An element has ccp packing with a face-centered cubic unit cell. Its density is 12400 kg/m3 and the unit cell volume is 5.50 x 10-29 m3. Calculate the molar mass (g/mol) of the element to three significant figures.
Please explain how you come to the answer.
#atoms/unit cell x molar mass/Avogadro's number = mass of unit cell.
You have # atoms/unit cell (4) and Avogadro's number. That leaves only molar mass to calculate after mass is determined
Next, mass = volume x density. You have volume and density, that calculates mass. Post your work if you get stuck.
To calculate the molar mass of the element, we need to use the given information about its density and unit cell volume.
Step 1: Calculate the number of atoms per unit cell
In a face-centered cubic (FCC) structure, there are 4 atoms per unit cell. Each corner atom is shared with 8 adjacent unit cells, contributing 1/8th of its contribution to each of the 8 cells. The 6 face-centered atoms are shared with 2 adjacent unit cells and contribute 1/2th of their contribution to each of the 2 cells. Thus, we can calculate the number of atoms per unit cell as follows:
Number of atoms per unit cell = (8 x 1/8) + (6 x 1/2) = 4
Step 2: Calculate the mass of the unit cell
The mass of the unit cell can be calculated using the equation:
Mass of unit cell = Volume of unit cell x Density
Given that the unit cell volume is 5.50 x 10^(-29) m^3 and the density is 12400 kg/m^3, we can substitute the values:
Mass of unit cell = 5.50 x 10^(-29) m^3 x 12400 kg/m^3
Step 3: Convert the mass of the unit cell to grams
To convert the mass from kilograms to grams, we multiply by 1000:
Mass of unit cell (in grams) = Mass of unit cell (in kg) x 1000
Step 4: Calculate the molar mass
To find the molar mass, we need to determine the mass of one atom in the unit cell. Dividing the mass of the unit cell by the number of atoms per unit cell gives us the molar mass.
Molar mass = Mass of unit cell (in grams) / Number of atoms per unit cell
By following these steps and performing the calculations, you can find the molar mass of the element to three significant figures.
Well, this is rather a question concerning both, physics as well as chemistry.
You certainly know from physics:
density = mass / volume
Even though your provided information seem to be in a disturbingly unmathematical order, I presume your familiarity with calculating the volume of a cube. Elementary transformation of the aforesaid equations immediately yields:
mass = density * volume
From this and the periodic system of elemnts, you can easily derive the answer.