# 8.16: Untitled Page 205

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## Chapter 8

leaves the tank at the same rate, how long will it take for the concentration in the tank to be reduced to a concentration of 1.01 lbm per gallon?

8‐2. A salt solution in a perfectly stirred tank is washed out with fresh water at a rate such that the average residence time, *V Q *, is 10 minutes. Calculate the following:

a) The time in minutes required to remove 99% of the salt

originally present

b) The percentage of the original salt removed after the addition of one full tank of fresh water.

8‐3. Two reactants are added to a stirred tank reactor as illustrated in Figure 8.3.

In the inlet stream containing reactant #2 there is also a miscible liquid catalyst which is added at a level that yields a concentration *in the reactor* of 0.002 moles per liter. The volumetric flow rates of the two reactant streams are equal and the total volumetric rate entering and leaving the stirred tank is 15 gallons per minute.

*Figure 8.3*. Catalyst mixing process

It has been decided to change the type of catalyst and the change will be made by a substitution of the new catalyst for the old as the reactant and catalyst are continuously pumped into the 10,000 gallon tank. The inlet concentration of the new catalyst is adjusted to provide a final concentration of 0.0030 moles per

*Transient Material Balances *

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liter when the mixing process is operating at steady state. Determine the time in minutes required for the concentration of the new catalyst to reach 0.0029 moles per liter.

8‐4. Three perfectly stirred tanks, each of 10,000 gallon capacity, are arranged so that the effluent of the first is the feed to the second and the effluent of the second is the feed to the third. Initially the concentration in each tank is *c *. Pure o

water is then fed to the first tank at the rate of 50 gallons per minute. You are asked to determine:

a) The time required to reduce the concentration in the first tank to 0.10 *c *

o

b) The concentrations in the second and third tanks at this time

c) A general equation for the concentration in the *nth* tank in the cascade system illustrated in Figure 8.4.

*Figure 8.4* Sequence of stirred tanks

In order to solve an ordinary differential equation of the form *d* *c *

*A*

*g*( *t*) *c * *f *( *t*)

(1)

*A*

*dt*

explore the possibility that this *complex equation* can be transformed to the *simple* *equation* given by

*d*

(

*a t*) *c *

(

*b t*)

(2)

*A*

*dt*

We refer to this as a simple equation because it can be integrated directly to obtain

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