Na₂SO₄. 10H₂O crystals are formed by cooling 100 Kg of 30% by weight aqueous solution of Na₂SO₄. The final concentration of the solute in the solution is 10%. The weight of crystals is

ANS:D - 58.65

To solve this problem, let's first calculate the initial and final masses of Na2SO4 in the solution.

1. Initial Mass of Na2SO4:
   • Initially, the solution contains 30% Na2SO4 by weight.
   • So, the initial mass of Na2SO4 in the solution is 0.30×100 kg=30 kg0.30×100kg=30kg.
2. Final Mass of Na2SO4:
   • After cooling, some of the water evaporates, and Na2SO4·10H2O crystals are formed.
   • The final concentration of Na2SO4 in the solution is 10% by weight.
   • Let's assume the final mass of the solution (including the crystals) is 𝑀𝑓Mf​ kg.
   • Therefore, the final mass of Na2SO4 in the solution is 0.10×𝑀𝑓0.10×Mf​ kg.

Now, let's apply the principle of mass conservation to find 𝑀𝑓Mf​:

• The initial mass of the solution is 100 kg.
• The mass of the Na2SO4·10H2O crystals formed is the difference between the initial and final masses of the solution.

Initial mass of solution=Final mass of solution+Mass of crystalsInitial mass of solution=Final mass of solution+Mass of crystals 100 kg=𝑀𝑓+Mass of crystals100kg=Mf​+Mass of crystals Now, let's substitute the expressions for the masses of the Na2SO4 in the solution: 30 kg=0.10×𝑀𝑓+Mass of crystals30kg=0.10×Mf​+Mass of crystals Mass of crystals=30 kg−0.10×𝑀𝑓Mass of crystals=30kg−0.10×Mf​ We also know that the weight of the crystals is the weight of the water evaporated, which is given by the difference in the initial and final masses of the solution: Mass of crystals=100 kg−𝑀𝑓Mass of crystals=100kg−Mf​ Now, we can set up the equation: 30 kg−0.10×𝑀𝑓=100 kg−𝑀𝑓30kg−0.10×Mf​=100kg−Mf​ 0.10×𝑀𝑓=70 kg0.10×Mf​=70kg 𝑀𝑓=70 kg0.10=700 kgMf​=0.1070kg​=700kg Now, we can calculate the mass of the crystals: Mass of crystals=100 kg−𝑀𝑓=100 kg−700 kg=−600 kgMass of crystals=100kg−Mf​=100kg−700kg=−600kg The negative sign indicates an error in the calculation. Let's reassess the problem.