An fcc metal has density 10.5 g cm^-3 and unit cell edge 409 pm. Using N_A=6.022x10^23 mol^-1, calculate its molar mass in g mol^-1 (nearest integer).

JEE Advanced levelNumerical answerDifficulty 3 of 3ss038

An fcc metal has density $10.5 g c m^{- 3}$ and unit cell edge $409 pm$ . Using $N_{A} = 6.022 \times 1 0^{23} mo l^{- 1}$ , calculate its molar mass in $g mo l^{- 1}$ (nearest integer).

Numerical answer type, answer in g/mol, tolerance 0.5.

For fcc

Z = 4

and

M = \frac{ρ N _{A} a ^{3}}{Z}

. With

a = 4.09 \times 1 0^{- 8} cm

a^{3} = 6.8418 e - 23 c m^{3}

M = \frac{10.5 \times 6.022 \times 1 0 ^{23} \times 6.8418 e - 23}{4} = 108.15 \approx 108 g mo l^{- 1}