The compound MX (molar mass= 100 g mol-1) occurs in zinc blende structure. If rc= 80 pm and ra= 120 pm, its density will be

# The compound MX (molar mass= 100 g mol-1) occurs in zinc blende structure. If rc= 80 pm and ra= 120 pm, its density will be

1. A

6.25 g cm-3

2. B

8.11 g cm-3

3. C

9.56 g cm-3

4. D

10.4 g cm-3

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### Solution:

We have $\rho =\frac{4\left({M}_{\mathrm{MX}}/{N}_{\mathrm{A}}\right)}{{\left[4\left({r}_{\mathrm{a}}+{r}_{\mathrm{c}}\right)/\sqrt{3}\right]}^{3}}=\frac{3\sqrt{3}\left({M}_{\mathrm{MX}}/{N}_{\mathrm{A}}\right)}{16{\left({r}_{\mathrm{a}}+{r}_{\mathrm{c}}\right)}_{3}}$ $=\frac{\left(3\sqrt{3}\right)\left[\left(120\mathrm{g}{\mathrm{mol}}^{-1}\right)/\left(6.022×{10}^{23}{\mathrm{mol}}^{-1}\right)\right]}{16{\left[\left(120+80\right)×{10}^{-10}\mathrm{cm}\right]}^{3}}$ $=\frac{\left(3\sqrt{3}\right)\left(20×{10}^{-23}\right)\mathrm{g}}{16×8.0×{10}^{-24}{\mathrm{cm}}^{3}}=8.11\mathrm{g}{\mathrm{cm}}^{-3}$  