Chapter 9, Problem 9.16P

Interpretation Introduction

(a)

Interpretation:

The state of the reaction at the end of two-hour period is to be stated. Also, the percent decomposition of dimethyl ether is to be determined if the reaction has not proceeded to completion.

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.

Equation of states for an ideal gas is:

$PV=nRT$ ......(1)

Here, $P$ is the pressure of the gas, $V$ is the volume of the gas, $n$ is the moles of the gas, $T$ is the temperature of the gas and $R$ is the universal gas constant.

Stoichiometry is the calculation of the reactants and the products involved in aa chemical reaction. It is based on the law of mass conservation. According to the stoichiometry, total mass of the reactants equals the total mass of the products.

Interpretation Introduction

(b)

Interpretation:

The input-output enthalpy table is to be prepared and filled using elemental species as reference.

Concept introduction:

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.

Interpretation Introduction

(c)

Interpretation:

The values of $\Delta H_r\left({600}^{\circ }\text{C}\right)$ and $\Delta U_r\left({600}^{\circ }\text{C}\right)$ for the decomposition reaction of dimethyl ether are to be calculated.

Concept introduction:

The energy balance equation to be used is:

$\Delta H=\sum _{\text{out}}{n}_i{\hat{H}}_i-\sum _{\text{in}}{n}_i{\hat{H}}_i$ ......(3)

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

$\xi =\frac{{\left|n_f-n_0\right|}_i}{\left|v_i\right|}$ ......(4)

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.

The formula to calculate heat of the reaction is:

$\Delta {\hat{H}}_r=\frac{\Delta \hat{H}}{\xi }$ ......(5)

The formula to calculate the internal energy of the reaction is:

$\Delta {\hat{U}}_r=\Delta {\hat{H}}_r-RT\left(\sum v_{\text{product gas}}-\sum v_{\text{reactant gas}}\right)$ ......(6)

Interpretation Introduction

(d)

Interpretation:

The amount heat transferred to or from the reactor during the two hours of the reaction is to be calculated.

Concept introduction:

The formula to calculate the value of $Q$, the amount of heat transfer is:

$Q=\xi \Delta {\hat{U}}_r\left({600}^{\circ }\text{C}\right)$ ......(7)

Interpretation Introduction

(e)

Interpretation:

The final volume of the reactor and the required amount of heat transfer are to be calculated is the reactor used is expandable. Also, the reason for the difference in the values of calculated $Q$ is to be explained.

Concept introduction:

Equation of states for an ideal gas is:

$PV=nRT$ ......(1)

Here, $P$ is the pressure of the gas, $V$ is the volume of the gas, $n$ is the moles of the gas, $T$ is the temperature of the gas and $R$ is the universal gas constant.

For the system at constant pressure but variable volume, the mount of heat transfer is calculated as:

$Q=\xi \Delta {\hat{U}}_r+P\Delta V$ ......(8)