An element has bcc packing with a body-centered cubic unit cell. Its density is 19300 kg/m3 and the unit cell volume is 3.17 x 10-26 L. Calculate the molar mass (g/mol) of the element to three significant figures.
The element rubidium has bcc packing with a body-centered cubic unit cell. The volume of the unit cell is 1.85 x 10-22 cm3. Calculate the density (g/cm3) of the element.
# atoms/unit cell * molar mass/Avogadro's number = mass unit cell.
Calculate mass unit cell from
mass = volume x density. The only unknown is molar mass.
Post your work if you get stuck. The second problem is done essentially the same way. Try it. Repost if you run into trouble but show your work to the point you don't know how to continue.
thats wrong. don't listen to him
No that's correct. Im having trouble finding the # atoms/unit cell.
Remember these.
A bcc unit cell has 2 atoms/unit cell.
A fcc unit cell has 4 atoms/unit cell.
A simple cubic unit cell has 1 atom/unit cell.
To calculate the molar mass of the element with bcc packing, we need to use the following formula:
Molar mass = (density * unit cell volume) / Avogadro's number
First, let's convert the given unit cell volume from liters to cubic meters:
Unit cell volume = 3.17 x 10^(-26) L = 3.17 x 10^(-26) * 10^(-3) m^3 = 3.17 x 10^(-29) m^3
Next, we substitute the given values into the formula:
Molar mass = (19300 kg/m^3 * 3.17 x 10^(-29) m^3) / 6.022 x 10^23 mol^(-1)
Calculating this expression gives us the molar mass of the element. Let's carry out the calculation:
Molar mass ≈ (19300 kg/m^3 * 3.17 x 10^(-29) m^3) / 6.022 x 10^23 mol^(-1)
≈ 1.0164 x 10^(-22) kg/mol
To get the molar mass in grams per mole (g/mol), we convert the unit from kilograms to grams:
Molar mass ≈ 1.0164 x 10^(-22) kg/mol = 1.0164 x 10^(-19) g/mol
Therefore, the molar mass of the element with bcc packing is approximately 1.0164 x 10^(-19) g/mol, or about 1.02 x 10^(-19) g/mol to three significant figures.
Now let's calculate the density of the element rubidium with bcc packing. We can use a similar formula:
Density = (molar mass * Avogadro's number) / unit cell volume
First, we need to convert the given unit cell volume from cm^3 to cubic meters:
Unit cell volume = 1.85 x 10^(-22) cm^3 = 1.85 x 10^(-22) * 10^(-6) m^3 = 1.85 x 10^(-28) m^3
Next, we substitute the given values into the formula:
Density = (molar mass * 6.022 x 10^23 mol^(-1)) / 1.85 x 10^(-28) m^3
To calculate the density, we need to know the molar mass of rubidium, which is approximately 85.468 g/mol.
Substituting this value into the formula:
Density = (85.468 g/mol * 6.022 x 10^23 mol^(-1)) / 1.85 x 10^(-28) m^3
Calculating this expression gives us the density of rubidium with bcc packing. Let's carry out the calculation:
Density ≈ (85.468 g/mol * 6.022 x 10^23 mol^(-1)) / 1.85 x 10^(-28) m^3
≈ 2.77 g/cm^3
Therefore, the density of rubidium with bcc packing is approximately 2.77 g/cm^3.