Chapter 20, Problem 20.59P

(a)

Interpretation Introduction

Interpretation:

For given gaseous reaction the enthalpy ${\text{ΔH}}^{\text{o}}$ and entropy ${\text{ΔS}}^{\text{o}}$ value have to be calculated at $298K$.

Concept introduction:

Entropy change: The sign of ${\text{ΔS}}^{\text{o}}$ for a reaction is determined by using the following rules:

• When a molecule is broken down and gives two or more smaller molecules.
• When the moles of gas is increases (by the breaking of molecules)
• Solid changes to liquid or gas state or liquid state changes to gas state.

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.

  ${\text{ΔS}}^{\text{°}}{}_{\text{rxn}}\text{ = }{\displaystyle \sum \text{m }}{\text{S}}^{\text{°}}{}_{\text{Products}}-{\displaystyle \sum \text{n}}{\text{S}}^{\text{°}}{}_{\text{reactants}}$

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

Entropy changes: it is used to describe the disorder. It is the amount of arrangements possible in a system at a particular state.

If the disorder increases in a system, then $\Delta S>0$ positive

If the disorder decreases in a system, then $\Delta S<0$ negative

If the disorder equal in a system, then $\Delta S=0$

Enthalpy is the amount energy absorbed or released in a process.

The enthalpy change in a system $\text{(Δ}{{\rm H}}_{\text{sys}}\text{)}$ can be calculated by the following equation.

  ${\text{ΔH}}_{\text{rxn}}\text{ = }{\displaystyle \sum {\text{ΔH}}^{\text{°}}{}_{\text{produdcts}}}\text{-}{\displaystyle \sum {\text{ΔH}}^{\text{°}}{}_{\text{reactants}}}$

Where,

  ${\text{ΔH}}_{\text{f}}^{\text{o}}{}_{\left(\text{reactants}\right)}$ is the standard enthalpy of the reactants

  ${\text{ΔH}}_{\text{f}}^{\text{o}}{}_{\left(\text{produdcts}\right)}$ is the standard enthalpy of the products

(b)

Interpretation Introduction

Interpretation:

For given decomposition reaction the standard free energy ${\text{ΔG }}^{\text{o}}$ value has to be calculated at ${28}^{o}C,{128}^{o}Cand228{}^{o}C$.

Concept introduction:

Free energy (or) entropy change 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.  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.

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

Where,

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

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

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

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

(c)

Interpretation Introduction

Interpretation:

For the given reaction the significance of $\text{ΔG}$ values have to be founded.

Concept introduction:

In thermodynamics a process is spontaneous if it is taking place by itself without the help of external energy.  All spontaneous process will have highly energetic initial state than the final state.  This indicates that while the process occurs, there is a decrease in free energy of the system. The increase in randomness also favors the spontaneity of a process.

In non-spontaneous process, there is a requirement of external energy source.  The free energy of the system increases.  The entropy decreases in non-spontaneous process.

(d)

Interpretation Introduction

Interpretation:

For the given reaction, in which temperature become spontaneous has to be determined.

Concept introduction:

In thermodynamics a process is spontaneous if it is taking place by itself without the help of external energy.  All spontaneous process will have highly energetic initial state than the final state.  This indicates that while the process occurs, there is a decrease in free energy of the system. The increase in randomness also favors the spontaneity of a process.

In non-spontaneous process, there is a requirement of external energy source.  The free energy of the system increases.  The entropy decreases in non-spontaneous process.