Question

An organic compound crystallises in an ortho rhombic system will two molecules per unit cell. The unit cell dimensions are $12.05,15.05$ and $2.69\stackrel{o}{A}$. If the density of the crystal is $1.419$g $c{m}^{-3}$, then molar mass of compound will be:

• A. $207$g $mo{l}^{-1}$
• B. $209$g $mo{l}^{-1}$
• C. $308$g $mo{l}^{-1}$
• D. $317$g $mo{l}^{-1}$

Answer 1

Answer: (B)

$209$g $mo{l}^{-1}$

Density, $\rho =\frac{Z\times M}{a^3\times N_A}$

Given,

Orthorhombic system has different edge length, width and height

$\therefore a=12.05\stackrel{o}{A}=12.05\times {10}^{-8}cm$

$b=15.05\stackrel{o}{A}=15.05\times {10}^{-8}cm$

$c=2.69\stackrel{o}{A}=2.69\times {10}^{-8}cm$

$\because$ System has $2$ molecules per unit cell,

$\therefore Z=2$

and $N_A=6.023\times {10}^{23}$

Now, molecular mass will be

$M=\frac{\rho \times a\times b\times c\times N_A}{Z}$

$M=\frac{1.419\times 12.05\times {10}^{-8}\times 15.05\times {10}^{-8}\times 2.69\times {10}^{-8}\times 6.023\times {10}^{23}}{2}$

$M=2084.6\times {10}^{-1}=209$ $gmo{l}^{-1}$.