A hypothetical salt $MX$ (formula mass $80 g mo l^{- 1}$ ) has the NaCl structure with the anions ( $r = 206 pm$ ) just touching each other along the face diagonal (limiting radius ratio). Use $N_{A} = 6.022 \times 1 0^{23} mo l^{- 1}$ . Taking $2 = 1.414$ , calculate the density in $g c m^{- 3}$ (two decimals).

Numerical answer type, answer in g/cm^3, tolerance 0.03.

Answer: 2.69 g/cm^3

Anions touch along the face diagonal:

2 a = 4 r

, so

a = 22 r = 2 \times 1.414 \times 206 = 582.6 pm

ρ = \frac{4 \times 80}{6.022 \times 1 0 ^{23} \times ( 5.826 \times 1 0 ^{- 8} ) ^{3}} = 2.69 g c m^{- 3}