A 30wt% solution of sodium carbonate (Na 2 CO 3 ) is fed to an evaporator/crysta

Question

A 30wt% solution of sodium carbonate (Na2CO3) is fed to an evaporator/crystallizer system with a mass flow rate of 10,000 lb/hr, as shown below. The feed solution is mixed with recycle before entering an evaporator. The evaporator removes water, concentrating the solution and permitting crystallization to occur. The filter cake contains 3.5 lb of crystals per lb of entrained solution (liquid that is carried along with the filter cake). The entrained solution and the recycle solution both contain 0.177 lb of sodium carbonate per pound of solution.

What is the production rate of the crystals?

Explanation / Answer

Writing overall balance of the system. Entering solution contains 30 wt% Na2CO3.

mass of Na2CO3 enternig = 10000*0.3 =3000 lb/hr

Filter cake contains amount of crystals = 3.5*x

the entrained solution contains 0.177 lb Na2CO3 per lb solution

mass of entrained solution =0.177x

hence total mass of solids in the crystals entrained solution = 3.5x+0.177x=3.677x

hence 3.677x =3000

x= 3000/3.677=815.88 lb

mass of crystals produced = 818.5*3.5 =2855.3 lb crystals/hr

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