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1) DIFFERENCE BETWEEN HOMOGENEOUS AND HETEROGENEOUS REACTION.

In chemistry, homogeneous and heterogeneous reactions are two different types of
chemical reactions.
The main difference between the two is the degree of uniformity of the reaction
mixture.
In a homogeneous reaction, the reactants and the products are present in a single
phase.
In a heterogeneous reaction, the reactants and the products are present in different
phases.
Heterogeneous reactions commonly occur at the interface between two phases,
such as between a gas and a solid, or between a liquid and a solid.
In summary, the main difference between homogeneous and heterogeneous
reactions is the uniformity of the reaction mixture.
Homogeneous reactions have a uniform composition, while heterogeneous reactions
have a non-uniform composition with distinct phases.

2) WHAT WILL ONE OBTAIN FROM STUDY OF CHEMICHAL KINETICS.

The study of chemical kinetics provides important information about the rates and
mechanisms of chemical reactions.
Chemical kinetics is the branch of chemistry that deals with the study of the rate of
chemical reactions, how they occur, and the factors that influence their rate.
Reaction rate: Chemical kinetics provides a way to determine the rate at which a
reaction occurs, which is essential for understanding how the reaction proceeds.
Activation energy: Chemical kinetics can be used to determine the activation energy
of a reaction, which is the energy required for the reaction to occur.
Overall, the study of chemical kinetics provides important insights into the
mechanisms and rates of chemical reactions, which is critical for understanding and
controlling chemical processes in various fields, including chemistry, biology, and
engineering.

3) DRAW A SIMPLE FLOW DAIGRM SHOWING INFORMATION REQUIRED FOR

CHEMICAL REACTOR DESIGN.
Sure, here's a simple flow diagram showing the information typically required for
chemical reactor design:
Chemical Reaction
Reactor Type
Reactor Design Parameters
This includes the reaction rate, order, and mechanism.
 Thermodynamic Properties: The thermodynamic properties of the reactants and
products, such as heat of reaction, heat capacity, and equilibrium constant, are also
important to know in order to design an efficient and effective reactor.
Reactor Type: Based on the reaction kinetics and thermodynamic properties, the
appropriate type of reactor is chosen.
Examples include batch, continuous stirred tank, plug flow, and fluidized bed
reactors.
Product Specifications: Finally, the desired product specifications such as yield,
purity, and selectivity are established and the reactor is operated accordingly

4) BY HOW MANY WAYS AN INTERMEDIATE CAN APPEAR IN A REACTION

MECHANISM? GIVE EXAMPLE ?
As a reactant in the first step and a product in the second step.
As a reactant in the first step and a product in the second step.
For example, consider the reaction mechanism for the conversion of ozone to
oxygen gas:
In this mechanism, the NO2 intermediate is formed in the first step and used as a
reactant in the second step.
The intermediate is not observed as a stable species, as it is rapidly consumed in the
second step.
Another example is the reaction mechanism for the conversion of ethanol to
acetaldehyde:
In this mechanism, the CH3CHO intermediate is formed in the first step and used as
a reactant in the third step.

5) WHY PFR AND CSTR ARE CALLED IDEAL REACTORS? GIVE REASONABLE
JUSTIFICATION
PFR (plug flow reactor) and CSTR (continuous stirred tank reactor) are often called
ideal reactors because they are simple mathematical models that can be used to
describe a wide range of chemical reactions in a relatively accurate and practical
manner.
Complete mixing: In a CSTR, the reactants are continuously stirred, which ensures
that the reactor contents are well mixed, and there are no concentration gradients
inside the reactor.
Ideal gas assumption: Both CSTR and PFR assume that the reactants and products
are ideal gases.
This assumption simplifies the thermodynamic calculations, as it allows for the use of
the ideal gas law to calculate the concentrations of the reactants and products.
While these assumptions may not be accurate for every chemical reaction or reactor
design, they are often reasonable approximations for many practical cases.
As a result, PFR and CSTR are widely used as ideal reactor models to describe and
design many industrial chemical processes.
 6) GIVE TECHNICAL REASON FOR IMPLEMENTING RECYCLE IN A PFR.
Recycling is the process of taking a portion of the product stream and returning it to
the reactor inlet, where it mixes with the fresh feed.
Increased conversion: By recycling a portion of the product stream, the
concentration of reactants in the reactor is increased.
This results in a higher reaction rate and increased conversion of reactants to
products.
By recycling a portion of the product stream, the concentration of desired products
is increased, while the concentration of undesired byproducts is decreased.
By recycling a portion of the product stream, the temperature of the reactants can
be increased, which can improve the reaction rate.
By increasing the concentration of reactants in the reactor, the reaction can be
completed in a shorter length of tube, reducing the overall size of the reactor.
Overall, implementing recycle in a PFR can be a beneficial strategy for improving
conversion, selectivity, heat transfer, and reducing the size of the reactor

