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# Answer to Question #186067 in Chemical Engineering for sheyi

Question #186067

CaCO3 precipitate is made by reacting CaO with an aqueous solution of Na2CO3, the by-product being NaOH. After decanting, slurry leaving the precipitation tank is 5% w/w CaCO3, 0.1% NaOH, and the balance water. 100 000 kg hr–1 of slurry is fed to a two-stage counter-current continuous washing system to be washed by 200 000 kg hr–1 of fresh water. Underflow from each unit contains 20% w/w solids. Calculate fraction of NaOH recovered and mass percentage NaOH of dried product. Would adding a third stage be worthwhile?

1
2021-04-29T07:57:55-0400

Overall Mass balance: 100 000 + 20,000=U + E

Now, overall solid balance, as 20% 20 led from both thickenes F. Xacoz + NX Cacoz = E. XCacoz + U. cacos

=> 100000×0-05 + 20000 x0 E×0 + Ux0.2 -

U= 25000 lb/hr. Putty U25OOD in B, E = 9500020/hr

Now, U': 1 (207. solid in both thickenes U/F)

So, U'= 25000 lb/hr, 20% solid (Cacoz) E' = U²+W-U (applying mass balance around 2nd

FE: 25000+20000-25000 E'= 20000 lb/hr

Applying Cantic (NaOH) belance about 1st thickener

same can be written for 2nd thickere, Now, if equilibrium in achieved in each of the thickeners.

the ratio of NaOH to wath will be same under flows & Oveffor,

ie for 1st thickenes. E.H Cassan's no soud (cacos) in O/F). E (1-NaOH) 1' (1-2 NADH)

Similarly, XH = 250 NOOH

Thus, from ) & (10), if we write for overall system (for both thickens)

Ñ…Ð¼Ð°Ð¾Ð½ = Ñ… Ð¼Ð°Ð¾Ð½

Now, overall

caustic balance gives

F. X NaOH EX NAOH + U2

100000 ×0.001 + WXD = 95000xx NaOH + 25000 × x NaOH

Ðµ Ð»Ð°Ð¾Ð½ = 0.0008@Ð¾Ñ…Ð¸ Ð¼Ð°Ð¾Ð½ % recovery of Naout in the extract = 0.0008x95000

0.0008 90H = 0.083%. (by wt.)

{ 2 per E F

X Naon X NaOH Naon 0.083%

1.e wt% NaOH in the dried Calog =

U. X soud + U. NADH

25000x 0.00083

25000 x 0.20 +25000x0 00 089

0.004149

1.e wt% NOOOH in dried Cacoz ( without watter)

= 0.4149%.

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