Chapter 20, Problem 20.108P

(a)

Interpretation Introduction

Interpretation:

For the formation of ammonia reaction the temperature has to be calculated at which $K_p=1.00$ and using given assumption that $\Delta H^{o}and\Delta S^o$ are constant.

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

Entropy is a thermodynamic quantity, which is the measure of randomness in a system.  The term entropy is useful in explaining the spontaneity of a process. For all spontaneous process in an isolated system there will be an increase in entropy. Entropy is represented by the letter ‘S’.  It is a state function.  The change in entropy gives information about the magnitude and direction of a process.  The entropy changes associated with a phase transition reaction can be found by the following equation.

  ${\text{ΔS}}^{\text{o}}\text{}\text{=}\text{}\text{}\frac{{\text{ΔΗ}}^{\text{o}}-{\text{ΔG}}^{\text{o}}}{\text{Τ}}$

Where,

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

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

(b)

Interpretation Introduction

Interpretation:

For the given ammonia formation reaction the ${\text{K}}_{\text{p}}$ value has to be calculated at $400{}^{o}C$.

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.

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

Free energy change$\text{ΔG}$: change in the free energy takes place while reactants convert to product where both are in standard state. It depends on the equilibrium constant $\text{K}$,

  $\begin{array}{l}\text{ΔG =}{\text{ΔG}}^{\text{o}}\text{+}\text{RT}\ln \left(\text{K}\right)\\ \\ {\text{ΔG}}^{\text{o}}\text{=}{\text{ΔH}}^{\text{o}}-{\text{TΔS}}^{\text{o}}\end{array}$

  Where,

  $\text{T}$ is the temperature

  $\text{ΔG}$ is the free energy

  ${\text{ΔG}}^{\text{o}}$, ${\text{ΔH}}^{\text{o}}$ and ${\text{ΔS}}^{\text{o}}$ is standard free energy, enthalpy and entropy values.

(c)

Interpretation Introduction

Interpretation:

The reason that why industrial ammonia formation process requires lower ${\text{K}}_{\text{p}}$ at higher temperature has to be given.

Concept introduction:

Equilibrium pressure$\left({\text{K}}_{\text{p}}\right)$: For gaseous substances the concentration will be proportional to its partial pressure.  The equilibrium constant for gaseous reactions can be expressed in terms of the partial pressures of the gaseous products and reactants, and it is called equilibrium constant ${\text{K}}_{\text{p}}$. The value of ${\text{K}}_{\text{p}}$ is different from ${\text{K}}_c$.  The relation between ${\text{K}}_{\text{p}}$ and ${\text{K}}_c$ is given below.

    ${\text{K}}_{\text{p}}={\text{K}}_{\text{c}}{\text{RT}}^{\text{Δn}}$

Where,

    R is the universal gas constant

    T is the temperature

    $\text{Δn}$ is the difference between the number of gaseous products to reactants.

Le Chatelier’s principle:  When a system at equilibrium is disturbed, the system will adjust itself to nullify the effect and maintain the equilibrium.