of an impurity. Before crystallization, the impurity is to be removed by adsoppion on a deoolorizing carbon which adsorbs only insignificant amounts of the principal solule. A serices of laboratory tests was made by stirring various amounts of the adsorbeat into batches of be original solution until equilibrium was established, yielding the following data at constant tertperature:

$\backslash$table$[[kg$ carbon $\frac{?}{kg}$ soln,$0,0\mathrm{.}001,0\mathrm{.}004,0\mathrm{.}008,0\mathrm{.}02,0\mathrm{.}04],[$Equilibrium color,$9\mathrm{.}6,8\mathrm{.}1,6\mathrm{.}3,4\mathrm{.}3,1\mathrm{.}7,0\mathrm{.}7]]$

The color intensity was measured on an arbitrary scale, proportional to the concentration of the colored substance, It is desired to reduce the color to $10\%$ of its original value, $9\mathrm{.}6.$ Determine the quantity of fresh carbon required per $1000kg$ of solution for a singe$-$stage opration, for a two$-$stage crosscurtent process using the minimum total amount of carbon, and tor a two$-$stage countercurtent operation.