Chapter 18, Problem 73SCQ

(a)

Interpretation Introduction

Interpretation:

It should be explained that whether the sign of entropy change for system, surroundings and universe is greater than zero or not.

Concept introduction:

The universe consists of two parts, systems and surroundings. The entropy change for the universe is the sum of entropy change for the system and for surroundings.

  ${\text{ΔS}}^{\text{o}}\left(\text{universe}\right){\text{= ΔS}}^{\text{o}}\left(\text{system}\right){\text{+ΔS}}^{\text{o}}\left(\text{surroundings}\right)$

The ${\text{ΔS}}^{\text{o}}\left(\text{universe}\right)$ should be greater than zero for a spontaneous process.

The ${\text{ ΔS}}^{\text{o}}\left(\text{system}\right)$ can be calculated by the following expression,

  ${\text{ΔS}}^{\text{o}}\left(\text{system}\right){\text{= Δ}}_{\text{r}}{\text{S}}^{\text{°}}\text{= }\sum {\text{nS}}^{\text{°}}\left(\text{products}\right)\text{-}\sum {\text{nS}}^{\text{°}}\left(\text{reactants}\right)$

The ${\text{ΔS}}^{\text{o}}\left(\text{surroundings}\right)$ can be calculated by the following expression,

  ${\text{ΔS}}^{\text{o}}\left(\text{surroundings}\right)\text{=}\frac{{\text{- Δ}}_{\text{r}}{\text{H}}^{\text{o}}}{\text{T}}$

Here, ${\text{Δ}}_{\text{r}}{\text{H}}^{\text{°}}$ is the enthalpy change for the reaction.

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ${\text{ΔG}}^{\text{o}}$. It is related to entropy and entropy by the following expression,

  ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}{\text{=Δ}}_{\text{r}}{\text{H}}^{\text{o}}{\text{-TΔ}}_{\text{r}}{\text{S}}^{\text{o}}$

${\text{ΔG}}^{\text{o}}$ is also related to the equilibrium constant $\text{K}$ by the equation,

  ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}{\text{= -RTlnK}}_{\text{p}}$

The rearranged expression is,

  ${\text{K}}_{\text{p}}{\text{= e}}^{\text{- }\frac{{\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}}{\text{RT}}}$

(b)

Interpretation Introduction

Interpretation:

The sign of ${\text{Δ}}_{\text{r}}{\text{H}}^{\text{°}}$ and ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}$ value for the given reaction should be predicted.

Concept introduction:

The universe consists of two parts, systems and surroundings. The entropy change for the universe is the sum of entropy change for the system and for surroundings.

  ${\text{ΔS}}^{\text{o}}\left(\text{universe}\right){\text{= ΔS}}^{\text{o}}\left(\text{system}\right){\text{+ΔS}}^{\text{o}}\left(\text{surroundings}\right)$

The ${\text{ΔS}}^{\text{o}}\left(\text{universe}\right)$ should be greater than zero for a spontaneous process.

The ${\text{ ΔS}}^{\text{o}}\left(\text{system}\right)$ can be calculated by the following expression,

  ${\text{ΔS}}^{\text{o}}\left(\text{system}\right){\text{= Δ}}_{\text{r}}{\text{S}}^{\text{°}}\text{= }\sum {\text{nS}}^{\text{°}}\left(\text{products}\right)\text{-}\sum {\text{nS}}^{\text{°}}\left(\text{reactants}\right)$

The ${\text{ΔS}}^{\text{o}}\left(\text{surroundings}\right)$ can be calculated by the following expression,

  ${\text{ΔS}}^{\text{o}}\left(\text{surroundings}\right)\text{=}\frac{{\text{- Δ}}_{\text{r}}{\text{H}}^{\text{o}}}{\text{T}}$

Here, ${\text{Δ}}_{\text{r}}{\text{H}}^{\text{°}}$ is the enthalpy change for the reaction.

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ${\text{ΔG}}^{\text{o}}$. It is related to entropy and entropy by the following expression,

  ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}{\text{=Δ}}_{\text{r}}{\text{H}}^{\text{o}}{\text{-TΔ}}_{\text{r}}{\text{S}}^{\text{o}}$

${\text{ΔG}}^{\text{o}}$ is also related to the equilibrium constant $\text{K}$ by the equation,

  ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}{\text{= -RTlnK}}_{\text{p}}$

The rearranged expression is,

  ${\text{K}}_{\text{p}}{\text{= e}}^{\text{- }\frac{{\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}}{\text{RT}}}$

(c)

Interpretation Introduction

Interpretation:

It should be identified that whether the value of ${\text{K}}_{\text{p}}$ is very large, very small or nearer to 1 also that the equilibrium constant will be larger or smaller for temperatures greater than $298K$.

Concept introduction:

The universe consists of two parts, systems and surroundings. The entropy change for the universe is the sum of entropy change for the system and for surroundings.

  ${\text{ΔS}}^{\text{o}}\left(\text{universe}\right){\text{= ΔS}}^{\text{o}}\left(\text{system}\right){\text{+ΔS}}^{\text{o}}\left(\text{surroundings}\right)$

The ${\text{ΔS}}^{\text{o}}\left(\text{universe}\right)$ should be greater than zero for a spontaneous process.

The ${\text{ ΔS}}^{\text{o}}\left(\text{system}\right)$ can be calculated by the following expression,

  ${\text{ΔS}}^{\text{o}}\left(\text{system}\right){\text{= Δ}}_{\text{r}}{\text{S}}^{\text{°}}\text{= }\sum {\text{nS}}^{\text{°}}\left(\text{products}\right)\text{-}\sum {\text{nS}}^{\text{°}}\left(\text{reactants}\right)$

The ${\text{ΔS}}^{\text{o}}\left(\text{surroundings}\right)$ can be calculated by the following expression,

  ${\text{ΔS}}^{\text{o}}\left(\text{surroundings}\right)\text{=}\frac{{\text{- Δ}}_{\text{r}}{\text{H}}^{\text{o}}}{\text{T}}$

Here, ${\text{Δ}}_{\text{r}}{\text{H}}^{\text{°}}$ is the enthalpy change for the reaction.

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ${\text{ΔG}}^{\text{o}}$. It is related to entropy and entropy by the following expression,

  ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}{\text{=Δ}}_{\text{r}}{\text{H}}^{\text{o}}{\text{-TΔ}}_{\text{r}}{\text{S}}^{\text{o}}$

${\text{ΔG}}^{\text{o}}$ is also related to the equilibrium constant $\text{K}$ by the equation,

  ${\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}{\text{= -RTlnK}}_{\text{p}}$

The rearranged expression is,

  ${\text{K}}_{\text{p}}{\text{= e}}^{\text{- }\frac{{\text{Δ}}_{\text{r}}{\text{G}}^{\text{o}}}{\text{RT}}}$