Chapter 9, Problem 9.90P

(a)

Interpretation Introduction

Interpretation:

$\Delta H_{\text{rxn}}^{°}$ for the formation of dimethyl ether $\left({\text{CH}}_3{\text{OCH}}_3\right)$ and ethanol $\left({\text{CH}}_3{\text{CH}}_2\text{O}\mathrm{H}\right)$ is to be calculated.

Concept introduction:

The heat of the reaction $\left(\Delta H_{\text{rxn}}^{°}\right)$ is defined as the heat released or absorbed during a chemical reaction as a result of the difference in the bond energies (BE) of reactant and product in the reaction. $\Delta H_{\text{rxn}}^{°}$ is negative for exothermic reaction and $\Delta H_{\text{rxn}}^{°}$ is positive for an endothermic reaction.

The formula to calculate $\Delta H_{\text{rxn}}^{°}$ of reaction is as follows:

$\Delta H_{\text{rxn}}^{°}=\sum \Delta H_{\text{reactant bond broken}}^{°}+\sum \Delta H_{\text{product bond formed}}^{°}$

Or,

$\Delta H_{\text{rxn}}^{°}=\sum {\text{BE}}_{\text{reactant bond broken}}-\sum {\text{BE}}_{\text{product bond formed}}$

The bond energy of reactants is positive and the bond energy of products is negative.

(b)

Interpretation Introduction

Interpretation:

Among the formation reaction of dimethyl ether and ethanol, the more exothermic reaction is to be identified.

Concept introduction:

In the case of a reaction, the change in enthalpy $\left(\Delta H\right)$ is the difference in the energy of the product and reactant. The general expression to calculate $\Delta H$ is,

$\Delta H=H_{\text{Product}}-H_{\text{Reactant}}$ (1)

Here,

$\Delta H$ is the change in enthalpy of the system.

$H_{\text{Product}}$ is the enthalpy of the products.

$H_{\text{Reactant}}$ is the enthalpy of the reactants.

Endothermic reactions are the reactions in which energy in the form of the heat or light is absorbed by the reactant for the formation of the product. $H_{\text{Product}}$ is greater than $H_{\text{Reactant}}$ in the endothermic reactions.

Exothermic reactions are the reactions in which energy in the form of the heat or light is released with the product. $H_{\text{Reactant}}$ is greater than $H_{\text{Product}}$ in the exothermic reactions.

(c)

Interpretation Introduction

Interpretation:

$\Delta H_{\text{rxn}}^{°}$ for the conversion of ethanol to dimethyl ether is to be calculated.

Concept introduction:

Hess’s law is used to calculate the enthalpy change of an overall reaction that can be derived as a sum of two or more reaction. According to Hess’s law $\Delta H$ of an overall reaction is equal to the sum of the enthalpy change for each individual reaction. $\Delta H_{\text{overall rxn}}=\Delta H_1+\Delta H_2+\mathrm{.......}+\Delta H_{\text{n}}$

Enthalpy is a state function so the value depends upon the initial state and final state not on the path so $\Delta H$ of an overall reaction can be calculated by the addition or subtraction of the individual steps whose $\Delta H$ is known.