Question

The distribution coefficient, $K_D$ for an organic compound between water and methylene chloride is 3.40. An aqueous solution of the organic compound contains 0.500g per 100 $mL$ and is extracted with 50.0 $mL$ of methylene chloride. What percentage of the organic compound originally in water is extracted?
$$\begin{gathered} (A)31.5\mathrm{\%} \\ (B)63.0\mathrm{\%} \\ (C)72.0\mathrm{\%} \\ (D)92.6\mathrm{\%} \end{gathered}$$

Answer 1

Hint: Distribution coefficient is the ratio of concentration of two immiscible solvent mixtures which are in equilibrium. It compares solubility of solute in two liquids. Concentration is the ratio of mass of solute in g to Volume. Distribution coefficient is obtained by dividing concentration of solute in organic phase to in aqueous phase.

Complete step by step answer:
- Consider $x$g of organic compound extracted in methylene chloride.
- Amount of organic compounds remaining in water in$0.5-x$ g.
- As $x$ g of organic compound is extracted in $50mL$of methylene chloride and in aqueous solution the amount of organic compound present is$0.5-x$ in $100mL$.
- As we know, the distribution coefficient is the ratio of concentration of solute in organic solvent to concentration of solute in aqueous.
- Concentration in methylene chloride=${\displaystyle \frac{x}{50mL}}$
- Concentration in water =${\displaystyle \frac{0.5-x}{100mL}}$
As given distribution coefficient $Kd=3.40$
So we can write,
$Kd={\displaystyle \frac{x}{50mL}}\times {\displaystyle \frac{100mL}{0.5-x}}=3.40$
$\begin{array}{rl}& {\displaystyle \frac{2x}{0.5-x}}=3.40\\ & {\displaystyle \frac{x}{0.5-x}}=1.70\\ & x\text{ =0}\text{.85- 1}\text{.70 }x\\ & 2.70x=0.85\\ & x=0.315\end{array}$
So, 0.315 g of organic compound is extracted in water and 0.185 g of organic compound is extracted in methylene chloride.
The percentage of organic compound originally extracted in water is
$$={\displaystyle \frac{x}{0.5}}\times 100$$
$$\begin{array}{rl}& ={\displaystyle \frac{0.315}{0.5}}\times 100\\ & =0.63\times 100\\ & =63\mathrm{\%}\end{array}$$
Hence, option (B) $63\mathrm{\%}$ of organic compounds originally extracted in water.

Note: Distribution coefficient is ratio of concentration of both ionized and unionized species whereas partition coefficient considers ration of concentration of only unionized species. When molecules remain unionized, the partition coefficient is almost the same as the distribution coefficient. In distribution, one solvent is usually water and the other is hydrophobic.