Question

If the ether-water distribution coefficient is 4 and I have 5 g of solute in 100 g of water, what mass of solute can I extract with one 35 mL portion of ether?

Answer 1

The mass of solute extracted is 2.9 g.

Explanation:

The distribution coefficient is the ratio of the concentrations of the solute in the organic and the aqueous phases.

`color(blue)(|bar(ul(color(white)(a/a) K_D = C_"org"/C_"aq"color(white)(a/a)|)))" "`

Let `xcolor(white)(l) "g"` = mass of solute extracted into ether layer.

Then `(5-x)color(white)(l) "g"` = mass remaining in aqueous layer.

`4 =( (x color(red)(cancel(color(black)("g"))))/(35 color(red)(cancel(color(black)("mL")))))/(((5-x) color(red)(cancel(color(black)("g"))))/(100 color(red)(cancel(color(black)("mL"))))) = x/35 × 100/(5 -x)`

`x/("5 -"color(white)(l)x) = 4 × 35/100 = 1.4`

`x = 1.4(5-x) = 7-1.4x`

`2.4x = 7`

`x = 2.9`

Thus, 2.9 g of solute are extracted into the ether layer.