Question

If M is the molarity, d is the density (in g/ml), $M_B$ is the molar mass of solute and m is the molality, then choose the correct relation ?

• A. $\frac{1000M}{1000d+M.M_B}=m$
• B. $\frac{1000M}{1000d-m.M_B}=M$
• C. $\frac{1000M}{1000d-M.M_B}=m$
• D. $\frac{1000M}{1000d+m.M_B}=M$

Answer 1

Answer: (C)

$\frac{1000M}{1000d-M.M_B}=m$

Given that

Density of the solution $=d$ (in gm/ml)

Molarity of the solution $=M$

Molar mass of the solute $=M_B$ (in gm/mol)

Let's take $1000$ ml of the solution, then

Mass of the solution $=$ $Volume$ (ml) $\times$ density

$=$ $1000$ ml $\times$ $d$ gm/ml $=$ $1000$ $d$ gm

Moles of solute $=M\times Volume=M\times 1lit=Mmoles$ (Since, $1000ml=1liter$)

$\therefore$ Mass of the solute $=$ No. of moles$\times$ Molar mass $=M{M}_B$ gm

$\therefore$ Mass of the solvent $=$ mass of the solution $-$ mass of the solute$=(1000d-M{M}_B)$ gm

Now,

Molality (m) $=\frac{molesofsolute}{Kilogramsofsolvent}$

$\therefore$ $m=\frac{M}{(1000d-{MM}_B)\times \frac{1}{1000}}$

$\Rightarrow m=\frac{1000M}{1000d-{MM}_B}$

$\therefore$ (C) option is correct.