Chapter 20.3, Problem 20.7AFP

(a)

Interpretation Introduction

Interpretation:

The given reaction has to be determined that whether it is spontaneous at $298K$.

    $4NO\left(g\right)\stackrel{}{\to }{N}_{2}O\left(g\right)+N_2{O}_3\left(g\right)$

Concept introduction:

Entropy is the measure of randomness in the system.  Standard entropy change in a reaction is the difference in entropy of the products and reactants  ${\text{(ΔS}}^{\text{°}}{}_{\text{rxn}}\text{)}$ can be calculated by the following equation.

  ${\text{ΔS}}^{\text{°}}{}_{\text{rxn}}{\text{ = S}}^{\text{°}}{}_{\text{Products}}-{\text{ S}}^{\text{°}}{}_{\text{reactants}}$

Where,

  ${\text{S}}^{\text{°}}{}_{\text{reactants}}$ is the standard entropy of the reactants

  ${\text{S}}^{\text{°}}{}_{\text{Products}}$ is the standard entropy of the products

Standard free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter $G^o$.  All spontaneous process is associated with the decrease of free energy in the system.  The equation given below helps us to calculate the change in free energy in a system.

  ${\text{ΔG}}_{\text{rxn}}^{\text{o}}\text{ = }\Delta {{\rm H}}_{\text{rxn}}^{\text{o}}\text{- T}\Delta {\text{S}}_{\text{rxn}}^{\text{o}}$

Where,

${\text{ΔG}}_{\text{rxn}}^{\text{o}}$ is the change in standard free energy of the system

$\Delta {{\rm H}}_{\text{rxn}}^{\text{o}}$ is the change in standard enthalpy of the system

$\text{T}$ is the absolute value of the temperature

$\Delta {\text{S}}_{\text{rxn}}^{\text{o}}$ is the change in entropy in the system

(b)

Interpretation Introduction

Interpretation:

Following reaction become more or less spontaneous at higher temperature has to be determined.

    $4NO\left(g\right)\stackrel{}{\to }{N}_{2}O\left(g\right)+N_2{O}_3\left(g\right)$

Concept introduction:

 Standard free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter $G^o$.  All spontaneous process is associated with the decrease of free energy in the system.  The equation given below helps us to calculate the change in free energy in a system.

${\text{ΔG}}_{\text{rxn}}^{\text{o}}\text{ = }\Delta {{\rm H}}_{\text{rxn}}^{\text{o}}\text{- T}\Delta {\text{S}}_{\text{rxn}}^{\text{o}}$

Where,

${\text{ΔG}}_{\text{rxn}}^{\text{o}}$ is the change in standard free energy of the system

$\Delta {{\rm H}}_{\text{rxn}}^{\text{o}}$ is the change in standard enthalpy of the system

$\text{T}$ is the absolute value of the temperature

$\Delta {\text{S}}_{\text{rxn}}^{\text{o}}$ is the change in entropy in the system

(c)

Interpretation Introduction

Interpretation:

For following reaction under given condition that $\Delta Sand\Delta H$ doesn’t change with $T$, the free energy $\Delta G$ has to be calculated at ${500}^{o}C$.

    $4NO\left(g\right)\stackrel{}{\to }{N}_{2}O\left(g\right)+N_2{O}_3\left(g\right)$

Concept introduction:

Standard free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter $G^o$.  All spontaneous process is associated with the decrease of free energy in the system.  The equation given below helps us to calculate the change in free energy in a system.

  ${\text{ΔG}}_{\text{rxn}}^{\text{o}}\text{ = }\Delta {{\rm H}}_{\text{rxn}}^{\text{o}}\text{- T}\Delta {\text{S}}_{\text{rxn}}^{\text{o}}$

Where,

${\text{ΔG}}_{\text{rxn}}^{\text{o}}$ is the change in standard free energy of the system

$\Delta {{\rm H}}_{\text{rxn}}^{\text{o}}$ is the change in standard enthalpy of the system

$\text{T}$ is the absolute value of the temperature

$\Delta {\text{S}}_{\text{rxn}}^{\text{o}}$ is the change in entropy in the system