Chapter 4, Problem 4.57P

Interpretation Introduction

(a)

Interpretation:

The mole fractions of the components of the product streams are to be determined using atomic species balance in the calculations.

Concept introduction:

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

$\mathrm{input}+generation-output-consumpumtion=accumulation$

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.

The formula for the percent conversion $\left(f\%\right)$ is:

$f\%=\frac{\text{moles reacted}}{\text{moles fed}}\times 100\%$                  …… (1)

Mole fraction $\left(y_i\right)$ of any component is given by:

$y_i=\frac{n_i}{\sum n_i}$                  …… (2)

Here, $n_i$ is the moles of component $i$ and $\sum n_i$ is the total moles of all the components present in the mixture.

Interpretation Introduction

(b)

Interpretation:

The mole fractions of the components of the product streams are to be determined using extent of reaction in the calculations.

Concept introduction:

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

$\mathrm{input}+generation-output-consumpumtion=accumulation$

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.

The formula for the percent conversion $\left(f\%\right)$ is:

$f\%=\frac{\text{moles reacted}}{\text{moles fed}}\times 100\%$                  …… (1)

Mole fraction $\left(y_i\right)$ of any component is given by:

$y_i=\frac{n_i}{\sum n_i}$                  …… (2)

Here, $n_i$ is the moles of component $i$ and $\sum n_i$ is the total moles of all the components present in the mixture.

For a single reaction system, the extent of reaction for each of the components present in the products can be estimated by the equation:

$n_i=n_{io}+v_i\xi$                  …… (4)

Here, $n_i$ is the final moles of the component $i$, $n_{io}$ is the initial moles of the component $i$, $v_i$ is the stoichiometric coefficient of the component $i$ in the reaction and $\xi$ is the extent of the reaction. $v_i$ is taken as negative for reactants and positive for products.

Interpretation Introduction

(c)

Interpretation:

The factors on which the choice of process should be used is to be stated. Also, the factors on which cost and savings of the alternative process is to be determined.

Concept introduction:

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

$\mathrm{input}+generation-output-consumpumtion=accumulation$

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.