Chemistry please help! calculate an approximate atomic radius for gold.?
2018-01-23 12:20 pm
The coinage metals -- copper, silver, and gold -- crystallize in a cubic closest packed structure. Use the density of gold (19.3 g/cm3) and its molar mass (197 g/mol) to calculate an approximate atomic radius for gold.
回答 (1)
2018-01-23 3:14 pm
Each mole of gold contains 6.022 × 10²³ gold atoms.
Number of moles of gold in each unit cell
= 4 / (6.022 × 10²³ /mol)
= 6.642 × 10⁻²⁴ mol
Mass of each unit cell
= (6.642 × 10⁻²⁴ mol) × (197 g/mol)
= 1.308 × 10⁻²¹ g
Volume of each unit
= (1.308 × 10⁻²¹ g) / (19.3 g/cm³)
= 6.777 × 10⁻²³ cm³
4 × (Atomic radius for gold) = Diagonal of a face of unit cell
Atomic radius of gold
= (1/4) × √2 × ∛(6.777 × 10⁻²³ cm³)
= 1.44 × 10⁻⁸ cm (or 144 pm)
Number of moles of gold in each unit cell
= 4 / (6.022 × 10²³ /mol)
= 6.642 × 10⁻²⁴ mol
Mass of each unit cell
= (6.642 × 10⁻²⁴ mol) × (197 g/mol)
= 1.308 × 10⁻²¹ g
Volume of each unit
= (1.308 × 10⁻²¹ g) / (19.3 g/cm³)
= 6.777 × 10⁻²³ cm³
4 × (Atomic radius for gold) = Diagonal of a face of unit cell
Atomic radius of gold
= (1/4) × √2 × ∛(6.777 × 10⁻²³ cm³)
= 1.44 × 10⁻⁸ cm (or 144 pm)
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