A saturated aqueous solution of sodium chloride at \(100^{\circ} \mathrm{C}\) is fed to a steady-state evaporative crystallizer system that operates at \(100^{\circ} \mathrm{C} . \mathrm{F}_{\mathrm{W}, \text { in }}=2000 \mathrm{~kg} / \mathrm{h}\) of water(on a saltfree basis). We evaporate \(\mathrm{V} \mathrm{kg} / \mathrm{h}\) of pure water vapor. The product mixture of crystals and solution at \(100^{\circ} \mathrm{C}\) from the crystallizer is sent to a solid-liquid separator. The solid crystals plus entrained saturated liquid are removed as product that is sent to a drier and the remainder of the saturated liquid is recycled. Volumetric entrainment of saturated liquid with the solid salt can be approximated as \(\mathrm{e} \times\) (volume solid salt) with \(\mathrm{e}=0.2\). Solubility data are in Table 17-1. Additional data are in Problem 15.D23. Determine flow rates in \(\mathrm{kg} / \mathrm{h}\) of V, A (anhydrous crystals), and entrained saturated solution.

Data From Problem D23.

A saturated sodium nitrate, \(\mathrm{NaNO}_{3}\), solution at \(100^{\circ} \mathrm{C}\) at a feed rate of \(1000 \mathrm{~kg} / \mathrm{h}\) of water is sent to a steady-state evaporative crystallizer also operating at \(100^{\circ} \mathrm{C}\). The evaporative crystallizer evaporates \(300 \mathrm{~kg} / \mathrm{h}\) of pure water vapor. The mixture of the liquid and crystals from the evaporative crystallizer is cooled to \(35^{\circ} \mathrm{C}\) and sent to a steady-state cooling crystallizer also operating at \(35^{\circ} \mathrm{C}\). Data are in Table \(17-1\).

a. How many \(\mathrm{kg}\) of water, how many \(\mathrm{kg}\) of crystals, and how many \(\mathrm{kg}\) of dissolved \(\mathrm{NaNO}_{3}\) are in the product from the evaporative crystallizer?

b. How many \(\mathrm{kg}\) of water, how many \(\mathrm{kg}\) of crystals, and how many \(\mathrm{kg}\) of dissolved \(\mathrm{NaNO}_{3}\) are in the product from the cooling crystallizer?

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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 NH4NO 118.3 192 297 421 580 871 nitrate Ammonium (NH4)2SO4 70.6 75.4 81 88 95 103 sulfate Barium chloride BaCl2 Calcium chloride CaCl2 Cobalt chloride CoCl2 Copper sulfate CuSO4 Lithium chloride LiCI 26 56 31.2 35.8 40.8 46.2 52.5 59.4 59.5 74.5 128 137 147 159 43.5 52.9 69.5 93.8 97.6 106 14.3 20.7 28.5 40.0 55.0 75.4 69.2 83.5 89.8 98.4 112 128 52.9 54.6 57.5 61.0 66.1 73.3 Magnesium MgCl2 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 fluoride KF FF 44.7 94.9 138 142 150 Potassium nitrate KNO3 Sodium acetate NaC2H3O2 Sodium acetate NaC2H3O2 3 Sodium chloride NaCl Sodium nitrate NaNO3 73 Sodium sulfate Na2SO4 Citric acid Sodium sulfate Na2SO4 7 19.5 44.1 Sodium sulfate Na2SO4 10 5.0 19.4 Benzoic acid C6H3COOH C3H4OH(COOH); 1 - Fructose C6H12O6 - Glucose Cotiz 1 46 Sucrose C12H22O11 | | 8 p 13.3 31.6 63.9 110 169 247 139 153 170 36.3 46.5 65.5 139 35.7 36.0 36.6 37.1 38.0 39.2 88 104 124 148 180 48.8 45.3 43.7 42.5 0.17 0.29 0.56 1.16 2.72 5.88 146 215 277 372 526 80 85 90 - 179 92 160 280 440 179 204 238 287 362 487