KF has the same type of crystal structure as NaCl. The unit cell of KF has an edge length of 5.39 Å. Find the density of KF in g/cm3
You probably know the edge length for NaCl but I do not.
mass of NaCl molecule = molecular mass of NaCl/6*10^23
mass of KF Molecule = molecular mass of KF/6*10^23
density of KF = length of KF^3/length of NaCl^3 * (Mass of KF/Mass of NaCl)
note Avagadro's number cancels
Oh, times density of NaCl of course
To find the density of KF (potassium fluoride), we need to know its molar mass and the volume of its unit cell.
1. Start by finding the molar mass of KF. Potassium (K) has a molar mass of approximately 39.10 g/mol, and fluoride (F) has a molar mass of approximately 18.99 g/mol. The molar mass of KF is the sum of these two masses: 39.10 g/mol + 18.99 g/mol = 58.09 g/mol.
2. Next, calculate the volume of the unit cell. Since KF has the same type of crystal structure as NaCl, we can assume that its unit cell is face-centered cubic (FCC). In an FCC unit cell, there are four ions (one K+ cation and four F- anions) at the corners and one ion (one K+ cation) at the center of each face.
The edge length of the unit cell is given as 5.39 Å (angstroms). In FCC crystal structures, the length of the body diagonal (diagonal that connects two opposite corners of the cube) is √8 times the edge length. Therefore, the body diagonal length for KF is √8 * 5.39 Å = 7.62 Å.
However, for simplicity, let's convert the edge length and body diagonal length from angstroms to centimeters, since the density is typically expressed in g/cm3. 1 Ångstrom = 1 x 10^-8 centimeters.
Edge length in cm = 5.39 Å * (1 x 10^-8 cm/Å) = 5.39 x 10^-8 cm.
Body diagonal length in cm = 7.62 Å * (1 x 10^-8 cm/Å) = 7.62 x 10^-8 cm.
The volume of the unit cell (V) can be calculated as V = (edge length)^3, so V = (5.39 x 10^-8 cm)^3 = 1.56 x 10^-23 cm3.
3. Finally, calculate the density of KF by dividing the molar mass by the volume of the unit cell.
Density = (molar mass)/(volume of unit cell) = 58.09 g/mol / 1.56 x 10^-23 cm3 = 3.72 x 10^22 g/cm3.
Therefore, the density of KF is approximately 3.72 x 10^22 g/cm3.