$1.$ If a solvent has a selectivity of $2\mathrm{.}5$ for solute A over solute B and the concentration of solute A in the feed is $100$ g$/$L$,$ what is the expected concentration of solute A in the solvent phase?

$2.$ In a ternary phase diagram for a system containing components X$,$ Y$,$ and Z$,$ if the mass fractions of X and Y in a mixture are $40\%$ and $35\%$ respectively, what is the mass fraction of Z$?$

$3.$ A counter$-$current extraction process recovers $80\%$ of the solute in the first stage and $50\%$ of the remaining solute in the second stage. If the initial solute amount is $200$ grams, how much solute remains after the second stage?

$4.$ During a single$-$stage extraction, $120$ mL of solvent is used to extract a solute from $240$ mL of an aqueous solution. What is the volume ratio of solvent to aqueous solution?