Chapter 15.5, Problem 46PP

Interpretation Introduction

(a)

Interpretation:

Whether the given reactions are spontaneous or not needs to be determined.

Concept introduction:

A reaction is spontaneous if its Gibbs free energy change is negative. Gibbs free energy change is given by:

$\begin{array}{l}\Delta G=\Delta H-T\Delta S\\ where\\ \Delta GischangeinGibbsfreeenergy\\ \Delta Hischangeinenthalpy\\ \Delta Sischangeinentropy\\ TisTemperatureofreaction\end{array}$

Answer to Problem 46PP

The given reaction is spontaneous.

Explanation of Solution

Information given:

$\begin{array}{c}\Delta H=-75.9kJ\\ \Delta S=138J/K\\ =0.138kJ/K\\ T=273K\end{array}$

Putting the values into the formula:

$\begin{array}{c}\Delta G=\Delta H-T\Delta S\\ =-75.9-\left(273\times 0.138\right)\\ =-75.9-37.7\\ =-114kJ\end{array}$

As Gibbs free energy change is negative, therefore reaction is spontaneous.

Interpretation Introduction

(b)

Interpretation:

Whether the given reactions are spontaneous or not needs to be determined.

Concept introduction:

A reaction is spontaneous if its Gibbs free energy change is negative. Gibbs free energy change is given by:

$\begin{array}{l}\Delta G=\Delta H-T\Delta S\\ where\\ \Delta GischangeinGibbsfreeenergy\\ \Delta Hischangeinenthalpy\\ \Delta Sischangeinentropy\\ TisTemperatureofreaction\end{array}$

Answer to Problem 46PP

The given reaction is non- spontaneous.

Explanation of Solution

Information given:

$\begin{array}{c}\Delta H=-27.6kJ\\ \Delta S=-55.2J/K\\ =-0.0552kJ/K\\ T=535K\end{array}$

Putting the values into the formula:

$\begin{array}{c}\Delta G=\Delta H-T\Delta S\\ =-27.6-\left(535\right)\times \left(-0.0552\right)\\ =-27.6+29.5\\ =1.9kJ\end{array}$

As Gibbs free energy change is positive, therefore reaction is non- spontaneous.

Interpretation Introduction

(c)

Interpretation:

Whether the given reactions are spontaneous or not needs to be determined.

Concept introduction:

A reaction is spontaneous if its Gibbs free energy change is negative. Gibbs free energy change is given by:

$\begin{array}{l}\Delta G=\Delta H-T\Delta S\\ where\\ \Delta GischangeinGibbsfreeenergy\\ \Delta Hischangeinenthalpy\\ \Delta Sischangeinentropy\\ TisTemperatureofreaction\end{array}$

Answer to Problem 46PP

The given reaction is spontaneous.

Explanation of Solution

Information given:

$\begin{array}{c}\Delta H=365kJ\\ \Delta S=-55.2J/K\\ =-0.552kJ/K\\ T=388K\end{array}$

Putting the values into the formula:

$\begin{array}{c}\Delta G=\Delta H-T\Delta S\\ =365-\left(388\right)\left(-0.0552\right)\\ =365+21.4\\ =386.4kJ\end{array}$

As Gibbs free energy change is positive, therefore reaction is non-spontaneous.

Interpretation Introduction

(d)

Interpretation:

Whether the given reactions are spontaneous or not needs to be determined.

Concept introduction:

A reaction is spontaneous if its Gibbs free energy change is negative. Gibbs free energy change is given by:

$\begin{array}{l}\Delta G=\Delta H-T\Delta S\\ where\\ \Delta GischangeinGibbsfreeenergy\\ \Delta Hischangeinenthalpy\\ \Delta Sischangeinentropy\\ TisTemperatureofreaction\end{array}$

Answer to Problem 46PP

The given reaction is spontaneous.

Explanation of Solution

Information given:

$\begin{array}{c}\Delta H=452kJ\\ \Delta S=55.7J/K\\ =0.0557kJ/K\\ T=165K\end{array}$

Putting the values into the formula:

$\begin{array}{c}\Delta G=\Delta H-T\Delta S\\ =452-\left(165\times 0.0557\right)\\ =452-9.19\\ =442.81kJ\end{array}$

As Gibbs free energy change is positive, therefore reaction is non-spontaneous.