The density of solid W is 19.3 g/cm3. How many atoms are present per cubic centimeter of W?
As a solid, W adopts a body-centered cubic unit cell. How many unit cells are present per cubic centimeter of W?
What is the volume of a unit cell of this metal?
What is the edge length of a unit cell of W?
Please explain! Thanks!
6.326
To calculate the number of atoms per cubic centimeter of solid W, we need to use the molar mass and the density of W.
Step 1: Calculate the molar mass of W.
The molar mass of W is given as the atomic weight, which is 183.84 g/mol.
Step 2: Calculate the volume of one mole of W.
Since the density is given as 19.3 g/cm3, this means that one mole of W occupies a volume of 19.3 cm3.
Step 3: Calculate the number of atoms in one mole of W.
Using Avogadro's number (6.022 × 10^23 atoms/mol), we know that one mole of W contains 6.022 × 10^23 atoms.
Step 4: Calculate the number of atoms per cubic centimeter.
Divide the number of atoms in one mole by the volume of one mole in cubic centimeters.
Number of atoms per cubic centimeter = (6.022 × 10^23 atoms/mol) / (19.3 cm3)
Now let's move on to the second part of your question.
Step 5: Find the number of unit cells per cubic centimeter.
In a body-centered cubic (BCC) structure, there is one unit cell at each corner of the cube and one additional unit cell in the center of the cube. Therefore, there are a total of 2 unit cells in each cube.
Step 6: Calculate the volume of one unit cell.
To find the volume of a unit cell, we need to know the edge length of the unit cell.
Finally, let's determine the edge length of a unit cell of W.
Step 7: Calculate the edge length of a unit cell.
Since a BCC unit cell has atoms at the corners and one atom in the center, the edge length (a) can be calculated using the formula:
a = (4 * r) / sqrt(3), where r is the atomic radius.
By knowing the atomic radius of W, you can substitute it into the formula to find the edge length.
I hope this step-by-step explanation helps!
To determine the number of atoms per cubic centimeter of W, we need to convert the density from grams per cubic centimeter to the number of atoms per cubic centimeter.
Step 1: Determine the molar mass of W.
The atomic mass of W is 183.84 g/mol.
Step 2: Convert the mass of one mole of W to the number of atoms.
Avogadro's number (6.022 x 10^23) represents the number of atoms in one mole of any substance. Therefore, one mole of W contains 6.022 x 10^23 atoms.
Step 3: Calculate the number of moles in one cubic centimeter of W.
To account for the density, we need to divide the given density (19.3 g/cm^3) by the molar mass (183.84 g/mol). This will give us the number of moles in one cubic centimeter of W.
Number of moles = density (g/cm^3) / molar mass (g/mol)
= 19.3 g/cm^3 / 183.84 g/mol
Step 4: Calculate the number of atoms in one cubic centimeter of W.
Finally, we multiply the number of moles by Avogadro's number to obtain the number of atoms in one cubic centimeter of W.
Number of atoms = Number of moles x Avogadro's number
= (19.3 g/cm^3 / 183.84 g/mol) x (6.022 x 10^23 atoms/mol)
To determine the number of body-centered cubic (BCC) unit cells present per cubic centimeter of W, we need to know the volume of a unit cell and the edge length of the unit cell.
The volume (V) of a BCC unit cell is calculated using the formula:
V = (edge length)^3
To find the volume of a unit cell of W, we would need additional information or calculations specific to W. Unfortunately, the given information does not provide the necessary data.
Similarly, to determine the edge length of a unit cell, we would need additional information or calculations specific to W.
Therefore, without additional information, we cannot determine the volume or edge length of the unit cell of W.
In 1 cc of W you have 19.3 grams. There are 6.02E23 atoms in 183.84
# atoms 19.3 g = 19.3/6.02E23 = ?
The volume of a unit cell is v = mass/density.
mass unit cell = 2*183.84/6.02E23 = 6.2E-22 but you need to do that more accurately. (Note: The 2 comes from "there are two atoms per unit cell".)
Density = 19.3 from the problem.
volume = 3.2E-23 cc = volume unit cell.
edge length = V1/3