Question

`How many unit cells can be made out of an 18 carat pure 197g sample of gold? (Gold has fcc structure, Atomic mass of gold = 197 u)

Answer 1

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24k=100%gold

22k=91.7%gold

18k=75%gold

Here 75%of 197g is pure gold.

0.75moles of gold .

No. of atoms (Au) = 0.75×6×10²³ = 45×10²².

1 FCC str have 4 atoms .

Hence no. of unit cells = 11.25×10²¹ .

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Answer 2

Given:

The carat of gold = 18 carat

Mass of 18 carat gold = 197 gm

Atomic mass of gold = 197 gm

Gold has FCC structure.

To Find:

The number of unit cells that can be made out of the given mass of gold.

Calculation:

- For FCC structure, z = 4

- 18 carat gold means there are 18 parts of pure gold and 6 parts of some other metal.

- The mass of pure gold in 197 gm = 197 × 18/24 = 147.75 gm

- The no of moles of gold = 147.75/197 = 0.75 moles

- No of atoms in 0.75 moles = 0.75 × 6.022 × 10²³ = 4.5165 × 10²³

- No of unit cells = 4.5165 × 10²³/4

⇒ N ≈ 1.129 × 10²³

- So, 1.129 × 10²³ unit cells can be made out from the given mass of 18 carat gold.