The flowchart of a steady-state process to recover crystalline chromate (K_2 CrO

Question

The flowchart of a steady-state process to recover crystalline chromate (K_2 CrO_4) from an aqueous solution of this salt is shown below: Forty-five hundred kilograms per hour of a solution that is one-third K_2 CrO_4 by mass is joined by a recycle stream containing 36.4% K_2 CrO_4, and the combined stream is fed into an evaporator. The concentrated stream leaving the evaporator contains 49.4% K_2 CrO_4 this stream is fed into a crystallizer in which it is cooled (causing crystals of K_2 CrO_4 to come out of solution) and then filtered. The filter cake consists of K_2 CrO_4 crystals and a solution that contains 36.4% K_2 CrO_4 by mass: the crystal account for 95% of the total mass of the filter cake. The solution that passes through the filter, also 36.4% K_2 CrO_4, is the recycle stream. Calculate the rate of evaporation, the rate of production of crystalline K_2 CrO_4, the feed rates that the evaporator and crystallizer must be designed to handle, and the recycle ratio (mass of recycle)/(mass of fresh feed). Suppose that the filtrate were discarded instead of being recycled. Calculate the production rate of crystals. What are the benefits and costs of the recycling?

Explanation / Answer

let us take basis of 1 hour.

part 1

feed F = 4500 kg

K2CrO4 incoming = 4500/3 = 1500 kg

water incoming= 300 kg

take oveall mass balance

Feed F= output stream of cake solid O + H20 stream H

4500 = O+H

Now take component mass overall balance

for K2CrO4

1500= .95 *O + (.05*.364 * O)

solve for O ,H

O= 1549.26 Kg

H=2950.73

Rate of evporation =2650.73 kg/hr

rate of production of crystalline K2CrO4= 1471.8 Kg/hr

for calculating recycle ratio we assign M to stream entering crystallizer and R to recycle feed

overall balance to crystallizer gives

M= R+1549.26

K2CrO4 balance on crystallizer gives

.494 M = 1500 + .364 R

solvinfg both eqution gives

R= 734.66 Kg/hr

M= 2283.9Kg/hr

part b

1. Using recycle help toachieve a wider range of separations

2. By using recycle, it is possible to recover expensive catalysts and reagents

3. By using recycle, in combination with some sort of separation process, a company can increase the overall conversion of an equilibrium reaction

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