Chapter 4: Fundamentals of Material Balances
Introduction
Chemical engineering begins with a simple observation: matter moves, transforms, and redistributes, but
it is never created or destroyed. Atoms may rearrange into new molecules, liquids may evaporate into
vapor, solids may dissolve into solution, and gases may react to form entirely different compounds. Yet
through all of these transformations, the total mass within a defined system must be conserved. This
principle forms the foundation of material balance analysis. Industrial processes consist of interconnected
units through which materials continuously flow. Streams of raw materials enter reactors, separators
divide mixtures into components, recycle streams return unreacted species for further processing, and
product streams leave the plant for downstream use. Within this network, molecules are constantly
moving, mixing, reacting, and separating. Understanding where every atom goes becomes essential for
designing, operating, and improving these systems.
Material balances provide the framework for this accounting. By defining a system boundary and tracking
all streams that cross it, engineers quantify how matter enters, leaves, accumulates, and transforms inside
the system. The analysis applies equally to a simple mixing tank, a catalytic reactor, or an entire chemical
plant. Regardless of complexity, the same conservation principle governs the flow of mass. The practice of
material balances is therefore less about algebra and more about structured thinking. A physical process
is translated into a diagram, the relevant variables are identified, and conservation equations are written
that connect known and unknown quantities. Once this structure is established, even complicated
processes become solvable.
Mastery of material balances represents one of the first major analytical steps in chemical engineering. It
provides the language through which processes are described and the foundation upon which energy
balances, reaction engineering, and transport phenomena are later built.
4.1 Systems, Boundaries, and Streams
Before equations appear, the process must first be seen clearly. Real chemical systems contain pipes,
tanks, reactors, and separators connected in complicated ways. Reading a written description of such a
system is like trying to understand a city by reading a list of street names. Engineers therefore begin by
drawing a process diagram, a simple visual map that shows how material moves through the system.
In this diagram, arrows represent streams carrying matter from one location to another. Each stream
contains material flowing at a certain rate and composition. Boxes represent pieces of equipment where
mixing, separation, or reaction may occur. Once the diagram is drawn, the process becomes a network of
flows rather than a confusing paragraph.
The key concept is the system boundary. A boundary is an imaginary surface drawn around the region
being analyzed. Everything crossing this boundary must be accounted for. Material may enter, leave,
accumulate inside, or change identity through chemical reaction. Nothing else is allowed. Defining this
boundary converts a physical process into an accounting problem.
A helpful analogy is a bank account. Deposits add money, withdrawals remove it, and the account balance
reflects the difference between the two. Material balances operate in the same way, except the currency
is mass instead of money. Streams entering the system are deposits, streams leaving are withdrawals, and
accumulation represents the changing balance inside.
Another analogy is traffic at an intersection. Cars enter from several roads and leave through others. If
more cars arrive than depart, traffic builds up. If departures exceed arrivals, the intersection empties.
When traffic flow becomes steady, the number of cars entering equals the number leaving. Chemical
processes behave in the same way, except the “cars” are molecules moving through pipes and equipment.
Once the system boundary and streams are identified, the process is ready for the central tool of this
chapter: the material balance equation.
4.2 The General Material Balance
Once the system and its boundaries are defined, the movement of matter can be expressed through a
single conservation statement. Every material balance used in chemical engineering comes from the same
principle: matter cannot be created or destroyed. Atoms may rearrange during reactions, phases may
change, and mixtures may separate, but the total mass within a defined system must follow a strict
accounting.
The general material balance is written as
Input − Output + Generation − Consumption = Accumulation
Each term represents a physical pathway by which material can change inside the system boundary.
Input represents material entering the system through feed streams or inflows.
Output represents material leaving the system through product or waste streams.
Generation accounts for material produced inside the system by chemical reaction.
Consumption accounts for material destroyed by reaction.
Accumulation represents material building up or decreasing inside the system over time.
A useful analogy is a bathtub with the drain partially open. Water enters through the faucet and leaves
