Question

Post 12, number 15

Gold has a face-centered cubic arrangement with a unit cell edge length of 4.08 Å . How many moles of gold fit in a gold nanoparticle sheet with a length of 72.3 nm , a width of 29.3 nm , and a thickness of 12.8 nm ?

Express your answer with the appropriate units.

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2.80•10−18mol

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Answer 1

Volume of Gold sheet = 73.4 x 20.5 x 12.4 = 18,658.28 nm³

Length of unit cell edge = 4.08 x 10^-8 cm
= 4.08 x 10^-10 m
= 0.408 x 10^-9 m
= 0.408 nm

Volume of unit cell = 0.408 x 0.408 x 0.408 = 0.06792 nm³

No. of unit cells in the gold sheet = 18,658.28 / 0.06792 = 2.7471 x 10⁵

The face centred cubic cell contains (8 x 1/8) + (6 x 1/2) = 4 atoms of gold.

So No. of atoms in the sheet = 4 x 2.741 x 10⁵
= 1.09884 x 10⁶ gold atoms

No. of moles of atoms in the sheet = 1.09884 x 10⁶ / 6.02 x 10²³

= 1.825 x 10^-18 moles of gold atoms