Question

A $6.5$ molal solution of $\mathrm{KOH}(\mathrm{aq}.)$ has a density of $1.89gc{m}^{-3}$.The molarity of the solution is __________ $mold{m}^{-3}$. (Round off to the Nearest Integer).

Answer 1

Step 1: Relation between molality and molarity

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

Where, $m=$molality of the solution

$M=$molarity of solution

$d=$density of solution

$MM=$molar mass of solute

Step 2: Calculate the molarity of the solution

Molar mass of $\mathrm{KOH}=39+16+1=56\mathrm{g}/\mathrm{mol}$

$$\begin{gathered} \frac{1}{6.5}=\frac{1.89}{M}-\frac{56}{1000} \\ \Rightarrow M=9molar \end{gathered}$$

Thus, the molarity of the solution is $\mathbf{9}mold{m}^{-3}$.