7) Write general design equation for BMR and PFR in terms of concentration rather
than fractional conversion using as capacity measures both t and τ
The design equations for a continuous stirred-tank reactor (CSTR) and a plug flow reactor (PFR)
in terms of concentration and using both residence time (t) and space time (τ) as capacity measures
are:

Q is the volumetric flow rate of the feed stream

C is the concentration of the reactant in the feed stream

F_A0 is the molar flow rate of the reactant in the feed stream

τ is the space time, which is the time required for the reactor to process its full volume of feed at the
given flow rate

dF_A / dV is the change in molar flow rate of the reactant with respect to reactor volume.

Note that the design equations for a CSTR and a PFR in terms of concentration are different due to
the differences in their flow patterns.

8) Explain in brief need of recycle in chemical industry

First, many chemical products and byproducts can be reused or reprocessed, which reduces
the need for raw materials and can lower costs.
For example, recycling solvents and other chemicals used in manufacturing processes can
reduce the amount of waste generated and save money on purchasing new materials.
Second, recycling can help reduce environmental pollution and the negative impacts
associated with waste disposal.
By reusing materials instead of extracting and processing new ones, recycling reduces the
amount of energy and resources needed for production.
Overall, recycling is important in the chemical industry because it can help reduce costs,
minimize environmental pollution, and promote sustainability.
9) explain detail how thermodynamics can help in determining process condition for
reactors.

