Chapter 4, Problem 4.65P

Interpretation Introduction

(a)

Interpretation:

The flow-chart for the given process is to be drawn and labelled. Also, the degree of freedom analysis is to be done on the process using extent of the reaction and then prove that information required to calculate the reaction composition at equilibrium is enough.

Concept introduction:

A flowchart is the complete representation of a process through boxes or other shapes which represents process units and arrows that represents the input and output of the process. The flowchart must be fully labelled to infer important data about the process involved.

Degree of freedom analysis is the procedure to analyze any missing information needed for material balance calculations. The procedure involves complete labelling of the flowchart representing the process and then determining number of unknown variables $\left(n_{\text{unknowns}}\right)$ and independent equations $\left(n_{\text{indep eqns}\text{.}}\right)$ from that flowchart.

Mathematically, degree of freedom $\left(n_{\text{df}}\right)$ is formulated as:

$n_{\text{df}}=n_{\text{unknowns}}-n_{\text{indep eqns}\text{.}}$   ....... (1)

Interpretation Introduction

(b)

Interpretation:

The total moles of gas at the equilibrium in the reactor is to be determined. Also, the equilibrium mole fraction of hydrogen in the product is to be determined.

Concept introduction:

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

$n_i=n_{io}+v_i\xi$   ....... (3)

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.

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

$y_i=\frac{n_i}{\sum n_i}$   ....... (4)

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

(c)

Interpretation:

The explanation for the discrepancy between the calculated and measured hydrogen yields is to be determined.

Concept introduction:

In a chemical reaction, the state in which both the reactants and the products are present in concentration that has no tendency to change with time is the state of equilibrium.

Interpretation Introduction

(d)

Interpretation:

An excel spreadsheet is to be written for the input value of reactor temperature and feed component mole fraction to calculate the mole fraction of hydrogen in the product gas at equilibrium. Test the result for the values given in part (a) and then try the program for different values of input variables and draw the conclusion about the condition which will maximize the equilibrium yield of hydrogen.

Concept introduction:

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

$n_i=n_{io}+v_i\xi$   ....... (3)

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.

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

$y_i=\frac{n_i}{\sum n_i}$   ....... (4)

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.