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Principles of Material Balances

ChE 101 Fundamentals of Chemical Engineering

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Outline

¤ Process Diagrams

¤ Unit Operations

¤ General Material Balance Equation

¤ Mixing, ILAR¤ Tie Components

¤ Single Unit Balances

¤ Multiple-Unit Balances¤ Recycle and Bypass

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General Steps in Solving Material Balances

Read

  • Identify the streams and equipment involved

Draw  • Sketch a BFD or PFD with all streams

DFA    • Identify known and unknown parameters

Basis  • Choose and clearly state a convenient basis

MB  •  Write overall and component balances, and other relating equations

Check  • Consider the given conditions and common sense

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Tie Component

¤ Enters in one input stream only

¤ Exits in one output stream only

¤ Is easily traced, and can be used in relating other components

¤ Ex. Find the mass M4

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Tie Component

¤ Ex. You buy 100 kg of cucumbers that contain 99% water. A few

days later they are found to be 98% water. What is the remainingweight of the cucumbers?

¤ Ex. Drying: A batch dryer can handle 5000 kg feed per hour. 5000kg of a material containing 30% moisture is to be dried. How muchmoisture evaporates per hour if the dried material contains 5%moisture?

¤ Ex. Evaporation: An evaporator has a capacity to evaporate 30,000

kg of water per hour. We want to concentrate a NaCl-watersolution from 10% to 40%. If the evaporator is to operate at itsrated capacity, what must the feed rate be? How much product isobtained per hour?

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Tie Component

¤ Ex. Extraction: A copra batch contains 44% oil and is to be extracted

with n-hexane. The extracted meal contains 0.07 kg oil/kg oil-freematter, and the mass fraction of n-hexane is 0.05. The extractcontains 49% n-hexane. If 10,000 kg of copra are to be processed,how many kilograms of n-hexane is required?

¤ Ex. Gas Absorption: A gas mixture contains 6.0 mole % acetone, 1.7mole % water, and the rest, air. The acetone is to be recoveredusing an absorption tower that operates at 30°C and 101.325 kPa.10,000 kg water per hour will be used to scrub 180 kmol per h ofentering gas. If the recovery is 96%, calculate the mole fraction ofacetone in the outlet gas and in the outlet water. The outgoing gashas a partial pressure of water equal to 4.241 kPa. The water is fedat the top of the tower while the gas, at the bottom.

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Single-Unit Balance

¤ Ex. Distillation: We desire to produce two ethyl alcohol-watermixtures each containing 90% and 50% alcohol by mole from adilute mixture containing 20% mole alcohol by distillation. 98%of the ethyl alcohol in the feed is to be recovered in these two

products, that is, only 2% of the ethyl alcohol in the feed maygo into the bottoms. If the bottoms contains 0.6% alcohol,calculate the amount of the different streams per 1000 kmol of

feed stream.

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Single-Unit Balance

¤ Ex. Crystallization: One thousand kilograms of a 64% NaNO3

solution in water is at a temperature of 100°C. This is sent to acrystallizer where it is cooled to 30°C. At this temperature, thesolubility of NaNO3 is 96 parts per 100 parts of water (the

solubility of NaNO3 is maximum amount of NaNO3 that canstay in solution; the rests crystallizes out). Calculate theamount of crystals that precipitates out if 

a. No water evaporates during coolingb. 5% of the original water evaporates during cooling

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Single-Unit Balance

¤ Ex. Membrane Separations: The figure below illustrates a

nanoporous membrane used for separating nitrogen fromoxygen in air. What is the composition of the waste stream ifthe waste stream amounts to 80% of the input stream?

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