"Published in Newark, California, USA"
After a crystallization operation, the solution of calcium chloride in water contains 60 g of CaCl2 per 100 g of water. Calculate the amount of this solution necessary to dissolve 200 kg of CaCl2·6H2O crystals at a temperature of of 298K (25°C). The solubility of CaCl2 at 298K (25°C) is 819.2 g of CaCl2 per 1000 g of water. (Atomic Weights: Ca = 40, Cl = 35, O = 16, H = 1)
Solution:
The given word problem is about mixing of calcium chloride crystals with enough calcium chloride solution to dissolve the crystals completely which involves the principles of Stoichiometry. The total amount of a substance in the reactants or incoming ingredients must be equal to the total amount of a substance in the final products. In short, the Law of Conservation of Mass must be followed all the time. To illustrate the given problem, it is better to draw the flow diagram as follows
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Basis: 200 kg of CaCl2·6H2O Crystals
Let x = be the amount of CaCl2 Solution
y = be the amount of Final Solution
Molecular Weight Data:
CaCl2 = 110
CaCl2·6H2O = 218
H2O = 18
Overall Material Balance of Mixer:
Consider CaCl2 Solution:
Consider CaCl2·6H2O Crystals:
Consider Final Solution:
Material Balance of CaCl2:
Substitute the value of x to the first equation, we have
Substitute the value of y to the first equation, we have
Therefore,
The amount of CaCl2 Solution is 144.1887 kg.