The principles of thermodynamics can be used to calculate the energy balance of a reactor
and to determine the optimum process conditions.
This equilibrium constant can help determine the optimum temperature, pressure, and
reactant concentrations required to achieve the desired reaction conditions.
These calculations can help determine the optimum temperature, pressure, and reactant
concentrations required to achieve the desired phase behavior.
The activation energy can help determine the optimum temperature and pressure required
to achieve the desired reaction rate.
In summary, thermodynamics is a valuable tool for determining the process conditions
required for successful operation of reactors.
It can help calculate heat transfer rates, determine equilibrium constants, predict phase
equilibria, and estimate reaction rates.
10) WHAT IS A ROLE OF CHEMICAL KINETICS IN DESIGN OF CHEMICAL REACTOR?
In the design of chemical reactors, chemical kinetics plays a crucial role in determining the
conditions required for efficient and effective operation of the reactor.
For example, if the reaction rate is slow, a larger reactor may be required to achieve the
desired production rate.
This information is important for designing a reactor that produces the desired product with
high selectivity.
In summary, chemical kinetics plays a crucial role in the design of chemical reactors by
providing information about reaction rate, reaction mechanism, reaction selectivity, catalyst
design, and reactor control.
This information is essential for designing a reactor that operates efficiently and effectively,
producing the desired product with high selectivity and yield.
11) HOW WILL ONE DECIDE SENSITIVITY OF ANY CHEMICAL REACTION WITH
PRESSURE?
It is determined by the magnitude of the pressure dependence of the reaction rate
constant.
 Obtain experimental data: Conduct experiments to measure the rate of the reaction
at different pressures.
If the reaction is pressure-insensitive, the reactor can be operated at lower
pressures, which may result in lower costs and improved safety.
In summary, the sensitivity of a chemical reaction to pressure can be determined by
measuring the rate of the reaction at different pressures and analyzing the resulting
pressure dependence curve.
The activation volume can be calculated from the curve, and the implications for
reactor design can be considered based on whether the reaction is pressure-
sensitive or pressure-insensitive
12) The rate of increase of number of bacteria under certain conditions is proportional
to the number of bacteria.if the number double in 4 hours ,how much increase in
number of bacteria can be expected after 12 hours?
We know that the number of bacteria doubles in 4 hours, which means that the
growth rate is proportional to N(t) and the constant of proportionality is ln(2)/4.
This is a separable differential equation, which we can solve using separation of
variables:
Now, we can use this equation to find the increase in the number of bacteria after 12
hours:
Therefore, the increase in the number of bacteria after 12 hours is 8 times the initial
number.
13) WHY CHEMICAL REACTORS ARE CONSIDERED TO BE A HEART OF CHEMICAL
INDUSTRIES
These reactions are the foundation of the chemical industry and are used to produce
a wide variety of products, including pharmaceuticals, fertilizers, plastics, and fuels.
Chemical reactors provide the controlled environment necessary for these chemical
reactions to take place.
Overall, chemical reactors are the core of the chemical industry, providing the
essential environment for chemical reactions to take place and enabling the
production of a wide range of products that are essential to modern life
14) B106 catalyst was used to study reaction kinetics of water gas shift reaction of CO.
The activation energy of the forward reaction was measured as 9.629 10 J/mol. If
the reverse reaction can be ignored, find the ratio of reaction rate at 550C to that
at 200C when the reaction mixture composition is the same.
The activation energy of the forward reaction, E_a, is given as 9.629 x 10^4 J/mol.
We can use the Arrhenius equation to find the ratio of the reaction rate at two
different temperatures:
where k is the rate constant, A is the pre-exponential factor, R is the gas constant,
and T is the temperature in Kelvin.
Taking the ratio of the rate constants at two different temperatures, we get:
k_550C/k_200C = exp(9.629 x 10^4 J/mol * (1/473 K - 1/823 K) / (8.314 J/mol K))
k_550C/k_200C = exp(15.51)
k_550C/k_200C = exp(15.51)
k_550C/k_200C = exp(15.51)
 Therefore, the ratio of the reaction rate at 550C to that at 200C when the reaction
mixture composition is the same is 4.61 x 10^6.
15) Give Advantages and limitations of Differential Method of Analysis over Integral
Method of Analysis
The differential method involves the computation of the slopes and deflections at
various points along the length of a member, while the integral method involves the
computation of the forces and moments that exist within a member.
This is because the differential method takes into account the variations in slope and
deflection along the length of the member, while the integral method assumes
constant values for these parameters.
By computing the slopes and deflections at various points along the length of a
member, the differential method allows engineers to identify the regions of the
structure that are most susceptible to failure.
The differential method allows for the accurate calculation of the slope and
deflection at any point along the member, regardless of the boundary conditions.
Limitations of Differential Method of Analysis over Integral Method of Analysis:
Limited Insight: While the differential method provides a detailed analysis of the
behavior of the structure, it does not provide insight into the internal forces and
moments that exist within the member.
16) Draw concentration history for an autocatalytic reaction. Compare same with that
of other reactions.
17) Compare Non elementary reactions to that of Elementary reactions.
Non-elementary reactions, on the other hand, occur via a more complex mechanism
that involves multiple steps and intermediates.
The rate law for non-elementary reactions cannot be determined directly from the
stoichiometry of the reaction and often involves the concentrations of
intermediates, which may not be directly observable.
Non-elementary reactions may involve catalysts or inhibitors, which can affect the
reaction rate and mechanism.
The reaction mechanism and rate law for non-elementary reactions can often be
determined through experimentation and kinetic analysis.
Elementary reactions occur in a single step and have a simple rate law, while non-
elementary reactions occur via multiple steps and have a more complex rate law
18 ) What would be maximum size of reactor required for a reaction A2B with 20% inert if
reaction goes to 100% conversion.
To determine the maximum size of the reactor required for a reaction A → 2B with 20% inert
if the reaction goes to 100% conversion, we need to consider the stoichiometry of the
reaction and the volume of the reactor.
The presence of 20% inert means that only 80% of the reactor volume is occupied by the
reactant A and the product B, while the remaining 20% is occupied by the inert gas.
Assuming that the initial volume of the reactor is V, and that the reaction goes to 100%
conversion, then the final volume of the reactor occupied by the products B will be 2V, since
2 moles of B are produced for every mole of A consumed.
The total number of moles in the reactor at any time during the reaction is given by:
 where n(A), n(B) and n(Inert) are the number of moles of reactant A, product B, and inert
gas, respectively.
At 100% conversion, all the reactant A is consumed, and the number of moles of A in the
reactor becomes zero.
Since the reaction goes to 100% conversion, all the initial moles of A will be consumed to
form 2 moles of B, i.e., n(B) = 2 * n(A).
Since the reaction goes to 100% conversion, the final number of moles in the reactor will be:
where M(B) is the molar mass of B.
where M(B) is the molar mass of B.
This equation gives us the maximum size of the reactor required for the reaction, assuming
100% conversion and 20% inert.
For example, if M(A) = 50 g/mol and M(B) = 75 g/mol, then:
V = 0.8 * 75 g/mol / 50 g/mol = 1.2
Therefore, the maximum size of the reactor required for the reaction would be 1.2 times the
volume of the reactants and products, assuming 100% conversion and 20% inert.

