Chapter 9, Problem 9.75P

(a)

Interpretation Introduction

Interpretation:

$\Delta H_{\text{f}}^{°}$ of $\text{MgCl}$ 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.

(b)

Interpretation Introduction

Interpretation:

Whether $\text{MgCl}$ is favoured energetically relative to $\text{Mg}$ and ${\text{Cl}}_2$ is to be determined.

Concept introduction:

The standard enthalpy of formation $\left(\Delta H_{\text{f}}^{°}\right)$ is the enthalpy change of the formation of $1\text{mol}$ of compound from its elements and the reactants and products, in this case, is also present in their standard state.

Standard state includes $1\text{atm}$ pressure for gases, $1M$ concentration for substances in the aqueous phase and the most stable form of substance at $1\text{atm}$ pressure and $298\text{K}$ temperature. For example, metal like sodium exists in solid state and molecular elements like halogen exist in a gaseous state.

(c)

Interpretation Introduction

Interpretation:

$\Delta H^{°}$ for the conversion of $\text{MgCl}$ to ${\text{MgCl}}_2$ and $\text{Mg}$ is to be calculated.

Concept introduction:

The standard enthalpy of reaction is calculated by the summation of standard enthalpy of formation of the product minus the summation of standard enthalpy of formation of product at the standard conditions. The formula to calculate the standard enthalpy of reaction $\left(\Delta H_{\text{rxn}}^{°}\right)$ is as follows:

$\Delta H_{\text{rxn}}^{°}=\sum m\Delta H_{\text{f (products)}}^{°}-\sum m\Delta H_{\text{f (reactants)}}^{°}$

Here, m and n are the stoichiometric coefficients of reactants and product in the balanced chemical equation.

(d)

Interpretation Introduction

Interpretation:

Whether $\text{MgCl}$ is favoured energetically relative to ${\text{MgCl}}_2$ is to be determined.

Concept introduction:

The standard enthalpy of formation $\left(\Delta H_{\text{f}}^{°}\right)$ is the enthalpy change of the formation of $1\text{mol}$ of compound from its elements and the reactants and products, in this case, is also present in their standard state.

Standard state includes $1\text{atm}$ pressure for gases, $1M$ concentration for substances in the aqueous phase and the most stable form of substance at $1\text{atm}$ pressure and $298\text{K}$ temperature. For example, metal like sodium exists in solid state and molecular elements like halogen exist in a gaseous state.