Question

An organic compound crystallises in an orthorhombic cell in the ratio of $2: 1$. The dimensions of the cell are $12.05,15.05$ and $2.69\,\mathring{A}$ and density is $1.419\, g / cm ^{3}$. Find molar mass of the compound.

• A. $207\, g / mol$
• B. $209\, g / mol$
• C. $308\, g / mol$
• D. $317\, g / mol$

Answer 1

Answer: (B)

Density $(d)=\frac{Z \times M}{a^{3} \times N_{A}}$
According to question, the length $(l)$,
breadth $(w)$ and
height $(h)$ of orthorhombic cell are different.
$a_{h}=12.05 \mathring{A}=12.05 \times 10^{-8} cm$
$a_{l}=15.05 \mathring{A}=15.05 \times 10^{-8} cm$
$a_{w}=2.69 \mathring{A}=2.69 \times 10^{-8} cm$
Each cell has $2$ molecules $Z=2$ and $N_{A}=6.022 \times 10^{23}$
Hence, molar mass
$M=\frac{d \times a_{h} \times a_{w} \times a_{l} \times N_{A}}{Z}$
$1.419 \times 12.05 \times 10^{-8} \times 15.05 \times 10^{-8}$
$=\frac{\times 2.69 \times 10^{-8} \times 6.023 \times 10^{23}}{2}$
$=2084.6 \times 10^{-1}=209\, g / mol$