through the drain. If the faucet runs faster than the drain removes water, the water level rises. If the drain
removes water faster than the faucet supplies it, the level drops. The water level represents accumulation,
while the faucet and drain correspond to input and output streams.
Most industrial processes operate under steady conditions, meaning that the system contents do not
change with time. When this occurs, accumulation becomes zero and the balance simplifies to
Input − Output + Generation − Consumption = 0
For systems where no chemical reaction occurs, generation and consumption also disappear. The equation
reduces further to
Input = Output
Despite its simplicity, this relationship is extremely powerful. It allows unknown flow rates, compositions,
and production capacities to be determined simply by tracking how material enters and leaves the system.
Balances can be written for the total mass of the system or for individual components within a mixture.
Component balances are particularly important because they reveal how specific substances move and
transform within a process. For example, in a separation unit the total mass entering may equal the total
mass leaving, while individual components redistribute among multiple streams.
The general balance equation therefore serves as the central accounting rule for all process analysis. Once
the system boundary is defined and the streams are identified, this equation connects physical reality to
quantitative calculation.
Conceptual question:
If a reactor operates at steady state but chemical reactions are occurring inside it, which terms in the
general balance equation remain nonzero and why?
4.3 Performing Material Balance Calculations
Once the system boundary is defined and the conservation equation is understood, the next step is
applying the balance to determine unknown quantities. Solving a material balance is not primarily a
mathematical exercise; it is a methodical procedure for organizing information about a process.
Engineers follow a structured workflow that converts a physical description into solvable equations. The
first step is always to draw the process diagram. Each stream entering or leaving the system must be
shown clearly, with arrows indicating the direction of flow. Known quantities—such as flow rates,
compositions, or operating conditions—are labeled on the diagram. Unknown quantities are assigned
symbols so they can later be solved.
A helpful analogy is assembling a puzzle. The process diagram provides the border pieces, establishing the
structure of the problem. The known values are pieces already placed, while the unknown variables
represent the missing pieces that must be fitted into the remaining spaces. Without first laying out the
puzzle clearly, attempting to solve equations becomes confusing and error-prone.
After the diagram is prepared, the next step is identifying all variables involved in the system. These may
include total mass flow rates, component mass fractions, or molar compositions. Each variable must
correspond to a measurable physical quantity crossing the system boundary.
Before writing equations, engineers perform a degrees-of-freedom check. This step determines whether
the problem contains enough information to be solved. The idea is simple: the number of independent
equations must equal the number of unknown variables. If more unknowns exist than equations, the
problem lacks sufficient information. If too many equations are written, some may be redundant or
inconsistent.
Once solvability is confirmed, the material balance equations are written. These balances may be applied
to the total mass of the system or to individual components. In many situations, writing component
balances provides additional independent equations that allow unknown quantities to be determined.
After the equations are established, the unknown variables can be solved through algebraic manipulation
or numerical methods. The final step is always to check the physical validity of the solution. Flow rates
must be positive, compositions must lie between zero and one, and the solution should make sense in the
context of the process.
This structured approach transforms complicated descriptions into organized calculations. The process
diagram provides clarity, the balance equations provide relationships, and the solution reveals how matter
moves through the system.
Conceptual question:
Why is it often easier to write component balances rather than only a total mass balance when analyzing
mixtures?
4.4 Balances on Multiple-Unit Processes
Real chemical processes rarely consist of a single piece of equipment. Instead, they are networks of
reactors, separators, heat exchangers, and mixers connected by streams that move material from one unit
to another. Analyzing such systems requires extending the material balance framework to multiple
interacting units.
The key idea is that a material balance can be written around any chosen system boundary. The boundary
may enclose a single unit, several units working together, or the entire process. Each choice provides a
different perspective on how matter moves through the system.
A useful analogy is tracking passengers through an airport. A traveler may pass through security, boarding
gates, and multiple connecting flights before reaching the destination. If one wishes to analyze the entire
