Answer:
Au
Explanation:
For the density of a face-centered cubic:
[tex]Density = \dfrac{4 \times M_w}{N_A \times a^3}[/tex]
where
[tex]M_w[/tex] = molar mass of the compound
[tex]N_A=[/tex] avogadro's constant
[tex]a^3 =[/tex] the volume of a unit cell
Given that:
Density [tex](\rho)[/tex] = 19.30 g/cm³
a = 0.408 nm
a = [tex]0.408 \times 10^{-9} \times 10^{2} \ cm[/tex]
a = [tex]4.08 \times 10^ {-8} \ cm[/tex]
∴
[tex]19.3 = \dfrac{4 \times M_w}{(6.023 \tmes 10^{23})\times (4.08 \times 10^{-8})^3}[/tex]
[tex]M_w= \dfrac{19.3\times (6.023 \times 10^{23})\times (4.08 \times 10^{-8})^3}{4}[/tex]
[tex]M_w=197.37 \ g/mol[/tex]
Thus, the molar mass of 197.37 g/mol element is Gold (Au).