19) For an series reaction ARS K1=0.5 min inverse and Ca0=1M calculate value of
maximum concentration of Rand time when it will reach this value
Step 1: Write down the rate expressions for each step of the reaction:
where k1 and k2 are the rate constants for the first and second steps of the reaction,
respectively, and [Ca] is the concentration of A at any given time.
Step 2: Write down the mass balance equations for each species:
where d[Ca]/dt, d[R]/dt, and d[S]/dt are the rates of change of the concentrations of A, R,
and S, respectively.
Step 3: Solve the first equation for [Ca] as a function of time:
Step 4: Substitute this expression for [Ca] into the second and third equations, and combine
them into a single differential equation for [R]:
Step 5: Solve this differential equation to obtain an expression for [R] as a function of time:
Step 6: Differentiate this expression with respect to time and set the result equal to zero to
find the time at which [R] is maximum:
Step 7: Substitute this value of t_max into the expression for [R] to find the maximum
concentration of R:
From the mass balance equations, we can see that at t=0, [R] = 0 M and [S] = 0 M.
t_max = (1/0.5)ln(0.51) = 0.693 min
[R]_max = (0.51/0.5)(1 - exp(-0.5*0.693)) = 0.432 M
Therefore, the maximum concentration of R is 0.432 M and it is reached at a time of 0.693
min.

20)what is the basic of defining ideality of any reactor ? how CSTR is different than PFR in
terms od ideality ?
The ideality of a reactor refers to how closely it operates to an idealized reactor model that
exhibits certain characteristics, such as perfectly mixed or plug flow behavior, or complete
conversion of reactants.
This type of reactor is often assumed to be perfectly mixed, which means that any point
within the reactor has the same composition as any other point at the same time.
This type of reactor is often assumed to exhibit plug flow behavior, meaning that the
concentration of reactants and products varies only in the axial direction of the reactor, and
not in the radial direction.
In reality, PFRs may not be perfectly plug flow, and there may be some degree of axial
mixing due to turbulence or diffusion.

21)prove that N equal size BMR is series give performance equal to that of one PFR of
same total value.
It is not true that a series of N equal size batch reactors (BMRs) will give the same
performance as one plug flow reactor (PFR) of the same total volume.
In fact, the performance of a series of BMRs will be inferior to that of a single PFR in most
cases.
In a PFR, the reactants flow through the reactor in a continuous stream, which allows for
uniform reaction conditions and efficient mass transfer.
This means that the reaction conditions can vary between each reactor, and there may be
mass transfer limitations between the batches.
Therefore, a single PFR will generally provide superior performance to a series of N BMRs of
the same total volume.

22) state the method for the determination of reaction order. explain any one
The method of initial rates involves measuring the initial rate of a reaction under different
initial concentrations of one of the reactants, while keeping the concentrations of the other
reactants constant.
By changing the initial concentration of one reactant and observing the corresponding
change in the initial rate of the reaction, it is possible to determine the reaction order with
respect to that particular reactant.
Here's an example of how the method of initial rates can be used to determine the reaction
order:
To determine the reaction order with respect to reactant A, we would keep the
concentration of reactant B constant while varying the concentration of reactant A.
We would then measure the initial rate of the reaction at different concentrations of A.
For example, we could conduct a series of experiments where the initial concentration of A
is changed while keeping the concentration of B constant, and the initial rate of the reaction
is measured for each concentration of A.
The initial rate can be determined by measuring the change in concentration of a reactant or
product over a short period of time at the beginning of the reaction.
If the initial rate of the reaction is directly proportional to the concentration of A, the
reaction is considered to be first order with respect to A.
If the initial rate is proportional to the square of the concentration of A, the reaction is
considered to be second order with respect to A, and so on.
By plotting the initial rate versus the concentration of A and examining the trend, we can
determine the reaction order with respect to A.
Similar experiments can be conducted with different reactants to determine their respective
reaction orders.