trip, the system boundary can include the whole airport network. If the goal is to study delays at security,
the boundary may be drawn only around the security checkpoint. In both cases, the same accounting
principle applies: passengers entering the boundary must either leave it or remain inside.
Chemical processes behave in the same way. Consider a system consisting of a reactor followed by a
separator. Raw materials enter the reactor, products and unreacted components flow to the separator,
and the separator divides the mixture into product streams. A material balance could be written around
the reactor alone, the separator alone, or the combined reactor–separator system. Each boundary
simplifies different parts of the calculation.
When analyzing multi-unit systems, engineers typically begin with an overall balance on the entire
process. This approach eliminates internal streams from the equations because streams that pass between
units do not cross the overall boundary. The result is often a simpler relationship between feeds and final
products.
After the overall balance is established, individual unit balances may be written to determine internal
stream flow rates or compositions. These balances reveal how material moves within the system and how
each unit contributes to the overall process performance.
Another helpful analogy is a series of water tanks connected by pipes. Water entering the first tank
eventually moves through the others before leaving the system. A balance on the entire network tracks
only the water entering the first tank and leaving the last. Balances on individual tanks reveal how water
flows between them.
This ability to shift system boundaries is one of the most powerful tools in material balance analysis. By
choosing boundaries carefully, engineers simplify complex processes into manageable calculations.
Conceptual question:
Why do internal streams disappear when a material balance is written around the entire process rather
than around individual units?
4.5 Recycle, Bypass, and Purge
Many industrial processes contain loops in which part of the material leaving a unit is returned to an
earlier stage. These loops improve efficiency, increase conversion, and reduce waste, but they also add
complexity to material balance calculations. Three common flow arrangements appear in process
diagrams: recycle, bypass, and purge.
A recycle stream returns unreacted material to an upstream unit so it can pass through the process
again. This arrangement is common when reactions do not go to completion in a single pass. Instead of
discarding valuable reactants, the process separates the products and sends the remaining reactants
back to the reactor. Over multiple passes, a much larger fraction of the feed is converted.
An analogy can be seen in studying for an exam. Material that is not fully understood during the first
reading is reviewed again. Each pass improves understanding until most of the information is mastered.
A recycle loop works in the same way: material that did not “finish reacting” during the first pass is sent
back for another attempt.
A bypass stream diverts part of the feed around a unit and later recombines it with the processed
stream. Bypass is often used to control temperature, concentration, or flow conditions. For example, if a
reactor produces heat, bypassing some of the incoming feed around the reactor can help regulate the
temperature of the final mixture.
This can be compared to mixing hot and cold water in a shower. If the water coming from the heater is
too hot, some cold water bypasses the heater and mixes with the hot stream to produce a comfortable
temperature.
A purge stream removes a portion of the recycle flow to prevent the buildup of unwanted substances.
Impurities or inert materials may enter with the feed but do not react or separate easily. If the recycle
loop operated indefinitely without removal, these species would gradually accumulate. Purging a small
fraction of the recycle stream prevents this buildup and stabilizes the process.
An everyday analogy is ventilating a room. If fresh air enters but no air leaves, carbon dioxide and other
contaminants slowly accumulate. Opening a window creates a purge that removes a portion of the
indoor air, preventing buildup.
Recycle, bypass, and purge streams appear frequently in industrial process design. Recognizing these
patterns in a process diagram allows engineers to apply material balances systematically and determine
how material circulates within the system.
Conceptual question:
Why would a process with recycle streams often achieve higher overall conversion than a process with
only a single pass through the reactor?
4.6 Chemical Reaction Stoichiometry
When chemical reactions occur inside a process, atoms are rearranged into new molecular structures.
Although the chemical identity of the substances changes, the atoms themselves remain conserved.
Stoichiometry provides the quantitative framework that describes how these atoms are redistributed
during reaction.
A balanced chemical equation expresses this relationship. Consider the reaction
𝐴+𝐵 →𝐶
The coefficients indicate that one mole of 𝐴reacts with one mole of 𝐵to produce one mole of 𝐶. These
