How many unit cells can be made out of an 18 carat pure 197 g sample of gold ?( FCC structure A = 197 u)?
First ball find out how many moles are given so we know that 197 grams of 18 carat gold is given hence one mole of 18 carat gold is present.. one fcc unit cell give the question has four particles..( 8 at the corners and 12 at face centre) previously we found that we have one mole of substance one mole of substance has NA amount of particles hence unitary method NA particles will have NA by 4 unit cell.... If it was 24 carat gold any by 4 unit cell was the answer but there is 18 carat gold given so show by unitary method we can solve or we could say that 24 carat gold is 100% pure but 18 karat gold is 75% pure so (NA by 4 ) X 75/100 = (3/16)NA this is ans
First find out normal unit cell that is by formula!... n×NA/Z..this will be the no of unit cells in 24 carat so.. Using unitary method find no of unit cell in 18 carat gold
To find the number of unit cells that can be made out of a given sample of gold, we need to calculate the number of moles of gold in the sample and then divide it by Avogadro's number.
1. First, let's calculate the number of moles of gold in the sample. To do this, we use the formula:
Moles = Mass / Molecular Weight
The molecular weight of gold (Au) is 197 g/mol, and the mass of the sample is given as 197 g.
Moles = 197 g / 197 g/mol
= 1 mol
2. Now, let's calculate the number of atoms in one unit cell of the face-centered cubic (FCC) structure. In an FCC structure, there are 4 atoms per unit cell.
3. Finally, we divide the number of moles of gold by Avogadro's number (6.022 × 10^23 atoms/mol) and multiply it by the number of atoms per unit cell (4).
Number of unit cells = (Number of moles / Avogadro's number) * Number of atoms per unit cell
= (1 mol / 6.022 × 10^23 atoms/mol) * 4 atoms
≈ 6.63 × 10^-24 unit cells
Therefore, approximately 6.63 × 10^-24 unit cells can be made out of an 18-carat pure 197 g sample of gold in the FCC structure.
To answer this question, we need to determine the number of unit cells in an 18-carat pure 197 g sample of gold with a face-centered cubic (FCC) crystal structure.
Step 1: Find the molar mass of gold.
The atomic mass of gold (Au) is 197 atomic mass units (u). Since gold is the only element mentioned, the molar mass of gold is also 197 grams per mole (g/mol).
Step 2: Calculate the number of moles of gold.
To do this, we divide the mass of the gold sample by its molar mass.
Number of moles = Mass / Molar mass
Number of moles = 197 g / 197 g/mol
Number of moles = 1 mole
Step 3: Determine the Avogadro's number.
Avogadro's number is defined as the number of atoms or molecules in one mole of a substance. It is equal to 6.022 x 10^23 particles/mol.
Step 4: Find the number of atoms in one unit cell.
For an FCC structure, each unit cell contains 4 atoms.
Step 5: Calculate the number of unit cells.
To find the number of unit cells, we need to divide the total number of atoms by the number of atoms in each unit cell.
Number of unit cells = Number of atoms / Number of atoms in one unit cell
Number of unit cells = (1 mole x 6.022 x 10^23 particles/mol) / (4 particles)
Number of unit cells = 1.5055 x 10^23 unit cells
Therefore, there can be approximately 1.5055 x 10^23 unit cells in an 18-carat, pure 197 g sample of gold with an FCC crystal structure.