An element has a body centred cubic structure with edge cell of 288 pm .The density of the element is 7.2 g/cm3.How many atoms are present in 208g of the element.
You must first determine the atomic mass of the element.
Convert 288 pm to cm then
volume = (?cm)^3 = volume unit cell
mass unit cell is volume x density = ?
Substitute for mass unit cell = [(#atoms/unit cell) x atomic mass/6.02E23] and solve for atomic mass of element.
Then moles element = 208/atomic mass.
mols x 6.02E23 = # atoms.
Post your work if you get stuck.
To determine the number of atoms present in 208 grams of the element, we can use the following steps:
Step 1: Calculate the volume of the unit cell. Since the edge length of the unit cell is given as 288 pm (picometers), we need to convert it to cm. There are 10^10 picometers in 1 meter and 100 centimeters in 1 meter, so 1 picometer is equal to 1 x 10^-8 centimeters. Therefore, the edge length of the unit cell is 288 x 10^-8 cm.
The volume of a cube is given by the formula V = a^3, where 'a' is the edge length. Thus, the volume of the unit cell is (288 x 10^-8)^3 cm^3.
Step 2: Calculate the number of unit cells in 208 grams of the element. To do this, we need to know the molar mass (grams/mole) of the element. Suppose the molar mass is M grams/mole. We can calculate the number of moles (n) of the element using the formula:
n = mass / molar mass.
In our case, n = 208 g / M grams/mole.
Step 3: Calculate the number of atoms in one unit cell. In a body-centered cubic structure, there are two atoms present in one unit cell.
Step 4: Calculate the number of atoms in 208 grams of the element.
The number of atoms = (Number of unit cells) x (Number of atoms in one unit cell).
Since there are two atoms in one unit cell, the number of atoms = n x 2.
To summarize, the formula to calculate the number of atoms in 208 grams of the element is:
Number of atoms = (208 g / M grams/mole) x 2.
Please note that to obtain the exact number of atoms, we need the molar mass of the specific element.