23) The rate ofr increase of number of bacteria under certain conditions is proportional to
the number of bacteria . if the number doubles in 4 hours, how much increase in number
of bacteria can be expected after 12 hours ?
The determination of reaction order is a critical step in understanding the rate law of a
chemical reaction, which describes how the concentration of reactants affects the rate of
the reaction.
There are several methods to determine the reaction order, and one common method is the
method of initial rates.
The method of initial rates involves measuring the initial rate of a reaction under different
initial concentrations of one of the reactants, while keeping the concentrations of the other
reactants constant.
By changing the initial concentration of one reactant and observing the corresponding
change in the initial rate of the reaction, it is possible to determine the reaction order with
respect to that particular reactant.
Here's an example of how the method of initial rates can be used to determine the reaction
order:
To determine the reaction order with respect to reactant A, we would keep the
concentration of reactant B constant while varying the concentration of reactant A.
We would then measure the initial rate of the reaction at different concentrations of A.
Let's denote the initial number of bacteria as "N0" (at the start of the 4-hour period) and the
expected increase in the number of bacteria after 12 hours as "ΔN" (change in the number
of bacteria).
N(t) = the number of bacteria at time "t"
N0 = the initial number of bacteria
k = the proportionality constant (rate of increase)
Given that the number of bacteria doubles in 4 hours, we can deduce that k = ln(2)/4, where
ln denotes the natural logarithm.
Since we are interested in the increase in the number of bacteria, we can subtract N0 from
both sides of the equation:
Thus, the expected increase in the number of bacteria after 12 hours is ΔN = N0 *
(e^[(ln(2)/4) * 12] - 1).

24)when the conce4ntration of A in a simple reaction A B was changed from 0.51 M to

1.03 M, the half-life dropped from 150 sec to 75 sec at 25 c. what is thw order of reaction
and rate constant value?
Final concentration of A, [A]ₜ = 1.03 M
Initial half-life, t₁/₂(0.51 M) = 150 sec
Final half-life, t₁/₂(1.03 M) = 75 sec

To find the rate constant (k) of the reaction, we can use the equation for a first-order
reaction:

k = (1/t₁/₂) * ln([A]₀/[A]ₜ)

Plugging in the given values:

k = (1/150 sec) * ln(0.51 M/1.03 M)

k = 0.00462 sec^(-1)

So, the rate constant (k) for the reaction is approximately 0.00462 sec^(-1).

Since the reaction is a first-order reaction, the rate constant (k) remains constant regardless
of the change in concentration of A.
In summary, the given reaction is a first-order reaction with a rate constant (k) of
approximately 0.00462 sec^(-1).

