Question

For two isomorphous crystals $A$ and $B$, the ratio of density of $A$ to that of $B$ is $1.6$ while the ratio of the edge length of $B$ to that of $A$ is $2$. If the molar mass of crystal $B$ is $200\,g\,mol^{-1}$, then that of crystal $A$ is

• A. $240\,g\,mol^{-1}$
• B. $120\,g\,mol^{-1}$
• C. $80\,g\,mol^{-1}$
• D. $40\,g\,mol^{-1}$

Answer 1

Answer: (D)

$40\,g\,mol^{-1}$

Answer 2

Density of crystal lattice is directly proportional to molar mass and inversely proportional to edge length. $d \propto \frac{M}{a^{3}}$. If density and molar mass of isomorphous crystal $(A)$ are $d_{A}$ and $M_{A},$ density and molar mass of isomorphous crystal $(B)$ are $d_{B}$ and $M_{B}$ respectively.

then, $\frac{d_{A}}{d_{B}}=\frac{M_{A}}{M_{B}} \times\left(\frac{a_{B}}{a_{A}}\right)^{3}$

Given, $M_{A} =?, M_{B}=200\, g / mol$
$\frac{d_{A}}{d_{B}} =1.6, \frac{a_{B}}{a_{A}}=2$
$m_{A} =\frac{1.6 \times 200}{8}=40\, g / mol$