An engineer suggests that an air stream containing $0\mathrm{.}5$ mol$\%$ hydrogen

sulphide $($H$2$S$)$ can be contacted with an aqueous solution of $1$ wt$\%$

sodium hydroxide $($NaOH$)$ in a small counter$-$current staged column. The

H$2$S will react with NaOH by the reaction

H$2$S $+2$ NaOH Na$2$S $+2$ H$2$O

The Na$2$S is non$-$volatile and the reaction is very rapid and irreversible

so that at equilibrium the concentration of H$2$S in the gas phase is

essentially zero.

Consider the mole ratio of sulphur in the water, X$,$ to be the total free

dissolved hydrogen sulphide $($H$2$S$)$ plus the fixed sulphur as Na$2$S$.$

Atomic weights are: H $=1,$ S $=32,$ Na $=23,$ O $=16,$ N $=14$

a$.$ Convert all concentrations into mole fractions. What is the

minimum flow rate of the aqueous solution of $1$ wt$\%$ NaOH

required to remove all but $2$ ppm $($w$/$w$)$ of H$2$S from the air stream?

$[10$ marks$]$

b$.$ The flow rate of water used is twice that found in $($a$).$ Use

Figure $2\mathrm{.}1($or your own graph paper or Excel$)$ to construct a

McCabe$-$Thiele diagram of the process. What is the number of

theoretical equilibrium stages required? Include your diagram

with your answer sheet.

$[6$ marks$]$

c$.$ If the mass transfer rate is slow so that the stage efficiency is

$90\%,$ how many stages are needed at the same flow rates as part

$($b$)?$

$[5$ marks$]$

d$.$ If a counter$-$current packed column is used instead of a plate

column, what is the number of transfer units, NOG, for this

process? The flow rates of the air and gas streams are the same

as in part $($b$).$

$[4$ marks$]$