$195$ of $695$

t industrial chemical soda ash, $N{a}_{2}C{O}_3,$ is produced from lime$,$ salt, NaCl, and coke, $C,$ using the Solvay process. In this cess, the hypothetical chemical reaction

$CaC{O}_3+2$NaCl$CaC{l}_2+N{a}_{2}C{O}_3$

which does not occur under industrially acceptable conditions, is carried out indirectly via a sequence of reactions involving the intermediate, ammonia. In the flowsheet shown in Fig. P$3\mathrm{.}33,$ coke $($assumed to be $100\%$ carbon$)$ and limestone $($assumed to be pure $CaC{O}_3)$ are charged to a kiln in the ratio of $3$molCto$4molCaC{O}_3.$ In the kiln, the carbon burns completely with air $(21\%O_2,79\%N_2)$ :

$C+O_{2}C{O}_2$

Problems

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and provides the heat required to effect the thermal decomposition of $CaC{O}_3$ :

$CaC{O}_3$CaO$+C{O}_2$

Part of the flue gases from the kiln analyzing $36\mathrm{.}75\%C{O}_2$ is purged and the remainder $(64\%)$ is sent to the carbonating unit. The solid residue from the kiln, assumed to consist entirely of CaO, is reacted with water in a unit called the slaker to produce a $35\%$ calcium hydroxide solution, via the reaction

CaO$+H_{2}OCa(OH{)}_2$

This hydroxide solution is reacted in the ammonia recovery unit with the ammonium chloride recycle from the carbonating unit to produce ammonia and by$-$product $CaC{l}_2$ :

$2N{H}_{4}Cl+Ca(OH{)}_{2}2N{H}_3+CaC{l}_2+2H_{2}O$

The recycle stream $($stream $13)$ contains $4\mathrm{.}7\%$ dissolved $C{O}_2,7\mathrm{.}65\%$NaCl, $61\mathrm{.}54\%H_{2}O,$ and the remainder the ammonium compounds. The $CaC{l}_2$ byproduct stream also contains $80\%H_{2}O$ and a small amount $N{H}_{4}OH.$ Because

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Species Balances in Reacting Systems

of this ammonia loss, some make$-$up $N{H}_3$ must be supplied to the process. produced. The $N{H}_3$ introduced as make$-$up as well as the $N{H}_3$ produced by reaction immediately hydrolyze to ammonium hydroxide in the ammonia recovering unit:

$N{H}_3+H_{2}ON{H}_{4}OH$

Stream $12,$ the concentrated $($only $50\mathrm{.}57\%H_{2}O)$ ammonium hydroxide stream from the recovery unit, is next introduced into the carbonating unit in which the hydroxide reacts with NaCl, fed as a saturated brine solution containing $34\mathrm{.}37\%NaC{l}_{,\text{a}\text{n}\text{d}a}-$O $C{O}_2-$rich flue gas to produce $NaHC{O}_3$ via the reaction

$N{H}_{4}OH+C{O}_2+$NaCl$NaHC{O}_3+N{H}_{4}Cl$

The residual flue gases from the carbonating unit are vented while the product slurry, containing the NaHCO, precipitate, is sent to a separation subprocess. In the separator unit, the bicarbonate is filtered and washed in stages to produce a wet bicarbonate stream consisting of bicarbonate and some small amounts of NaCl. The residual liquid stream from the separation unit is recycled to the ammonia recovery unit while the wet bicarbonate stream is charged to a rotary furnace, called a calciner, in which bicarbonate is thermally decomposed to produce sodium carbonate:

$2NaHIC{O}_{3}N{a}_{2}C{O}_3+C{O}_2+H_{2}O$

$1$

The resulting solid product contains $2$molNaCl per $100$ mol sodium carbonate. The $C{O}_2$ and $I{I}_{2}O$ driven off in the calciner are cooled to condense out the $H_{2}O.$ The $C{O}_2$ is mixed with the flue gases from the lime kiln and fed to carbonating unit. Assume all compositions are in mole fractions or $\%.$

$($a$)$ Construct a degree$-$of$-$freedom table and show that the process is correctly specified.

$($b$)$ Outline the order in which the calculations ought to be carried out in order to determine all flows and compositions in the flowsheet.

$($c$)$ Calculate the moles of $CaC{l}_2$ solution produced $($stream $11)$ per mole of brine feed $($stream $14).$