In crystallization of potassium chloride with a \(100^{\circ} \mathrm{C}\) feed and the crystallizer operating at \(20^{\circ} \mathrm{C}\), we obtain \(\mathrm{G}=4.0 \times 10^{-7} \mathrm{~m} / \mathrm{s}\). The crystallizer's volume is \(0.2 \mathrm{~m}^{3}\), and the feed rate is \(1000 \mathrm{~kg} / \mathrm{h}\). When operated without seeds, the crystals produced are too small. Your boss decides to seed and use a new crystallizer with volume \(=1.0 \mathrm{~m}^{3}\) but with the same throughput of feed and the same supersaturation, \(\mathrm{C}-\mathrm{C}^{*}\), as the current crystallizer. Desired crystal size is \(2.56 \mathrm{~mm}\). If the seed crystals are available with a very tight size distribution, what size of seed crystals, \(\mathrm{L}_{\mathrm{S}}(\mathrm{mm})\), and what weight of seed crystals \((\mathrm{kg} / \mathrm{h})\) should be used?

Data: \(ho_{\text {feed }}=1209 \mathrm{~kg} / \mathrm{m}^{3}\). Crystals are cubic in shape with equal growth on all faces, and \(\mathrm{k}_{\mathrm{v}}\) \(=1.0\). Solubility and hydrate data are in Table 17-1. Note: Watch your units!

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TABLE 17-1. Solubilities of selected inorganic and organic compounds in water Compound Formula Stable Hydrate T, C, Solubility, kg Anhydrous Compound/100 kg Water # HO 0 20 40 60 80 100 Ammonium NH4Br 60.6 75.5 91.2 108 126 146 bromide Ammonium NH4Cl 29.4 37.2 45.8 55.3 65.6 77.3 chloride Ammonium NH 155 172 191 209 229 250 iodide Ammonium NH4NO3 118.3 192 297 421 580 871 nitrate Ammonium (NH4)2SO4 70.6 75.4 81 88 95 103 sulfate Barium chloride BaCl2 2 31.2 35.8 40.8 46.2 52.5 59.4 Calcium chloride CaCl2 6 59.5 74.5 128 137 147 159 Cobalt chloride CoCl2 43.5 52.9 69.5 93.8 97.6 106 Copper sulfate CuSO4 5 14.3 20.7 28.5 40.0 55.0 75.4 Lithium chloride LiCI 69.2 83.5 89.8 98.4 112 128 Magnesium MgCl2 6 52.9 54.6 57.5 61.0 66.1 73.3 chloride Manganese MnCl2 63.4 73.9 88.5 109 113 115 chloride Nickel chloride NiCl2 6 53.4 60.8 73.2 81.2 86.6 87.6 Potassium KCI 28.0 34.2 40.1 45.8 51.3 56.3 chloride Potassium KF 44.7 94.9 138 142 150 fluoride Potassium nitrate KNO3 13.3 31.6 63.9 110 169 247 Sodium acetate NaCH3O2 139 153 170 Sodium acetate NaC2H3O2 3 36.3 46.5 65.5 139 Sodium chloride NaCl 35.7 36.0 36.6 37.1 38.0 Sodium nitrate NaNO3 73 88 104 124 148 Sodium sulfate Na2SO4 48.8 45.3 43.7 Sodium sulfate Na2SO4 7 Sodium sulfate Na2SO4 10 Benzoic acid Citric acid C6H3COOH C3H4OH(COOH); 1 - 96 Fructose C6H12O6 75 - not on 19.5 44.1 5.0 19.4 0.17 0.29 0.56 1.16 2.72 146 215 277 372 526 80 85 90 Glucose C6H12O6 1 46 Sucrose C12H22O11 179 92 160 280 440 | | | | 39.2 42.5 5.88 179 204 238 287 362 487