Certain solid substances, known as hydrated compounds, have well-defined molecul

Question

Certain solid substances, known as hydrated compounds, have well-defined molecular ratios of 'water to some other species. For example, calcium sulfate dihydrate (commonly known as gypsum, CaSO_4, 2H_2O), has 2 moles of water per mole of calcium sulfate; alternatively, it may be said that 1 mole of gypsum consists of 1 mole of calcium sulfate and 2 moles of water. The water in such substances is called water of hydration. (More information about hydrated salts is given in Chapter 6.) In order to eliminate the discharge of sulfuric acid into the environment, a process has been developed in which the acid is reacted with aragonite (CaCO_3) to produce calcium sulfate. The calcium sulfate then comes out of solution in a crystallizer to form a slurry (a suspension of solid particles in a liquid) of solid gypsum particles suspended in an aqueous CaSO_4 solution. The slurry flows from the crystallizer to a filter in which the particles are collected as a filter cake. The filter cake, which is 95.0 wt% solid gypsum and the remainder CaSO_4 solution, is fed to a dryer in which all water (including the water off hydration in the crystals) is driven off to yield anhydrous (water-free)CaSO_4 as product. A flowchart and relevant process data are given below. Solids content of slurry leaving crystallizer: 0.35 kg CaSO_4 middot 2H_2O/L slurry CaSO_4 content of slurry liquid: 0.209 g CaSO_4/100 g H_2O Specific gravities: CaSO_4 middot 2H_2O(s), 2.3 liquid solutions, 1.05 Briefly explain in your own words the functions of the three units (crystallizer, filter and dryer). Take a basis of one liter of solution leaving the calculate the mass (kg) and sol of solid gypsum, the mass of CaSO_4, in the gypsum, and the mass of in the liquid Calculate the percentage recovery of Cason-that is, the of the total caso percentage (precipitated plus dissolved) leaving the crystallizer recovered a solid anhydrous CaSO_4.

Explanation / Answer

b) for 1 L solution coming out of the crystallizer,

total mass of solid(mix of gypsum and CaSO4(s)) =0.35 kg

a)mass of CaSO4(s) in the liquid solution=0.209g/100g water

so mass of 1L or 1000 ml solution =density of liquid solution *volume=1.05g/ml*1000ml=1050g

mass of CaSO4(s)in 1L water=0.209g/100g water *1050g =2.19 g

b)mass of solid gypsum(CaSO4.2H2O)=mass of total solid in the liq solution- (mass of CaSO4 in the solution)=0.35kg-(2.19g)=350g-2.19g=347.81g

volume of solid gypsum=mass/density=347.81/2.32=149.92 ml[specific gravity=density of substance/density of water=density of subs in g/ml /1g/ml water]

c) mass of CaSO4 in gypsum=total mass of gypsum-mass of water of crystallization

moles of gypsum=mass of gypsum/molar mass of gypsum=347.81g/172.172g/mol=2.02 moles

each mole of gypsum has 2 moles of water of crytallization,

So moles of water of crystallization in 2.02 moles gypsum =2*2.02=4.04 moles=4.04 moles*18 g/mol=72.75 g

Hence ,the mass of CaSO4 in gypsum=total mass of gypsum-mass of water of crystallization=347.81-72.75=275.08g

b. % recovery of CaSO4=(anhydrous CaSO4 recovered/total CaSO4 dissolved)*100

1)total CaSO4.2H2O or solid fed=0.35 kg=350g

2) total CaSO4 anhydrous recovered=mass of CaSO4.2H2O-mass of CaSO4

one mole CaSO4.2H2O contains 2 moles H2O,

Moles of CaSO4.2H2O fed=350 g/molar mass =350 g/172.172g/mol=2.03 moles

moles of water of crystallization =2.03 moles*2=4.06 moles

mass of water of crystallization=4.06 moles*18 g /mol=73.18 g

so,mass of anhydrous CaSO4=350-73.18=276.81g

% recovery of CaSO4=276.81/350*100=79.09%

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