Question

For a solution of density, $d$ in g/ml containing solute of molecular weight $W$, the molarity $M$ and molality $m$ are related by:

• A. $\frac{d}{M}=\frac{1}{m}+\frac{W}{1000}$
• B. $\frac{d}{m}=\frac{1}{M}+\frac{W}{1000}$
• C. $\frac{W}{M}=\frac{1}{m}+\frac{d}{1000}$
• D. $\frac{d}{m}=\frac{W}{M}+\frac{1}{1000}$

Answer 1

The correct option is A $\frac{d}{M}=\frac{1}{m}+\frac{W}{1000}$

Given that:

$d$ - density of solution (g/ml)

$M$ - Molarity of the solution

$m$ - Molality of the solution

$W$ - molecular weight of the solute

We know that-

$d=\frac{w}{V}\left(g/ml\right)$

So, in $1ml=\text{d gram of the solution}$

$Molesofsolute=M\times V$

If $V=1000ml$

$\frac{weight}{W}=M$

$weight=M\times W$

$m=M\times \frac{1000}{(\frac{d\times 1000}{1}-MW)}$

$(\frac{d\times 1000}{1}-MW)\frac{1}{M\times 1000}=\frac{1}{m}$

$\frac{d}{M}-\frac{W}{1000}=\frac{1}{m}$

$\frac{d}{M}=\frac{1}{m}+\frac{W}{1000}$

Hence, option $A$ is correct.