NaCl has an fcc arrangement of Cl- ions with an edge length a = 562 pm. Taking the molar mass as 58.5 g mol^-1 and N_A = 6.022x10^23 mol^-1, calculate the density of the crystal in g cm^-3 (two decimals).

JEE Main levelNumerical answerDifficulty 2 of 3ss173

$NaCl$ has an fcc arrangement of $Cl X^{-}$ ions with an edge length $a = 562 pm$ . Taking the molar mass as $58.5 g mo l^{- 1}$ and $N_{A} = 6.022 \times 1 0^{23} mo l^{- 1}$ , calculate the density of the crystal in $g c m^{- 3}$ (two decimals).

Numerical answer type, answer in g/cm^3, tolerance 0.01.

A rock-salt cell has

Z = 4

formula units, so

ρ = \frac{ZM}{N _{A} a ^{3}} = \frac{4 \times 58.5}{6.022 \times 1 0 ^{23} \times ( 5.62 \times 1 0 ^{- 8} ) ^{3}}

. The cell volume is

1.775 \times 1 0^{- 22} c m^{3}

, and the density is

2.19 g c m^{- 3}