24 g, 9.1094x10^ -28 g, and 1.6749x10^ -24 g, respectively. The volume of a sphere is (4)(pie)(r)^3. Express the answer in grams per cubic cm. The density of aluminum is found experimentally to be 2.7g/cm3. What does that suggest about the packing of aluminum atoms in the metal?

I have no idea...any suggestions??

Answer 1

Spheres do not fill the entire volume even when packed as closely as possible; e.g. hexagonal-close pack. I assume the question is to determine the amount of void space and determine which packing model is the most likely. x-ray crystallography is the way scientists actually determine the packing ("crystal") structure.

Answer 2

Use the above information to determine the mass of an atom of aluminum.

Convert the radius from nanometers to centimeter,

Calculate the volume of the sphere

Density = Mass * Avogadro number / volume

The packing portion of the question is that there is empty space in the solid

Answer 3

Good luck.

Answer 4

Density is mass over volume.  We know mass: just add up the masses of all particles in the atoms.  We can find the volume of a sphere from the radius.

To find mass, multiply each particle mass by the quantity of those particles, and sum them.  Multiply the electron mass by 13, the proton mass by 13, and the neutron mass by 14, and then add all of these products together.

The volume of a sphere is actually (4/3)*pi*r^3 - use this formula to get volume.

Just divide mass by volume to get your answer.

The answer will be higher than the actual density of aluminum because there is empty space in the packing of the atoms.  Hopefully this will be a complete enough answer for the last part.  If not, you should calculate how much empty space there would need to be to get the measured volume and look up the crystal structure of aluminum.