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When gold crystallizes, it forms face-ce...

When gold crystallizes, it forms face-centred cubic cells. The unit cell edge length is 408 pm. Calculate the density of gold. Molar mass of gold is 197 g/mol.

Text Solution

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` p = Mn/(a^3 N_4)`
M = 197 g `mol^(-1)` , n = 4 atoms for fcc,
`N_A = 6.022 xx 10^(23)` atoms `mol^(-1)`
a = 408 pm = 408 `xx 10^(-8)` cm
Substitution of these quantities in the equation gives
` p = (197 g cancel(mol^(-1)) xx 4 cancel(a"to"m))/((4.08 xx 10^(-8))^3 cm^3 xx 6.022 xx 10^(23) cancel(a"to"m)^(-1))`
= 1927 g/`m^3` 19.27 `xx 10^3` Kg/`m^3`
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