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 $1.419g/c{m}^3$. Find molar mass of the compound.

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

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
$M=\frac{d\times a_h\times a_w\times a_l\times N_A}{Z}$
$1.419\times 12.05\times 10^{-8}\times 15.05\times 10^{-8}$
$=\frac{\times 2.69\times 10^{-8}\times 6.023\times 10^{23}}{2}$
$=2084.6\times 10^{-1}=209g/mol$