Chapter 2, Problem 2.7P

(a)

Interpretation Introduction

Interpretation:

The volume of PFR to achieve $50\%$ conversion for the given reaction is to be calculated.

Concept Introduction:

Mole balance depends on the law of conservation of mass. To apply it, the boundary of a system must be specified, and the volume enclosed by this boundary is considered for the mole balance. At any point of time, mole balance applied on speciesiis defined by the equation as:

  $\left[\begin{array}{l}\text{Rate of molar}\\ \text{flow of }i\text{ into}\\ \text{the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]-\left[\begin{array}{l}\text{Rate of molar}\\ \text{flow of }i\text{ out}\\ \text{of the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]+\left[\begin{array}{l}\text{Rate of generation}\\ \text{of }i\text{ by chemical}\\ \text{reaction in the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]=\left[\begin{array}{l}\text{Rate of accumulation}\\ \text{of }i\text{ in the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]$

For a Continuous Stirred Tank Reactor (CSTR), the design equation to be used is:

  $V=\frac{F_{A0}-F_A}{-r_A}$ …… (1)

Here, $V$ is the volume of the reactor, $F_{A0}$ is the entering molar flowrate of species A , $F_A$ is the exit molar flowrate of A , and $-r_A$ is the rate of reaction of species A .

  $F_A$ can be further defined as:

  $F_A=C_{A}v$ …… (2)

Here, $C_A$ is the concentration of species A , and $v$ is the volumetric flowrate.

For a Plug Flow Reactor (PFR), the design equation to be used is:

  $\frac{d{F}_A}{dV}=-r_A$ …… (3)

Here, $V$ is the volume of the reactor, $F_A$ is the exit molar flowrate of A , and $-r_A$ is the rate of reaction of species A . $F_A$ is defined by equation (2).

(b)

Interpretation Introduction

Interpretation:

The volume necessary for CSTR achieve $50\%$ conversion for the given reaction is to be calculated.

Concept Introduction:

Mole balance depends on the law of conservation of mass. To apply it, the boundary of a system must be specified, and the volume enclosed by this boundary is considered for the mole balance. At any point of time, mole balance applied on species iis defined by the equation as:

  $\left[\begin{array}{l}\text{Rate of molar}\\ \text{flow of }i\text{ into}\\ \text{the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]-\left[\begin{array}{l}\text{Rate of molar}\\ \text{flow of }i\text{ out}\\ \text{of the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]+\left[\begin{array}{l}\text{Rate of generation}\\ \text{of }i\text{ by chemical}\\ \text{reaction in the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]=\left[\begin{array}{l}\text{Rate of accumulation}\\ \text{of }i\text{ in the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]$

For a Continuous Stirred Tank Reactor (CSTR), the design equation to be used is:

  $V=\frac{F_{A0}-F_A}{-r_A}$ …… (1)

Here, $V$ is the volume of the reactor, $F_{A0}$ is the entering molar flowrate of species A , $F_A$ is the exit molar flowrate of A , and $-r_A$ is the rate of reaction of species A .

  $F_A$ can be further defined as:

  $F_A=C_{A}v$ …… (2)

Here, $C_A$ is the concentration of species A , and $v$ is the volumetric flowrate.

For a Plug Flow Reactor (PFR), the design equation to be used is:

  $\frac{d{F}_A}{dV}=-r_A$ …… (3)

Here, $V$ is the volume of the reactor, $F_A$ is the exit molar flowrate of A , and $-r_A$ is the rate of reaction of species A . $F_A$ is defined by equation (2).

(c)

Interpretation Introduction

Interpretation:

The volume of the second CSTR added to the one in part (b) in series to achieve $80\%$ conversion is to be calculated.

Concept Introduction:

Mole balance depends on the law of conservation of mass. To apply it, the boundary of a system must be specified, and the volume enclosed by this boundary is considered for the mole balance. At any point of time, mole balance applied on species iis defined by the equation as:

  $\left[\begin{array}{l}\text{Rate of molar}\\ \text{flow of }i\text{ into}\\ \text{the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]-\left[\begin{array}{l}\text{Rate of molar}\\ \text{flow of }i\text{ out}\\ \text{of the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]+\left[\begin{array}{l}\text{Rate of generation}\\ \text{of }i\text{ by chemical}\\ \text{reaction in the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]=\left[\begin{array}{l}\text{Rate of accumulation}\\ \text{of }i\text{ in the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]$

For a Continuous Stirred Tank Reactor (CSTR), the design equation to be used is:

  $V=\frac{F_{A0}-F_A}{-r_A}$ …… (1)

Here, $V$ is the volume of the reactor, $F_{A0}$ is the entering molar flowrate of species A , $F_A$ is the exit molar flowrate of A , and $-r_A$ is the rate of reaction of species A .

  $F_A$ can be further defined as:

  $F_A=C_{A}v$ …… (2)

Here, $C_A$ is the concentration of species A , and $v$ is the volumetric flowrate.

For a Plug Flow Reactor (PFR), the design equation to be used is:

  $\frac{d{F}_A}{dV}=-r_A$ …… (3)

Here, $V$ is the volume of the reactor, $F_A$ is the exit molar flowrate of A , and $-r_A$ is the rate of reaction of species A . $F_A$ is defined by equation (2).

