Question

A $5\%$ solution of cane sugar with a molecular weight of $342$ is isotonic with a $1\%$ solution of a substance $X$. What is the molecular weight of $X$?

Answer 1

Step 1: Given data

$W_{\mathit{1}}=5g$

${\mathrm{V}}_1=100\mathrm{ml}=0.1\mathrm{l}$

${\mathrm{M}}_1=342$

$X$:

$W_{\mathit{2}}=1g$

${\mathrm{V}}_2=100\mathrm{ml}=0.1\mathrm{l}$

$M_{\mathit{2}}=?$

Step 2: We know that, for an isotonic solution, $C_{\mathit{1}}=C_{\mathit{2}}$

$\frac{W_{\mathit{1}}}{M_{\mathit{1}}{V}_{\mathit{1}}}=\frac{W_{\mathit{2}}}{M_{\mathit{2}}{V}_{\mathit{2}}}$

Step 3: Substituting the values.

$$\begin{gathered} \frac{5}{(341\times 0.1)}=\frac{1}{(M2x0.1)} \\ {M}_{\mathit{2}}=\frac{342}{5} \\ {M}_{\mathit{2}}=68.4\mathrm{g} \end{gathered}$$