25)the entropy of activation for bimolecular reaction was observed at 300k which was
found to be j/(K mol). Calculate the frequency factor and also the rate constant at 300 if
activation energy is 170kj/mol.use transition state theory.
In transition state theory, the rate constant for a bimolecular reaction can be expressed as:
k = kBT/h * e^(-ΔG‡/RT)
k is the rate constant
ΔG‡ is the activation energy in Joules
R is the ideal gas constant (8.314 J/(K mol))
Given that the activation energy (ΔG‡) is 170 kJ/mol, we need to convert it to Joules/mol:
ΔG‡ = 170 kJ/mol * 1000 J/kJ = 170000 J/mol
Now, we can plug in the values and calculate the frequency factor (A):
We are given that the entropy of activation (ΔS‡) is given in J/(K mol), which is equivalent to
J/(K mol), so we can use it directly in the calculation.
ΔG‡ = 170000 J/mol
k = A * e^(-ΔG‡/RT) / (6.626 x 10^-34 J s)
k = A * e^(-ΔG‡/RT) / (6.626 x 10^-34 J s)
k = A * e^(-ΔG‡/RT) / (6.626 x 10^-34 J s)
Plugging in the values:
Plugging in the values:
k = A * e^(-170000 J/mol / (8.314 J/(K mol) * 300 K)) / (6.626 x 10^-34 J s)
k = A * e^(-170000 J/mol / (8.314 J/(K mol) * 300 K)) / (6.626 x 10^-34 J s)
k = A * e^(-170000 J/mol / (8.314 J/(K mol) * 300 K)) / (6.626 x 10^-34 J s)
k = A * e^(-170000 J/mol / (8.314 J/(K mol) * 300 K)) / (6.626 x 10^-34 J s)
The calculated value of k will depend on the actual value of the frequency factor (A) which is
not provided in the given information.
Once the value of A is known, it can be plugged into the equation to obtain the rate constant
(k) at 300 K using transition state theory.
To determine the reaction order with respect to reactant A, we would keep the
concentration of reactant B constant while varying the concentration of reactant A.
We would then measure the initial rate of the reaction at different concentrations of A.
Let's denote the initial number of bacteria as "N0" (at the start of the 4-hour period) and the
expected increase in the number of bacteria after 12 hours as "ΔN" (change in the number
of bacteria).
According to the problem, the rate of increase of the number of bacteria is proportional to
the current number of bacteria.
N(t) = the number of bacteria at time "t"
N0 = the initial number of bacteria
k = the proportionality constant (rate of increase)
Given that the number of bacteria doubles in 4 hours, we can deduce that k = ln(2)/4, where
ln denotes the natural logarithm.
Now, we can plug in the given values and solve for ΔN when t = 12 hours:
Since we are interested in the increase in the number of bacteria, we can subtract N0 from
both sides of the equation:
Thus, the expected increase in the number of bacteria after 12 hours is ΔN = N0 *
(e^[(ln(2)/4) * 12] - 1).
26) obtain IRE for aq second order reaqction C2H4Br2+3KIC2H4+2KBr+KI3.(consider
order with respect to each reactant as 1 and both reactants are fed in stoichiometric
amount )
Step 1: Write the rate law for the reaction.
The rate law for a second-order reaction is given by the equation: rate = k[A]^m[B]^n, where
[A] and [B] are the concentrations of the reactants A and B, respectively, and k is the rate
constant.
Since the reaction is second-order, the sum of the exponents (m + n) in the rate law will be
equal to 2.
Step 2: Determine the orders with respect to each reactant.
According to the given information, the order with respect to each reactant is 1, so m = n =
1.
Step 3: Write the rate expression.
Based on the above information, the rate expression for the given reaction is: rate =
k[C2H4Br2]^1[3KI]^1
Step 4: Simplify the rate expression.
Since both C2H4Br2 and 3KI are fed in stoichiometric amounts, their concentrations can be
expressed in terms of a single variable, say x, which represents the concentration of C2H4.
The initial rate of the reaction is the rate at the beginning of the reaction, when the
concentrations of all the reactants are their initial concentrations.
Therefore, the initial concentrations of C2H4Br2 and 3KI are their stoichiometric
concentrations, which are equal to their respective stoichiometric ratios with respect to
C2H4, since both reactants are fed in stoichiometric amounts.
Substituting these initial concentrations into the simplified rate expression, we get:
rate_initial = kx_0(3x_0)
So, the Initial Rate Expression (IRE) for the given second-order reaction is: rate_initial =
kx_0(3x_0)

27)prove mathematically that N equal volumes BMRs is equivalent to single PFR of same
volume for a I order reaction as N tends to infinity.
The concentration of the reactant in each BMR at time t, denoted as A, can be described by
the first-order rate equation:
Now, let's consider a plug flow reactor (PFR) with a volume of N * V, which is the same total
volume as the combined BMRs. In a PFR, the concentration of the reactant A changes along
the length of the reactor, but at any given point in the reactor, the rate equation for a first-
order reaction can be described as:
where A is the concentration of the reactant A at a given point in the PFR at time t.
To prove that N equal volumes BMRs is equivalent to a single PFR of the same volume for a
first-order reaction as N tends to infinity, we need to show that the concentration of the
reactant A at any given time t is the same in both cases, i.e., [A]_BMR(t) = [A]_PFR(t), as N
tends to infinity.
Let's assume that at time t=0, the initial concentration of A is the same in both the BMRs and
the PFR, denoted as A = [A]_0.
First, we consider the BMRs. The total volume of all the BMRs combined is N * V, and since
the BMRs are identical, the concentration of A in each BMR at time t=0 is [A]_0.
Using equation (1), we can solve for the concentration of A in a BMR at any time t:
The concentration of A changes along the length of the PFR, but at any given point in the
reactor, the rate equation is described by equation (2).
Since the PFR has a volume of N * V, we can solve for the concentration of A at a given point
in the PFR at time t using equation (2):
Notice that the concentration of A in both the BMRs and the PFR at any given time t is the
same, denoted as [A]_0 * exp(-kt).
As a result, as N tends to infinity, the concentration of A at any given time t in both the BMRs
and the PFR approaches the same value, [A]_0 * exp(-kt), as shown in equations (3) and (4).
Therefore, we can conclude that N equal volumes BMRs is equivalent to a single PFR of the
same volume for a first-order reaction as N tends to infinity, mathematically proven.