(d)

Interpretation Introduction

Interpretation:

The volume of the second PFR added to the CSTR in part (b) in series to achieve $80\%$ conversion is to be calculated.

Concept Introduction:

Mole balance depends on the law of conservation of mass. To apply it, the boundary of a system must be specified, and the volume enclosed by this boundary is considered for the mole balance. At any point of time, mole balance applied on species iis defined by the equation as:

  $\left[\begin{array}{l}\text{Rate of molar}\\ \text{flow of }i\text{ into}\\ \text{the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]-\left[\begin{array}{l}\text{Rate of molar}\\ \text{flow of }i\text{ out}\\ \text{of the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]+\left[\begin{array}{l}\text{Rate of generation}\\ \text{of }i\text{ by chemical}\\ \text{reaction in the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]=\left[\begin{array}{l}\text{Rate of accumulation}\\ \text{of }i\text{ in the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]$

For a Continuous Stirred Tank Reactor (CSTR), the design equation to be used is:

  $V=\frac{F_{A0}-F_A}{-r_A}$ …… (1)

Here, $V$ is the volume of the reactor, $F_{A0}$ is the entering molar flowrate of species A , $F_A$ is the exit molar flowrate of A , and $-r_A$ is the rate of reaction of species A .

  $F_A$ can be further defined as:

  $F_A=C_{A}v$ …… (2)

Here, $C_A$ is the concentration of species A , and $v$ is the volumetric flowrate.

For a Plug Flow Reactor (PFR), the design equation to be used is:

  $\frac{d{F}_A}{dV}=-r_A$ …… (3)

Here, $V$ is the volume of the reactor, $F_A$ is the exit molar flowrate of A , and $-r_A$ is the rate of reaction of species A . $F_A$ is defined by equation (2).

(e)

Interpretation Introduction

Interpretation:

The conversion achieved for the given CSTR of volume $6\times {10}^4{\text{ m}}^3$ and PFR of volume $6\times {10}^4{\text{ m}}^3$ are to be calculated.

Concept Introduction:

Mole balance depends on the law of conservation of mass. To apply it, the boundary of a system must be specified, and the volume enclosed by this boundary is considered for the mole balance. At any point of time, mole balance applied on species iis defined by the equation as:

  $\left[\begin{array}{l}\text{Rate of molar}\\ \text{flow of }i\text{ into}\\ \text{the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]-\left[\begin{array}{l}\text{Rate of molar}\\ \text{flow of }i\text{ out}\\ \text{of the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]+\left[\begin{array}{l}\text{Rate of generation}\\ \text{of }i\text{ by chemical}\\ \text{reaction in the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]=\left[\begin{array}{l}\text{Rate of accumulation}\\ \text{of }i\text{ in the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]$

For a Continuous Stirred Tank Reactor (CSTR), the design equation to be used is:

  $V=\frac{F_{A0}-F_A}{-r_A}$ …… (1)

Here, $V$ is the volume of the reactor, $F_{A0}$ is the entering molar flowrate of species A , $F_A$ is the exit molar flowrate of A , and $-r_A$ is the rate of reaction of species A .

  $F_A$ can be further defined as:

  $F_A=C_{A}v$ …… (2)

Here, $C_A$ is the concentration of species A , and $v$ is the volumetric flowrate.

For a Plug Flow Reactor (PFR), the design equation to be used is:

  $\frac{d{F}_A}{dV}=-r_A$ …… (3)

Here, $V$ is the volume of the reactor, $F_A$ is the exit molar flowrate of A , and $-r_A$ is the rate of reaction of species A . $F_A$ is defined by equation (2).

(f)

Interpretation Introduction

Interpretation:

The answers in the above sub-parts are to be analyzed critically.

Concept Introduction:

Mole balance depends on the law of conservation of mass. To apply it, the boundary of a system must be specified, and the volume enclosed by this boundary is considered for the mole balance. At any point of time, mole balance applied on species iis defined by the equation as:

  $\left[\begin{array}{l}\text{Rate of molar}\\ \text{flow of }i\text{ into}\\ \text{the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]-\left[\begin{array}{l}\text{Rate of molar}\\ \text{flow of }i\text{ out}\\ \text{of the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]+\left[\begin{array}{l}\text{Rate of generation}\\ \text{of }i\text{ by chemical}\\ \text{reaction in the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]=\left[\begin{array}{l}\text{Rate of accumulation}\\ \text{of }i\text{ in the system}\\ \left(\text{moles}/\text{time}\right)\end{array}\right]$

For a Continuous Stirred Tank Reactor (CSTR), the design equation to be used is:

  $V=\frac{F_{A0}-F_A}{-r_A}$ …… (1)

Here, $V$ is the volume of the reactor, $F_{A0}$ is the entering molar flowrate of species A , $F_A$ is the exit molar flowrate of A , and $-r_A$ is the rate of reaction of species A .

  $F_A$ can be further defined as:

  $F_A=C_{A}v$ …… (2)

Here, $C_A$ is the concentration of species A , and $v$ is the volumetric flowrate.

For a Plug Flow Reactor (PFR), the design equation to be used is:

  $\frac{d{F}_A}{dV}=-r_A$ …… (3)

Here, $V$ is the volume of the reactor, $F_A$ is the exit molar flowrate of A , and $-r_A$ is the rate of reaction of species A . $F_A$ is defined by equation (2).