Chapter 6, Problem 6.67P

Interpretation Introduction

(a)

Interpretation:

The molar flowrates and mole fractions of the hexane in both the streams, liquid as well gas leaving the column are to be determined. Also, the average molar flow rates of gas and liquid streams in the column are to be calculated.

Concept introduction:

In a system, a conserved quantity (total mass, mass of a species, energy or momentum) is balanced and can be written as

$input+generation-output-consumpumtion=accumulation$

Here, ‘input’ is the stream which enters the system. ‘generation’ is the term used for the quantity that is produced within the system. ‘output’ is the stream which leaves the system. ‘consumption’ is the term used for the quantity that is consumed within the system. ‘accumulation’ is used for the quantity which is builds up within the system.

All the equations which are formed are then solved simultaneously to calculate the values of the unknown variables.

Average value is calculated as

$\text{Average}=\frac{\sum _i^N{x}_i}{N}$

Interpretation Introduction

(b)

Interpretation:

The mole fraction of hexane in the gas leaving the stage $y_N$ and in the liquid entering it $x_{N-1}$ are to be calculated at given conditions for the given process.

Concept introduction:

In a system, a conserved quantity (total mass, mass of a species, energy or momentum) is balanced and can be written as

$input+generation-output-consumpumtion=accumulation$

Here, ‘input’ is the stream which enters the system. ‘generation’ is the term used for the quantity that is produced within the system. ‘output’ is the stream which leaves the system. ‘consumption’ is the term used for the quantity that is consumed within the system. ‘accumulation’ is used for the quantity which is builds up within the system.

All the equations which are formed are then solved simultaneously to calculate the values of the unknown variables.

Antoine equation is used to determine the vapor pressure of any substance at the given temperature by the equation:

$\log P^{\ast }\left(\text{mmHg}\right)=A-\frac{B}{\left(T^{\circ }\text{C}\right)+C}$ ...... (3)

Here, $A,B\text{ and }C$ are the constants specific for a substance given in table B.4 of appendix B.

For two phase binary mixture, Raoult’s law states that,

$\begin{array}{c}{x}_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P\\ x_{\text{B}}{P}_{\text{B}}{}^{\ast }=y_{\text{B}}P\end{array}$ ...... (4)

Here, $x_{\text{A}}\text{ and }{x}_{\text{B}}$ are the mole fractions of A and B in liquid phase respectively, $P_{\text{A}}{}^{\ast }\text{ and }{P}_{\text{B}}{}^{\ast }$ are the vapor pressure of A and B respectively, $y_{\text{A}}\text{ and }{y}_{\text{B}}$ are the mole fractions of A and B respectively and $P$ is the total pressure of the system.

Interpretation Introduction

(c)

Interpretation:

The given equations are to be derived for the given conditions.

Concept introduction:

In a system, a conserved quantity (total mass, mass of a species, energy or momentum) is balanced and can be written as

$input+generation-output-consumpumtion=accumulation$

Here, ‘input’ is the stream which enters the system. ‘generation’ is the term used for the quantity that is produced within the system. ‘output’ is the stream which leaves the system. ‘consumption’ is the term used for the quantity that is consumed within the system. ‘accumulation’ is used for the quantity which is builds up within the system.

All the equations which are formed are then solved simultaneously to calculate the values of the unknown variables.

Antoine equation is used to determine the vapor pressure of any substance at the given temperature by the equation:

$\log P^{\ast }\left(\text{mmHg}\right)=A-\frac{B}{\left(T^{\circ }\text{C}\right)+C}$ ...... (3)

Here, $A,B\text{ and }C$ are the constants specific for a substance given in table B.4 of appendix B.

For two phase binary mixture, Raoult’s law states that,

$\begin{array}{c}{x}_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P\\ x_{\text{B}}{P}_{\text{B}}{}^{\ast }=y_{\text{B}}P\end{array}$ ...... (4)

Here, $x_{\text{A}}\text{ and }{x}_{\text{B}}$ are the mole fractions of A and B in liquid phase respectively, $P_{\text{A}}{}^{\ast }\text{ and }{P}_{\text{B}}{}^{\ast }$ are the vapor pressure of A and B respectively, $y_{\text{A}}\text{ and }{y}_{\text{B}}$ are the mole fractions of A and B respectively and $P$ is the total pressure of the system.

Interpretation Introduction

(d)

Interpretation:

The effect of operating temperature on the given absorption column is to be examined by estimating the number of ideal stages which are necessary to obtain the desired separation.

Concept introduction:

In a system, a conserved quantity (total mass, mass of a species, energy or momentum) is balanced and can be written as

$input+generation-output-consumpumtion=accumulation$

Here, ‘input’ is the stream which enters the system. ‘generation’ is the term used for the quantity that is produced within the system. ‘output’ is the stream which leaves the system. ‘consumption’ is the term used for the quantity that is consumed within the system. ‘accumulation’ is used for the quantity which is builds up within the system.

All the equations which are formed are then solved simultaneously to calculate the values of the unknown variables.

Antoine equation is used to determine the vapor pressure of any substance at the given temperature by the equation:

$\log P^{\ast }\left(\text{mmHg}\right)=A-\frac{B}{\left(T^{\circ }\text{C}\right)+C}$ ...... (3)

Here, $A,B\text{ and }C$ are the constants specific for a substance given in table B.4 of appendix B.

For two phase binary mixture, Raoult’s law states that,

$\begin{array}{c}{x}_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P\\ x_{\text{B}}{P}_{\text{B}}{}^{\ast }=y_{\text{B}}P\end{array}$ ...... (4)

Here, $x_{\text{A}}\text{ and }{x}_{\text{B}}$ are the mole fractions of A and B in liquid phase respectively, $P_{\text{A}}{}^{\ast }\text{ and }{P}_{\text{B}}{}^{\ast }$ are the vapor pressure of A and B respectively, $y_{\text{A}}\text{ and }{y}_{\text{B}}$ are the mole fractions of A and B respectively and $P$ is the total pressure of the system.

Interpretation Introduction

(e)

Interpretation:

The maximum temperature at which the separation can be achieved for the given absorption column is to be calculated.

Concept introduction:

In a system, a conserved quantity (total mass, mass of a species, energy or momentum) is balanced and can be written as

$input+generation-output-consumpumtion=accumulation$

Here, ‘input’ is the stream which enters the system. ‘generation’ is the term used for the quantity that is produced within the system. ‘output’ is the stream which leaves the system. ‘consumption’ is the term used for the quantity that is consumed within the system. ‘accumulation’ is used for the quantity which is builds up within the system.

All the equations which are formed are then solved simultaneously to calculate the values of the unknown variables.

Antoine equation is used to determine the vapor pressure of any substance at the given temperature by the equation:

$\log P^{\ast }\left(\text{mmHg}\right)=A-\frac{B}{\left(T^{\circ }\text{C}\right)+C}$ ...... (3)

Here, $A,B\text{ and }C$ are the constants specific for a substance given in table B.4 of appendix B.

For two phase binary mixture, Raoult’s law states that,

$\begin{array}{c}{x}_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P\\ x_{\text{B}}{P}_{\text{B}}{}^{\ast }=y_{\text{B}}P\end{array}$ ...... (4)

Here, $x_{\text{A}}\text{ and }{x}_{\text{B}}$ are the mole fractions of A and B in liquid phase respectively, $P_{\text{A}}{}^{\ast }\text{ and }{P}_{\text{B}}{}^{\ast }$ are the vapor pressure of A and B respectively, $y_{\text{A}}\text{ and }{y}_{\text{B}}$ are the mole fractions of A and B respectively and $P$ is the total pressure of the system.