coefficients represent molar ratios, showing the relative number of molecules involved in the reaction.
Because atoms are conserved, the same number of each type of atom appears on both sides of the
equation.
An intuitive analogy is building with Lego blocks. Imagine that two structures are dismantled and the
blocks are rearranged into a new structure. The shapes may change completely, but the number of
blocks of each type remains the same. Chemical reactions behave in the same way: molecules break
apart and recombine, yet the underlying atoms are conserved.
In material balance calculations, stoichiometry determines how much of each species is consumed or
produced as the reaction proceeds. Engineers often describe this change using the concept of the extent
of reaction, which measures how far the reaction has progressed. For each species in the reaction, the
amount present changes according to the stoichiometric coefficients.
For example, if one mole of reaction occurs in the reaction above, one mole of 𝐴and one mole of
𝐵disappear, while one mole of 𝐶forms. If the reaction proceeds twice as far, twice these amounts are
consumed and produced. Stoichiometry therefore links the change in each species to a single variable
describing the progress of the reaction.
Another key concept is the limiting reactant. When reactants are supplied in unequal proportions, one
reactant may be completely consumed while others remain in excess. The limiting reactant determines
the maximum amount of product that can be formed. Once it is exhausted, the reaction must stop
regardless of how much of the other reactants remain.
A useful analogy is baking bread. If a recipe requires two cups of flour for every cup of water but only
one cup of flour is available, the amount of dough that can be produced is limited by the flour. Even if
additional water is present, the recipe cannot proceed further without more flour.
Stoichiometry therefore acts as the bridge between chemistry and process analysis. Material balances
track how matter flows through the system, while stoichiometry determines how that matter transforms
during reaction.
Conceptual question:
If a reactor is fed with reactants in exactly the stoichiometric ratio required by the balanced equation,
would any excess reactant remain after complete reaction? Why or why not?
4.7 Material Balances on Reactive Systems
When chemical reactions occur inside a system, material balances must account for both physical
transport and chemical transformation. Streams still carry matter into and out of the system, but
reactions inside the boundary convert some species into others. The total mass remains conserved, yet
the distribution of individual components changes as the reaction proceeds.
In reactive systems the general material balance becomes especially useful:
Input − Output + Generation − Consumption = Accumulation
For species participating in a reaction, the generation and consumption terms are determined by
stoichiometry. Reactants are consumed as the reaction proceeds, while products are generated in
proportions dictated by the balanced chemical equation. The material balance therefore links the
movement of streams with the chemical changes occurring inside the reactor.
A helpful analogy is ingredients being cooked in a kitchen. Raw ingredients enter the kitchen pantry,
meals leave the kitchen, and cooking transforms the ingredients into entirely different dishes. Flour,
sugar, and eggs may disappear from the shelves while cakes and pastries appear. The total amount of
material in the kitchen changes only according to what enters, what leaves, and what is transformed
during cooking.
Reactive balances also introduce several practical measures used in process analysis. One of the most
common is conversion, which describes the fraction of a reactant that has reacted relative to the
amount fed to the reactor. If half of the entering reactant reacts, the conversion is 50%. Conversion
provides a direct measure of how effectively the reactor uses its feed.
Another important measure is yield, which relates the amount of desired product formed to the amount
of reactant consumed. In many real processes multiple reactions occur simultaneously, producing both
desired and undesired products. Yield indicates how selectively the reaction pathway produces the
target compound.
A third useful quantity is selectivity, which compares the formation rate of desired products to that of
unwanted byproducts. High selectivity means the reaction favors the desired chemical pathway.
An everyday analogy is harvesting fruit from a tree. Conversion represents how many fruits are picked
compared with the number available. Yield describes how many of those fruits are usable, while
selectivity reflects how many are undamaged versus spoiled.
In reactive process analysis, material balances, stoichiometry, and performance measures such as
conversion and yield work together to describe how matter flows and transforms inside the reactor.
Conceptual question:
If the conversion of a reactant in a reactor increases while the yield of the desired product decreases,
what might be occurring inside the reactor?
4.8 Combustion Reactions
Combustion reactions are among the most common chemical processes in energy and industrial
