Chapter 9, Problem 9.40P

Interpretation Introduction

Interpretation:

The fractional conversion and the volumetric flowrate of the product stream are to be calculated.

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.

In a system, a conserved quantity (total mass, mass of a particular 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.

The equation for energy balance is:

$\Delta \dot{H}+\Delta {\dot{E}}_{\text{k}}+\Delta {\dot{E}}_{\text{p}}=\dot{Q}-{\dot{W}}_{\text{s}}$   ..... (1)

Here, $\Delta \dot{H}$ is the rate of change in the enthalpy of the system, $\Delta {\dot{E}}_{\text{k}}$ is the rate of kinetic energy change of the system, $\Delta {\dot{E}}_{\text{p}}$ is the rate of potential energy change of the system, $\dot{Q}$ is the net rate at which energy is transferred to a system and ${\dot{W}}_{\text{s}}$ is the rate at which energy is transferred as shaft work.

Specific heat capacity $\left(C_p\right)$ of a substance is the amount of heat needed for a unit mass of substance to raise its temperature by $1^{\circ }\text{C}$. It is temperature dependent and varies with temperature of the substance.

Specific enthalpy $\left(\hat{H}\right)$ of any substance at temperature $T^{\circ }\text{C}$ is given by:

$\hat{H}={\int }_{T_{ref}}^T{C}_{p}dT$   ..... (2)

Here, $T_{ref}$ is the reference temperature taken for the calculations.

Equation of states for an ideal gas is:

$P\dot{V}=\dot{n}RT$   ..... (3)

Here, $P$ is the pressure of the gas, $\dot{V}$ is the volumetric flowrate of the gas, $\dot{n}$ is the molar flowrate of the gas, $T$ is the temperature of the gas and $R$ is the universal gas constant.

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

$f=\frac{\text{moles reacted}}{\text{moles fed}}$   ..... (4)

The formula to calculate the extent of reaction, $\xi$ is:

$\xi =\frac{{\left|n_f-n_0\right|}_i}{\left|v_i\right|}$   ..... (5)

Here, $v_i$ is the stoichiometric coefficient of the species i in the balanced chemical reaction, and $n_f\text{ and }{n}_0$ are the final and initial moles of i.