Experimental data for leaching sugar from sugarcane with water show that a reasonable value for effective equilibrium constant \(y / x=m_{E}\) is 1.18 where \(\mathrm{y}\) and \(\mathrm{x}\) are the solute weight fractions in liquid and solid, respectively. Batch leaching is similar to batch extraction, and if the terms are translated, the same equations can be used. We are doing a single-stage batch leaching of sugarcane with water to recover sugar. The feed to the leaching process is \(1.0 \mathrm{~kg}\) of solids (on a dry basis). In this feed, cane contains \(5.5 \mathrm{wt} \%\) sugar. The inlet solvent is pure water. Assume the overflow and underflow amounts are constant.

a. If \(3.0 \mathrm{~kg}\) of wash liquid are used in a normal batch leaching operation, what are the outlet overflow liquid weight fraction of sugar (y) and the weight fraction of sugar in the solid (x)?

b. If we want the outlet overflow liquid to be \(0.4 \mathrm{wt} \%\) sugar, how many \(\mathrm{kg}\) of wash water are required in a normal batch leaching operation?