systems. In these reactions, a fuel reacts with oxygen to release energy, producing oxidized products
such as carbon dioxide and water. Combustion powers engines, generates electricity, heats furnaces, and
drives many large-scale industrial operations.
At the molecular level, combustion is simply a rapid oxidation reaction. Carbon atoms combine with
oxygen to form carbon dioxide, hydrogen atoms combine with oxygen to form water, and chemical
energy stored in molecular bonds is released as heat. Although the reaction may appear dramatic—
flames, heat, and expanding gases—the same conservation principles still apply. Every atom entering the
system must appear in the products or remain in the system.
Consider the combustion of methane:
𝐶𝐻4 + 2𝑂2 → 𝐶𝑂2 + 2𝐻2 𝑂
The equation shows that one mole of methane reacts with two moles of oxygen to produce one mole of
carbon dioxide and two moles of water. Each carbon atom and hydrogen atom from the fuel appears in
the products, while oxygen atoms are redistributed among the new molecules.
A useful analogy is burning wood in a fireplace. The wood appears to disappear as it burns, but the
atoms are simply redistributed. Carbon becomes carbon dioxide that rises with the smoke, hydrogen
forms water vapor, and mineral components remain behind as ash. Nothing is lost; the atoms are merely
rearranged and dispersed.
In practical systems, combustion rarely occurs with exactly the stoichiometric amount of oxygen. Instead,
air is supplied in excess to ensure complete reaction of the fuel. Air contains approximately 21% oxygen
and 79% nitrogen by volume. While oxygen participates in the reaction, nitrogen typically remains inert
and passes through the system unchanged. As a result, nitrogen appears in the exhaust gases along with
the combustion products.
Combustion analysis often focuses on determining the composition of flue gases, the amount of excess
air supplied, and the conversion of fuel into products. Material balances allow engineers to determine
how much oxygen is required, how much carbon dioxide is produced, and how efficiently the fuel is
being utilized.
Another helpful analogy is a campfire with a bellows. Supplying more air intensifies the fire by providing
additional oxygen, but too much air cools the flame by carrying heat away. Engineers must therefore
balance the need for sufficient oxygen with the efficiency of the process.
Combustion systems illustrate how chemical reactions, stoichiometry, and material balances work
together to describe real energy-producing processes.
Conceptual question:
Why does supplying excess air help ensure complete combustion, yet too much excess air can reduce the
efficiency of a combustion system?
4.9 Additional Considerations in Chemical Processes
Real chemical processes rarely behave as perfectly as the simplified systems used in introductory
examples. Industrial operations involve uncertainties in measurements, fluctuations in operating
conditions, and complex physical phenomena that influence how materials move and react. Effective
material balance analysis therefore requires attention not only to equations but also to the practical
realities of process operation.
One important consideration is the accuracy of measurements. Flow meters, composition analyzers, and
temperature sensors all have limitations. Small measurement errors can propagate through calculations
and lead to significant differences in predicted results. Engineers must therefore evaluate whether
reported data are physically reasonable and consistent with conservation principles.
A helpful analogy is balancing a household budget. If the total spending appears to exceed income, the
discrepancy may arise from an overlooked expense, a rounding error, or an incorrect entry. Similarly, if a
material balance does not close properly, the engineer must investigate whether data are missing or
inaccurate.
Another practical issue is the presence of trace components. Industrial streams often contain small
amounts of impurities, inert materials, or side products that may not significantly affect the overall mass
balance but can influence equipment performance or environmental impact. Even small concentrations
may accumulate over time in recycle systems or separation units.
Processes may also involve multiple simultaneous reactions. While a simplified model may consider only
a single desired reaction, real systems often generate byproducts. These competing reactions influence
product composition, reactor performance, and separation requirements. Engineers must therefore
decide whether these additional reactions should be included in the balance analysis.
Physical phenomena such as phase changes, mixing behavior, and mass transfer may also influence how
materials distribute within the system. For example, gases may dissolve in liquids, solids may precipitate
from solution, or components may separate into multiple phases. Although the conservation of mass still
applies, the pathways through which materials move can become more complex.
An analogy can be drawn with traffic in a large city. While the total number of vehicles entering and
leaving the city may balance over time, local traffic patterns depend on road closures, accidents, and
varying driver behavior. Understanding the overall flow requires recognizing these additional factors.
