$($a$)$ The schematic below represents part of a lead$-$zinc

flotation plant operating at $500$tph$.$ Use the information

contained in the schematic and table below to answer the

following questions.

$($i$)$ What is the recovery of lead from the $Pb$ rougher

stage to the $Pb$ cleaner stage?

$($ii$)$ What is the mass of sphalerite which enters the $Zn$

cleaner stage? Sphalerite contains $64\mathrm{.}1\%$ Zn by

mass.

$($b$)$ The plant in Q$3($a$)$ is concerned with losses of sphalerite to

the $Pb$ cleaner stage. They want to investigate changing

the amounts of reagents used in the $Pb$ rougher stage to

reduce sphalerite loss. What changes would you

recommend investigating?

$($c$)$ The plant in Q$3($a$)$ uses mechanical cells for the rougher

stages and flotation columns in the cleaner stages. Why

might this be the case?

$($d$)$ Explain the importance of particle size in the physical

separation of copper contained within chalcopyrite?