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W et air containing 4.0 m ole% water v apor is p assed through a column o f calcium chloride pellets.

The pellets adsorb 97.0% o f t he w ater and n one o f t he o ther c onstituents o f t he air. The column

packing was initially dry and h ad a mass o f 3.40 kg. Following 5.0 h ours o f o peration, the pellets a re

r eweighed and found t o h ave a mass o f 3.54 kg.

( a) C alculate the molar flow r ate ( mol/h) o f t he feed gas a nd t he mole fraction o f w ater vapor in the

product gas.

.

( b) T he m ole fraction o f w ater i n the product gas is monitored and found t o have the value calculated in p art (a) for the first 10 h ours o f o peration, b ut t hen it begins to increase. What is the

most likely cause o f t he increase? I f t he process continues t o r un, what will t he m ole fraction o f

w ater in the product gas eventually be?

.t'robl~ms

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T he indicator dilution method is a technique used to determine flow rates o f fluids in channels for

which devices like rotameters and orifice meters cannot b e·used (e.g., rivers, blood vessels, i md largediameter pipelines). A stream o f a n easily measured substance (the tracer) is injected into the channel at a known r ate a nd the tracer concentration is measured a t a p oint far enough downstream o f

t he injection point for the tracer t o b e c ompletely mixed with the flowing fluid. The larger the flow

r ate o f t he fluid, the lower the tracer concentration a t t he measurement point.

A gas stream t hat c ontains 1.50 m ole% C 02 flows through a pipeline. Twenty (20.0) kilograms

o f C 02 p er m inute is i njected into the line. A sample o f t he gas is drawn from a point in the line 150

m eters downstream o f t he injection p oint a nd found t o c ontain 2.3 mole% C 0 2 .

( a) Estimate the gas flow r ate (kmoVrnin) upstream o f t he injection point.

( b) E ighteen seconds elapses from the instant the additional C 0 2 is first injected t o t he time the

C 0 2 c oncentration a t t he measurement point begins t o rise. Assuming t hat t he tracer travels a t

t he average velocity o f t he gas in the pipeline (i.e., neglecting diffusion o f C 02 ) , e stimate t he

r \ average velocity (m/s). I f the molar gas density is 0.123 kmoVm3 , what is the pipe diameter?

/ 4.25. 1 variation o f t he indicator dilution method (see preceding problem) is used t o m easure total blood

l~ olume. A known amount o f a t racer is injected into the bloodstream and disperses uniformly

throughout t he circulatory system. A blood sample is then withdrawn, the tracer concentration in

the sample is m easured, a nd t he measured concentration [which equals (tracer injected)/( total blood

volume) if n o t racer is lost through blood vessel walls] is used t o d etermine t he total blood volume.

I n o ne such experiment, 0.60 c m3 o f a s olution containing 5.00 mg/L o f a dye is injected into

an artery o f a grown man. A bout 10 minutes later, after the tracer has h ad time t o d istribute

itself uniformly throughout the bloodstream, a blood sample is withdrawn and placed in the

sample chamber o f a s pectrophotometer. A beam o f light passes through the chamber, and

the spectrophotometer measures the intensity o f t he transmitted beam a nd displays the value

o f t he solution absorbance (a quantity t hat increases with the amount o f light absorbed by the sample). The value displayed is 0.18. A c alibration curve o f a bsorbance A versus tracer concentration

C (micrograms dye/liter blood) is a straight line through the origin and the point (A = 0.9, C =

3 J.IWL). E stimate t he p atient's total blood volume from these data.

(7

A liquid mixture containing 30.0 m ole% benzene (B), 25.0% t oluene (T), and the balance xylene

(X) is fed t o a distillation column. The bottoms product contains 98.0 m ole% X and n oB, a nd 96.0%

o f t he X in the feed is recovered in this stream. T he o verhead product is fed t o a s econd column.

The overhead product from the second column contains 97 .0% o f t he B in t he feed t o this column.

The composition o f this stream is 94.0 m ole% B and the balance T.

(a) D raw a nd label a flowchart o f this process and do the degree-of-freedom analysis t o p rove t hat

f or an assumed basis o f calculation, molar flow rates and compositions o f all process streams

can be calculated from the given information. Write in o rder t he equations you would solve

to calculate unknown process variables. I n e ach equation ( or p air o f simultaneous equations),

circle the variable(s) for which you would solve. D o n ot d o the calculations.

(b) Calculate (i) the percentage o f t he benzene in the process feed (i.e., the feed t o t he first column)

t hat emerges in the overhead product from the second column and (ii) the percentage o f t oluene

in the process feed t hat emerges i n t he bottom product from the second column.

··· --- ---, -

~0 J Fresh orange juice contains 12.0 w t% solids a nd t he balance water, and concentrated orange juice

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":::::::!' contains 42.0 w t% solids. Initially a single evaporation process was used for the concentration, but

\

volatile constituents o f t he j uice escaped with t he water, leaving the concentrate with.a fiat taste. T he

c urrent process overcomes this problem by bypassing the evaporator with a fraction o f t he fresh

juice. T he juice t hat e nters the evaporator is c oncentrated to 58 w t% solids, a nd t he evaporator

product stream is mixed with the bypassed fresh juiCe to achieve the desired final concentration.

( a) D raw a nd label a flowchart o f this process, neglecting the vaporization o f everything in the juice

b ut water. First prove t hat t he subsystem containing the point where the bypass stream splits

off from the evaporator feed has one degree o f freedom. ( If you think i t has zero degrees, try

determining the unknown variables associated with this system.) Then perform the degree-offreedom analysis for the overall system, the evaporator, and t he b ypass-evaporator product

mixing point, and write i n o rder t he equations you would solve t o d etermine all unknown stream

variables. In each equation, circle the variable for which you would solve, b ut d on't d o any

calculations.

.

( b) C alculate the amount o f p roduct (42% c oncentrate) produced p er 100 kg fresh juice fed t o t he

process and t he fraction o f th~leed t hat bypasses the evaporator.

(c) Most o f t he volatile ingredients t hat p rovide the taste o f t he concentrate are contained i n t he

fresh juice t hat bypasses the evaporator. You could get more o f these ingredients in the final

product by evaporating t o (say) 90% solids instead o f 5 8%; you could then bypass a greater

fraction o f t he fresh juice and thereby obtain an even b etter tasting product. Suggest possible

drawbacks t o this proposal.