Material balances therefore serve as the first layer of analysis, providing a framework for tracking how
matter enters, leaves, and transforms within a process. More advanced analysis may later incorporate
energy balances, reaction kinetics, and transport phenomena to describe the system in greater detail.
Conceptual question:
If measured flow rates entering and leaving a system do not satisfy a material balance, what possible
explanations should an engineer consider before concluding that the conservation law has been violated?
4.10 Summary
Material balance analysis rests on a single physical law: matter is conserved. Atoms may rearrange
through chemical reactions, phases may change, and mixtures may separate, but the total mass within a
defined system must always follow a strict accounting. This principle allows engineers to track how
materials move through chemical processes and to determine unknown quantities such as flow rates,
compositions, and production capacities.
The first step in any analysis is defining the system boundary. By drawing a process diagram and
identifying all streams entering and leaving the boundary, a physical process becomes an organized
network of flows. Once the streams are identified, the general material balance equation provides the
relationship connecting them:
Input − Output + Generation − Consumption = Accumulation.
For many industrial processes operating at steady state, accumulation is zero, simplifying the equation
considerably. In systems without chemical reactions, generation and consumption also disappear,
reducing the balance to the simple relationship that total input equals total output.
Applying this equation requires a structured approach. Engineers begin by constructing a clear diagram
of the process, labeling known and unknown quantities, and identifying all relevant variables. A degreesof-freedom check ensures that enough independent equations exist to determine the unknowns.
Material balances may then be written for the total mass of the system or for individual components
within mixtures.
As systems become more complex, the same conservation principle extends naturally to multiple-unit
processes, recycle loops, and bypass streams. Chemical reactions introduce additional relationships
through stoichiometry, linking the consumption of reactants to the formation of products. In reactive
systems, performance measures such as conversion, yield, and selectivity help describe how effectively
the process transforms materials.
Combustion reactions provide a practical example of these principles in action, illustrating how fuels
react with oxygen and how material balances can determine flue gas compositions and oxygen
requirements.
Together, these ideas form the foundation for analyzing chemical processes. Material balances provide
the first quantitative framework through which engineers understand how matter moves, transforms,
and distributes within industrial systems.
Conceptual question:
Why does the same conservation principle allow material balances to be written around a single unit,
several connected units, or an entire chemical plant?
Exam 2: Prep.
Question 1
Which statement best represents the general material balance equation for a system?
A. Input + Output = Generation + Consumption
B. Input − Output + Generation − Consumption = Accumulation
C. Input − Output = Accumulation + Reaction Rate
D. Output − Input = Generation
Question 2
A chemical reactor operates at steady state with a chemical reaction occurring inside. Which term in the
general material balance equation must be zero?
A. Generation
B. Consumption
C. Accumulation
D. Input
Question 3
Why do internal streams disappear when writing a material balance around an entire process containing
several units?
A. They are assumed to have zero flow
B. They are neglected for simplicity
C. They do not cross the overall system boundary
D. They are equal to the recycle stream
Question 4
In a reactor, reactant A is supplied in excess while reactant B is completely consumed. What is reactant B
called?
A. Excess reactant
B. Limiting reactant
C. Inert reactant
D. Recycle reactant
Question 5
Why is a purge stream sometimes required in systems with recycle loops?
A. To increase the reaction rate
B. To reduce energy consumption
C. To prevent accumulation of inert or unwanted species
D. To increase product purity
Question 1
A stream of water flows into a mixing tank at 120 kg/h, and another stream enters at 80 kg/h. The
mixture leaves the tank through a single outlet.
What is the mass flow rate of the outlet stream?
Question 2
A gas stream entering a separator contains 70 kg/h nitrogen and 30 kg/h oxygen. The separator
removes 10 kg/h of oxygen in one outlet stream.
How much oxygen remains in the other outlet stream?
Question 3
A reactor is fed with 100 mol/h of reactant A. If the conversion of A is 40%, how many moles of A leave
the reactor unreacted?
Question 4
Methane burns according to the reaction
𝐶𝐻4 + 2𝑂2 → 𝐶𝑂2 + 2𝐻2 𝑂
If 5 mol of methane react completely, how many moles of oxygen are required?
Question 5
A recycle process sends 30 kg/h of material back to the reactor. The fresh feed entering the reactor is
120 kg/h.
What is the total flow rate entering the reactor?
Question 1
Two streams mix to form one outlet.