28)the following isothermal autocatalytic reaction A+B2B [-Ra=0.17CaCbmol/L s] is

carried out in an ideal CSTR operating at steady state. Pure A at 0.5 mol/L is fed and 85%
conversion of A is converted in CSTR. Calculate mean space time in CSTR.

To calculate the mean space time (θ) in a continuous stirred-tank reactor (CSTR), we can use
the equation:
where V is the volume of the reactor and V0 is the volumetric flow rate of the feed stream.
Pure A is fed at a concentration of Ca0 = 0.5 mol/L
85% conversion of A is achieved, so the concentration of A at the outlet is Ca = (1 - 0.85) *
Ca0 = 0.15 * 0.5 = 0.075 mol/L
The rate of reaction (-ra) is given as -0.17 * Ca^2 * Cb, where Ca and Cb are the
concentrations of A and B, respectively.
To solve for the mean space time, we need to find the volume of the reactor (V) and the
volumetric flow rate of the feed stream (V0).
Since the reaction is operating at steady state, the rate of formation of B (-rb) will be equal
to the rate of consumption of A (-ra) in the CSTR.
At steady state, -rb = -ra
Now, we can use the definition of conversion to find Cb0:
Now, we can use the definition of mean space time:
where Q0 is the volumetric flow rate of the feed stream.
We can use this to find the volume of the reactor V:
Q0 = 0.0916 mol/L*s
Finally, we can use the given conversion of A to calculate the volume of the reactor V:0

29) At present conversion is 75% for our elementary second order liquid phase reaction
2A2R when operating in an isothermal plug flow reactor with a recycle ratio of 2.what
will bathe conversion if recycle stream is shut off ?
In this case, the conversion is initially given as 75% with a recycle ratio of 2, which means
that 75% of the reactant A is converted to product R in each pass through the reactor, and
25% of A remains unconverted.
The recycle ratio of 2 indicates that two volumes of recycle stream are mixed with one
volume of fresh feed in each pass through the reactor.
When the recycle stream is shut off, the reactor will operate without any recycling of
unconverted reactants.
To determine the conversion without the recycle stream, we need additional information
such as the rate constant of the reaction (k), the initial concentration of A (C0), and the
reactor volume (V).
For example, if the reaction follows a simple first-order kinetics with rate constant k, the
conversion X can be calculated using the formula:
where V is the reactor volume and C0 is the initial concentration of A.
If you provide the rate constant (k), the initial concentration of A (C0), and the reactor
volume (V), I can calculate the conversion for you.

30)if you have a CSTR and a PFR both of a same volume available to carry out an
irreversible first order liquid phase reaction. How would you arrange them to achieve
maximum level of conversion? explain.
This helps in maintaining a constant concentration of reactants, which is ideal for achieving a
high level of conversion in a first-order reaction where the rate is dependent on the
concentration of the reactant.
In a CSTR, the reaction proceeds to a significant extent due to the high degree of mixing, and
it allows for a higher conversion level.
However, they provide a higher degree of plug flow, which means that the reactants move in
a plug-like manner along the length of the reactor, with different regions experiencing
different reaction extents.
In a first-order reaction, this concentration gradient can result in lower conversion levels as
the reaction may not have enough time to reach completion.
By placing the CSTR before the PFR, the initial reactant concentrations are uniformly mixed
and high in the CSTR, allowing the reaction to proceed to a significant extent.
This means that the majority of the reaction has already occurred in the CSTR, and the
partially reacted mixture then enters the PFR, where the concentration gradient can help in
further completing the reaction.
This arrangement allows for maximum utilization of the volume of the reactors, resulting in a
higher overall conversion level compared to other arrangements.
In summary, placing the CSTR before the PFR in a series arrangement allows for the
advantages of good mixing in the CSTR and the concentration gradient in the PFR to be
combined, resulting in a higher level of conversion in a first-order liquid phase reaction.
For example, if the reaction follows a simple first-order kinetics with rate constant k, the
conversion X can be calculated using the formula:
If you provide the rate constant (k), the initial concentration of A (C0), and the reactor
volume (V), I can calculate the conversion for you.

31)