Metallic sodium adopts a body-centered cubic structure at 25 degrees C and 1 atm. The density of sodium under these conditions is 0.97 g/cm^3. What is the unit cell length?
The body centered cubic structure has two Na atoms per unit cell.
mass of unit cell = (2 atom/unit cell)*(23 g/mol)*(1 mol/6.022 x 10^23 atoms) = ??[Check the atomic mass of Na on your periodic table.]
Knowing mass of unit cell and density of the unit cell, calculate volume of the unit cell.
Isn't volume = (edge unit cell)3?
Post your work if you get stuck.
If I have 1.27 cm^3, how do I convert into picometers?
You don't. cm^3 is volume. Plain pm = length. I assume you must mean convert to cubic picometers. This makes a lot of extra work if you do it that way. Why don't you convert from volume to edge length? That is volume = (edge length)^3. So take the cube root of the volume to obtain the length of the edge of the cube. That edge length will be in cm if you used density in g/cc. THEN convert to picometers.
100 cm = 1 meter
10^12 picometers = 1 meter.
OK?
To determine the unit cell length of a body-centered cubic (bcc) structure, we can use the formula:
Unit cell length = ((4 * molecular weight) / (Avogadro's number * density))^(1/3)
In this case, the molecular weight of sodium (Na) is 22.99 g/mol, Avogadro's number is 6.022 x 10^23 particles/mol, and the density is 0.97 g/cm^3.
Now let's plug these values into the formula:
Unit cell length = ((4 * 22.99 g/mol) / (6.022 x 10^23 particles/mol * 0.97 g/cm^3))^(1/3)
Calculating this expression gives us the unit cell length.
Unit cell length ≈ 4.29 Å (angstroms)
Therefore, the unit cell length of metallic sodium under the given conditions is approximately 4.29 Å.