Stream 1: 200 kg/h, 15 wt% solute S

Stream 2: 100 kg/h, 40 wt% solute S
The outlet goes to a filter that removes 25% of the solute S (only solute; the solvent all passes).
a) What is the mass flow rate of solute S in the outlet of the mixer (before the filter)?
b) What is the mass flow rate of solute S leaving the filter?
c) What is the wt% of solute S in the filtered stream?
Question 2
A single-pass reactor carries out:
𝐴→𝐵
Fresh feed contains 100 mol/h of A and 20 mol/h of inert I. The reactor conversion of A is 50%. The
reactor effluent goes to a separator that sends all of B to product, and splits A and I as follows:

90% of A goes to recycle, 10% of A purged

70% of I goes to recycle, 30% of I purged
a) Find the molar flow rates of A, B, and I leaving the reactor.
b) Find the molar flow rates of A and I in the recycle stream.
c) Find the molar flow rates of A and I in the purge stream.
Question 3
Combustion of propane:
𝐶3 𝐻8 + 5𝑂2 → 3𝐶𝑂2 + 4𝐻2 𝑂
A furnace burns 10 mol/h of propane with 20% excess air (air = 21% O
complete combustion.
a) How many mol/h of O 2 are fed?
b) How many mol/h of N 2 are fed?
c) Determine the molar composition (mol%) of dry flue gas (CO
2, O
2 , 79% N
2, N
2 by mole). Assume
2 ).
Question 4
A liquid feed of 1000 kg/h contains 30 wt% A and 70 wt% B. It enters a separator that produces:

Stream 1: 90 wt% A, flow rate unknown

Stream 2: 5 wt% A, flow rate unknown
a) Determine the flow rates of Stream 1 and Stream 2.
b) Determine the kg/h of A in each outlet stream.
Question 5
A tank initially contains 500 kg of water with 10 wt% salt. Brine containing 20 wt% salt flows in at 50
kg/h, and perfectly mixed liquid flows out at 40 kg/h. Assume constant density and perfect mixing.
a) Write the differential salt balance for the tank (in terms of salt mass in the tank).
b) At the instant when the tank contains 600 kg total liquid, what is the salt mass in the tank (kg)?
c) At that instant, what is the salt wt% in the tank?
Question 6: A process converts 𝐴 to desired product 𝐵with a side reaction to undesired 𝐷:
R1: 𝐴 → 𝐵 R2: 2𝐴 → 𝐷
Fresh feed contains only 𝐴and an inert 𝐼:

Fresh feed: 𝐹𝐴 = 100 mol/h of 𝐴, 𝐹𝐼 = 20 mol/h of 𝐼
The reactor is single-pass with these performance specs (based on 𝐴entering the reactor):

Conversion of 𝐴in the reactor 𝑋 = 0.60

Of the 𝐴that reacts, 75% goes by R1 and 25% goes by R2 (selectivity on reacted A)
The reactor effluent goes to a separator:

All 𝐵and 𝐷go to the product stream (none recycled, none purged separately)

The unreacted 𝐴and all 𝐼go to a recycle loop

A purge is taken from the recycle loop to prevent inert buildup:
o
Purge fraction 𝑝(same fraction of both 𝐴and 𝐼removed from the recycle loop)
o
The remaining fraction (1−𝑝)returns as recycle to the reactor feed
Design requirement: At steady state, the inert mole fraction in the reactor feed must be no more than
10 mol%, i.e.
𝐼to reactor
≤ 0.10
𝐴to reactor + 𝐼to reactor
Tasks
a) Determine the minimum purge fraction 𝑝that satisfies the inert constraint.
b) At that purge fraction, compute the molar flow rates (mol/h) of 𝐴, 𝐼, 𝐵,and 𝐷in the product stream.
c) At that purge fraction, compute the overall conversion of fresh 𝐴(fraction of fresh 𝐴that ends up as
𝐵or 𝐷).
Question 7 A hemodialyzer is modeled as two well-mixed channels separated by a semipermeable
membrane:

Blood side (B) volume 𝑉𝐵 = 3.0 L

Dialysate side (D) volume 𝑉𝐷 = 12.0 L
Flow rates (constant, steady operation):

Blood in/out: 𝑄𝐵 = 250 mL/min = 0.250 L/min

Dialysate in/out: 𝑄𝐷 = 500 mL/min = 0.500 L/min
A toxin 𝑋(think “urea-like”) transfers across the membrane with flux proportional to the concentration
difference:
Rate of transfer from blood to dialysate = 𝐾 (𝐶𝐵 − 𝐶𝐷 )
where 𝐶𝐵 and 𝐶𝐷 are the concentrations of 𝑋in blood-side and dialysate-side compartments (mg/L), and
𝐾 = 80 mL/min = 0.080 L/min.
Additional assumptions:

No reaction or generation of 𝑋in either compartment.

Each side is perfectly mixed (one concentration per compartment).

Fresh dialysate enters toxin-free: 𝐶𝐷,𝑖𝑛 = 0.

Blood enters with toxin concentration 𝐶𝐵,𝑖𝑛 = 120 mg/L.
Tasks (steady state)
a) Write the steady-state material balance equations for 𝑋on the blood compartment and the dialysate
compartment.
b) Solve for the steady-state outlet concentrations 𝐶𝐵,𝑜𝑢𝑡 and 𝐶𝐷,𝑜𝑢𝑡 . (Because each compartment is
well-mixed, 𝐶𝐵,𝑜𝑢𝑡 = 𝐶𝐵 and 𝐶𝐷,𝑜𝑢𝑡 = 𝐶𝐷 .)
c) Compute the removal rate of toxin 𝑋(mg/min) from the blood stream.
d) Define the “single-pass fractional removal” as
𝑅=
𝐶𝐵,𝑖𝑛 − 𝐶𝐵,𝑜𝑢𝑡
𝐶𝐵,𝑖𝑛
Calculate 𝑅.
e) Concept check: If 𝑄𝐷 were doubled (all else unchanged), would 𝐶𝐵,𝑜𝑢𝑡 go up, down, or stay about the
same? Briefly justify using the balances (no new solving required).