Chapter 22, Problem 22.52P

(a)

Interpretation Introduction

Interpretation:

The ${\text{ΔG}}^{\text{°}}$ has to be calculated at ${\text{25}}^{\text{°}}\text{C}$ for the reaction of ${\text{SO}}_{\text{2}}$ to form ${\text{SO}}_{\text{3}}$ at standard conditions. The reaction is spontaneous or not has to be given.

Concept Introduction:

Standard state free energy of formation (${\text{ΔG}}^{\text{°}}$):

It is the difference between the free energy of a substance and the free energy of its elements in thermodynamically stable states at standard conditions.

It can be calculated by the following expression:

  ${\text{ΔG}}^{\text{°}}\text{=}{\displaystyle \sum _{}^{}{\text{ΔG}}_{{\text{f}}_{\text{products}}}^{\text{°}}\text{-}}{\displaystyle \sum _{}^{}{\text{ΔG}}_{{\text{f}}_{\text{reactants}}}^{\text{°}}}$

If ${\text{ΔG}}^{\text{°}}\text{> 0}$, the reaction is non-spontaneous.

If ${\text{ΔG}}^{\text{°}}\text{< 0}$, the reaction is spontaneous.

(b)

Interpretation Introduction

Interpretation:

Consider the reaction of ${\text{SO}}_{\text{2}}$ to form ${\text{SO}}_{\text{3}}$ at standard conditions.

The reason has to be given for the reaction not performed at ${\text{25}}^{\text{°}}\text{C}$.

(c)

Interpretation Introduction

Interpretation:

Consider the reaction of ${\text{SO}}_{\text{2}}$ to form ${\text{SO}}_{\text{3}}$ at standard conditions.

The reaction is spontaneous or not at ${\text{500}}^{\text{°}}\text{C}$ has to be given (assume that ${\text{ΔH}}^{\text{°}}\text{and}{\text{ΔS}}^{\text{°}}$ are constant with changing $\text{T}$).

Concept Introduction:

${\text{ΔH}}^{\text{°}}$ can be calculated by the expression

  ${\text{ΔH}}^{\text{°}}\text{=}{\displaystyle \sum _{}^{}{\text{nH}}_{{\text{f}}_{\text{products}}}^{\text{°}}\text{-}}{\displaystyle \sum _{}^{}{\text{mH}}_{{\text{f}}_{\text{reactants}}}^{\text{°}}}$

${\text{ΔS}}^{\text{°}}$ can be calculated by the expression

  ${\text{ΔS}}^{\text{°}}\text{=}{\displaystyle \sum _{}^{}{\text{nS}}_{{}_{\text{products}}}^{\text{°}}\text{-}}{\displaystyle \sum _{}^{}{\text{mS}}_{{}_{\text{reactants}}}^{\text{°}}}$

From the values of ${\text{ΔH}}^{\text{°}}\text{and}{\text{ΔS}}^{\text{°}}$, ${\text{ΔG}}^{\text{°}}$ can be calculated by the expression

  ${\text{ΔG}}^{\text{°}}{\text{= ΔH}}^{\text{°}}{\text{- TΔS}}^{\text{°}}$

If ${\text{ΔG}}^{\text{°}}\text{> 0}$, the reaction is non-spontaneous.

If ${\text{ΔG}}^{\text{°}}\text{< 0}$, the reaction is spontaneous.

(d)

Interpretation Introduction

Interpretation:

Consider the reaction of ${\text{SO}}_{\text{2}}$ to form ${\text{SO}}_{\text{3}}$ at standard conditions.

The $\text{K}$ values has to be compared at ${\text{500}}^{\text{°}}\text{C}$ and at ${\text{25}}^{\text{°}}\text{C}$.

Concept Introduction:

The value of $\text{K}$ can be calculated by the expression of free energy and equilibrium constant.

  $\begin{array}{l}{\text{ΔG = ΔG}}^{\text{°}}\text{+ RT ln K}\\ \\ \text{where,}\text{ΔG = free}\text{energy}\\ \\ {\text{ΔG}}^{\text{°}}\text{=standard-state}\text{free}\text{energy}\\ \\ \text{R = ideal}\text{gas}\text{constant}\\ \\ \text{T = temperature}\end{array}$

If a reaction is at equilibrium, $\text{ΔG=0}$.

  $\begin{array}{l}{\text{0 = ΔG}}^{\text{°}}\text{+ RT ln K}\\ \\ {\text{ΔG}}^{\text{°}}\text{ = -RT ln K}\end{array}$

(e)

Interpretation Introduction

Interpretation:

Consider the reaction of ${\text{SO}}_{\text{2}}$ to form ${\text{SO}}_{\text{3}}$ at standard conditions.

The highest $\text{T}$ at which the reaction is spontaneous has to be given.

Concept Introduction:

${\text{ΔH}}^{\text{°}}$ can be calculated by the expression

  ${\text{ΔH}}^{\text{°}}\text{=}{\displaystyle \sum _{}^{}{\text{nH}}_{{\text{f}}_{\text{products}}}^{\text{°}}\text{-}}{\displaystyle \sum _{}^{}{\text{mH}}_{{\text{f}}_{\text{reactants}}}^{\text{°}}}$

${\text{ΔS}}^{\text{°}}$ can be calculated by the expression

  ${\text{ΔS}}^{\text{°}}\text{=}{\displaystyle \sum _{}^{}{\text{nS}}_{{}_{\text{products}}}^{\text{°}}\text{-}}{\displaystyle \sum _{}^{}{\text{mS}}_{{}_{\text{reactants}}}^{\text{°}}}$

From the values of ${\text{ΔH}}^{\text{°}}\text{and}{\text{ΔS}}^{\text{°}}$, ${\text{ΔG}}^{\text{°}}$ can be calculated by the expression

  ${\text{ΔG}}^{\text{°}}{\text{= ΔH}}^{\text{°}}{\text{- TΔS}}^{\text{°}}$