Q$2.$ A plate$-$and$-$frame dialyzer is to be used to process $0\mathrm{.}3$ m$3$

$/$h of an aqueous solution containing

$0\mathrm{.}25$ mol$/$L H$2$SO$4$ and $0\mathrm{.}12$ mol$/$L NiSO$4.$ Pure water is used as sweep liquid and flows counter

currently at $0\mathrm{.}35$ m$3$

$/$h$.$ It is desired to transfer $90\%$ of H$2$SO$4$ from feed to the diffusate. From batch

experiments, the overall $($total$)$ mass$-$transfer coefficient for H$2$SO$4$ is measured as $0\mathrm{.}06$ cm$/$min

and for NiSO$4$ as $0\mathrm{.}015$ cm$/$min$.$ Water transport through the membrane can be neglected and the

change in the volumetric flow rate of feed and sweep with permeation is negligible. For this

separation,

a$)$ Draw the membrane unit and show the streams with their concentrations. $[5$ pts$]$

b$)$ Determine the membrane area required for this separation in m$2$

$.[12$ pts$]$

c$)$ What is the flux of H$2$SO$4$ in mol$/$h$-$m$2$

$?[3$ pts$]$

d$)$ Determine the rate of NiSO$4$ permeated. $[11$ pts$]$

e$)$ What is the concentration of H$2$SO$4$ and NiSO$4$ in the retentate? $[4$ pts$]$