Question

Which of the following expressions correctly represents the conversion of $\text{molality}\left(m\right)$ to $\text{molarity (M)}$ of a solution?
($\rho$ and $M_2$ are the density of solution and molar mass of the solute respectively.)

• A. $\text{M}=\frac{(1-m\rho )}{m{M}_2}$
• B. $\text{M}=\frac{(1+m\rho )}{m{M}_2}$
• C. $\text{M}=\frac{m\rho }{(1+m{M}_2)}$
• D. $\text{M}=\frac{m\rho }{(1-m{M}_2)}$

Answer 1

The correct option is C $\text{M}=\frac{m\rho }{(1+m{M}_2)}$

Since, $\text{Molality,}m=\frac{n_2}{1\text{kg of solvent}}...\left(i\right)$
Where $n_2$ = Number of moles of solute
The molarity of solution is:
$M=\frac{n_2}{V}=\frac{n_2}{(1\text{kg}+n_2{M}_2)/\rho }$
Dividing numerator and denominator with $1\text{kg}$
$\Rightarrow M=\frac{(n_2/1\text{kg)}\rho }{1+\left(n_2/1\text{kg}\right)M_2}$
Using $\left(i\right)$
$\Rightarrow \text{M}=\frac{m\rho }{(1+m{M}_2)}$