Calculations related to crystallization
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2. A crystallization tank contains 10,000 kg of a saturated NaHCO3 solution at 60°C. When this solution is cooled to 20°C, what is the amount of NaHCO3 crystallized out of the solution in kilograms? It is known that at 60°C, the solubility of NaHCO3 in water is 16.4 g of NaHCO3 per 100 g of H2O. At 20°C, its solubility is 9.6 g of NaHCO3 per 100 g of H2O. (A) 556 (B) 585 (C) 505 (D) 520 Answer: () Main solution process: This can be solved using a linear equation. Calculations are done using the formulas from chemical engineering principles, but the meaning of V is unknown; it represents the solvent that is evaporated and removed. Please give some guidance.
Choose B. This problem is solved using the law of conservation of mass; the mass of water remains constant during the cooling process. Let the mass of water, the solvent, be x. Then 16.4x/100 + x = 10000, from which x can be calculated. The crystals that precipitate at 20 degrees are: 10000 – x – 96x/100
V=0, c1=0.164, c2=0.096; G=W(c1-c2)=10000*100/116.4*(0.164-0.096)=584.2
During the cooling process, the water quality remains unchanged, V=0
10000*16.4/（100+16.4）=（1000-x)*9.6/（100+9.6）， an elementary school math problem
=10000*((16.4/(100+16.4)-(9.6/(100+9.6))))=533.0223kg
=533.0223 kg of dry material – the simplest material balance calculation
I also calculated it as 533, but this option isn’t available; it must be wrong. My calculation method is the same as that of the person in floor 6. Can anyone help me figure out where the mistake lies?
The formula is incorrect; there’s a missing ‘x’ on the right side. Additionally, 10000 was written as 1000 – it should be 10000*16.4/（100+16.4）=x+（10000-x)*9.6/（100+9.6）
Wrong, it should be =10000*((16.4/(100+16.4)-(9.6/(100+16.4))))=584.1924kg
By applying the conservation of water mass, let the concentration of the solution at 20 degrees Celsius be x; then 10000*（100/116.4) = x*(100/109.6). Subsequently, using the conservation of total mass, 10000-x gives the desired result.