CRYSTALLIZATION SOLUBILITY CURVE

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Leonard Cunningham
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1 CRYSTALLIZATION saturated solution cooled/evaporated forms crystal important industrially because: i) a crystal formed from an impure solution and itself pure ii) Practical method of obtaining pure chemical substances in a satisfactory condition for packaging and storing solid-liquid separation process yield, purity, sizes & shapes of crystals important crystals - uniform in size SOLUBILITY CURVE 1

SOLUBILITY CURVE equilibrium is attained when the solution or mother liquor is saturated (represented by solubility curve) solubility dependent mainly on temperature (pressure negligible effect)

2 SOLUBILITY CURVE equilibrium is attained when the solution or mother liquor is saturated (represented by solubility curve) solubility dependent mainly on temperature (pressure negligible effect) solubilities of most salts increase slightly or markedly with temperature Solubility curve for some typical salts in water Solubility curve for sodium thiosulfate SOLID-LIQUID PHASE DIAGRAM Solid-liquid phase diagram for the MgSO 4 -nh 2 O system at 1 atm 2

3 YIELD & HEAT & MATERIAL BALANCES yield of crystals can be calculated by knowing: initial concentration of solute final temperature solubility at this temperature material balances F kg Hot solution X 1 kg solute/ 100 kg H 2 O kg H 2 O evaporate Mass balance : S kg solution X 2 kg solute/ 100 kg H 2 O Water balance : Input = Output Solute balance : Input = Output solute crystals are anhydrous - simple water & solute material balances crystals are hydrated - some water in the solution is removed with crystals C kg Crystal EXAMPLE A salt solution weighing kg with 30 wt % Na 2 CO 3 is cooled to 293K (20 o C). The salt crystallized as the decahydrate. What will be the yield of Na 2 CO 3.10H 2 O crystals if the solubility is 21.5 kg anhydrous Na 2 CO 3 /100 kg of total water? a)assume that no water evaporated. b) Assume that 3% of the total weight of the solution is lost by evaporation of water in cooling. Ans: 6370 kg, 6630 kg 3

4 EXAMPLE Solution: Molecular weights: Na 2 CO 3 = 106.0, 10H 2 O = 180.2, Na 2 CO 3 10H 2 O = (a) W = 0, water balance: Na 2 CO 3 balance: C = 6370 kg of Na 2 CO 3 10H 2 O crystals and S = 3630 kg solution (b) W = 0.03(10000) = 300 kg, water balance: C = 6630 kg of Na 2 CO 3 10H 2 O crystals and S = 3070 kg solution. EXAMPLE 27.1(McCabe, Smith & Harriott) A solution consisting of 30 wt% MgSO 4 is cooled to 60 o F. During cooling, 5 % of the total water in the system evaporates. How kg of crystals are obtained per 1000 kg of original mixture? Data: Molecular weight of MgSO 4 = Ans: 261 kg 4

5 EXAMPLE (P ) A hot solution containing 1000 kg of MgSO 4 and water having a concentration of 30 wt% MgSO 4 is cooled to K (60 o F) where crystals of MgSO 4.7H 2 O are precipitated. The solubility at K is 24.5 wt % anhydrous MgSO 4 in the solution. Calculate the yield of crystals obtained if 5 % of the original water in the system evaporates on cooling. Data: Molecular weight of MgSO 4 = Ans: 261 kg HEAT BALANCES IN CRYSTALLIZATION normally, crystallization is exothermic W kg H 2 O H V kj/kg F kg Hot solution h F kj/kg S kg solution h S kj/kg Total heat absorbed, q (kj): When T datum = 32 o F, or C kg Crystal h C kj/kg Fh F + q = (S + C)h M + WH V Fh F + q = Sh S + Ch C + WH V When T datum = T equil./sat., Fh F + q = Wλ + Ch C = Wλ + CΔH crys heat of crystallization, ΔH crys = - heat of solution at infinite dilution, "H Heat absorbed, q = + ve,heat given off, q = - ve # soln 5

6 ENTHALPY-CONCENTRATION DIAGRAM Enthalpy-concentration diagram for the MgSO 4 - nh 2 O system at 1 atm ENTHALPY-CONCENTRATION DIAGRAM 6

7 EXAMPLE A 32.5% solution of MgSO 4 at 120 o F (48.9 o C) is cooled, without appreciable evaporation to 70 o F (21.1 o C) in a batchcooled crystallizer. How much heat must be removed from the solution per 100 Ib of the feed solution? The average heat capacity of the feed solution is 0.72 Btu/Ib o F and the heat of solution at 18 o C is 23.2 Btu/Ib of MgSO 4.7H 2 0. Ans: Btu Enthalpy-concentration diagram for the MgSO 4 - nh 2 O system at 1 atm EXAMPLE A feed solution of 2268 kg at K (54.4 o C) containing 48.2 kg MgSO 4 /100 kg total water is cooled to K (20 o C) where MgSO 4.7H 2 O crystals are removed. The solubility of the salt is 35.5 kg MgSO 4 /100 kg total water. The average heat capacity of the feed solution can be assumed as 2.93 kj/kg.k. The heat of solution at K (18 o C) is x 10 3 kj/kg mol MgSO 4.7H 2 O. Calculate the yield of crystals and make a heat balance to determine the total heat evolved and removed from the crystalliser, q, assuming that no water is vaporized. Data: Molecular weight of MgSO 4 7H 2 0 is Ans: kg crystal, kj Enthalpy-concentration diagram for the MgSO 4 - nh 2 O system at 1 atm 7

8 EXAMPLE Solution: Molecular weights: MgSO 4 = 120.4, 7H 2 O = 126, MgSO 4 7H 2 O = kg 48.2 kg MgSO 4 /100 kg H 2 O S kg solution 35.5 kg MgSO 4 /100 kg H 2 O C kg MgSO 4 7H 2 O W = 0, water balance: MgSO 4 balance:! 100 $! 100 $! 2268# & = S # &+C 126 $ # & " % " % " 246.4%! 48.2 $! 35.5 $! 2268# & = S # &+C $ # & " % " % " 246.4% Total balance: 2268 = C + S C = kg MgSO 4 7H 2 O crystals, S = kg solution. EXAMPLE Solu&on T ref. = 293.2K (T datum ) Heat balance : Fh F + q = Wλ + Ch C = Wλ + CΔH crys Enthalpy of the feed, h F = C p ΔT = (2.93)( ) Heat of solution = 13.31x10 3 / = 54.0 kj/kg crystals. Heat of crystallization = -(54.0) = kj/kg crystals Total heat absorbed, q 2268(2.93)( ) + q = 631.9(54.0) q = 631.9(54.0) (2.93)( ) = kj 8

9 EXAMPLE A solution of 500 kg of Na 2 SO 4 in 2500 kg water is cooled from 333K to 283K in an agitated mild steel vessel. At 283K, the solubility of the anhydrous salt is 8.9 kg/100kg water and the stable crystalline phase is Na 2 SO 4.10H 2 O. At 291K, the heat of solution is MJ/kmol and the specific heat capacity of the solution is 3.6 kj/kg.k. If, during cooling, 2% of the water initially present is lost by evaporation, estimate the heat which must be removed. Ans: kj CRYSTALLIZER 9

PHEN 612 SPRING 2008 WEEK 13 LAURENT SIMON

PHEN 612 SPRING 2008 WEEK 13 LAURENT SIMON Crystallization Crystallization is a common separation process in Commodity inorganic industry (e.g., salts) Food industry (e.g., sugars) Pharmaceutical manufacturing