Chapter 2, Problem 2.23P

(a)

Interpretation Introduction

Interpretation:

Standard enthalpies of the given reaction whether increases (or) decreases with increasing temperature should be decided.

Concept introduction:

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.

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

Where,

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

${\text{ΔH}}^{\text{°}}{}_{\text{produdcts}}$ is the standard entropy of the products

Standard free energy change:

Standard free energy change is measured by subtracting the product of temperature and standard entropy change from the standard enthalpy change of a system.

  $\begin{array}{l}{\text{ΔG}}^{\text{o}}\text{=}{\text{ΔH}}^{\text{o}}\text{-}{\text{TΔS}}^{\text{o}}\\ \text{where,}\\ {\text{ΔG}}^{\text{o}}\text{-}\text{standard}\text{free}\text{energy change}\\ {\text{ΔH}}^{\text{o}}\text{-}\text{standard}\text{enthalpy}\text{change}\\ {\text{ΔS}}^{\text{o}}\text{-}\text{standard}\text{entropy change}\text{and T}\text{-}\text{temperature}\text{.}\end{array}$

Explanation of Solution

According to second law of thermodynamic changes in enthalpy

  $\Delta H=\Delta U+\Delta nRT------[1]$

Where

  $\begin{array}{l}\left(\Delta n\right)sumofstoichiometriccoefficientofproducts-\\ sumofstoichiometriccoefficientof\text{Reactants}\end{array}$

Given enthalpy reaction is,

  $2H_2\left(g\right)+O_2\left(g\right)\stackrel{}{\to }2H_{2}O\left(g\right)$

Plugging in $\left(\Delta n\right)$ in equation (1),

  $\Delta n=\left(2\right)-\left(2+1\right)=-1$

Therefore, the $\Delta H=\Delta U+\Delta nRT$ as temperature increase and $\left(\Delta H\right)$ value is decreases

(b)

Interpretation Introduction

Interpretation:

Standard enthalpies of the given reaction whether increases (or) decreases with increasing temperature should be decided.

Concept introduction:

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.

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

Where,

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

${\text{ΔH}}^{\text{°}}{}_{\text{produdcts}}$ is the standard entropy of the products

Standard free energy change:

Standard free energy change is measured by subtracting the product of temperature and standard entropy change from the standard enthalpy change of a system.

  $\begin{array}{l}{\text{ΔG}}^{\text{o}}\text{=}{\text{ΔH}}^{\text{o}}\text{-}{\text{TΔS}}^{\text{o}}\\ \text{where,}\\ {\text{ΔG}}^{\text{o}}\text{-}\text{standard}\text{free}\text{energy change}\\ {\text{ΔH}}^{\text{o}}\text{-}\text{standard}\text{enthalpy}\text{change}\\ {\text{ΔS}}^{\text{o}}\text{-}\text{standard}\text{entropy change}\text{and T}\text{-}\text{temperature}\text{.}\end{array}$

Explanation of Solution

Second law of thermodynamic changes in enthalpy

  $\Delta H=\Delta U+\Delta nRT------[1]$

Where

  $\begin{array}{l}\left(\Delta n\right)sumofstoichiometriccoefficientofproducts-\\ sumofstoichiometriccoefficientof\text{Reactants}\end{array}$

Given enthalpy reaction is,

  $C{H}_4\left(g\right)+2O_2\left(g\right)\stackrel{}{\to }C{O}_2\left(g\right)+2H_{2}O\left(g\right)$

Plugging in $\left(\Delta n\right)$ in equation (1),

  $\Delta n=\left(2+1\right)-\left(2+1\right)=0$

Hence, the internal energy $\left(\Delta U\right)$ depended only on temperature; it is increase as temperature increase and same for $\left(\Delta H\right)$.

As temperature increase and $\left(\Delta H\right)$ value is Increases

(c)

Interpretation Introduction

Interpretation:

Standard enthalpies of the given reaction whether increases (or) decreases with increasing temperature should be decided.

Concept introduction:

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.

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

Where,

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

${\text{ΔH}}^{\text{°}}{}_{\text{produdcts}}$ is the standard entropy of the products

Standard free energy change:

Standard free energy change is measured by subtracting the product of temperature and standard entropy change from the standard enthalpy change of a system.

$\begin{array}{l}{\text{ΔG}}^{\text{o}}\text{=}{\text{ΔH}}^{\text{o}}\text{-}{\text{TΔS}}^{\text{o}}\\ \text{where,}\\ {\text{ΔG}}^{\text{o}}\text{-}\text{standard}\text{free}\text{energy change}\\ {\text{ΔH}}^{\text{o}}\text{-}\text{standard}\text{enthalpy}\text{change}\\ {\text{ΔS}}^{\text{o}}\text{-}\text{standard}\text{entropy change}\text{and T}\text{-}\text{temperature}\text{.}\end{array}$

Explanation of Solution

Second law of thermodynamic changes in enthalpy

  $\Delta H=\Delta U+\Delta nRT------[1]$

Where

  $\begin{array}{l}\left(\Delta n\right)sumofstoichiometriccoefficientofproducts-\\ sumofstoichiometriccoefficientof\text{Reactants}\end{array}$

Given enthalpy reaction is,

  $N_2\left(g\right)+3H_2\left(g\right)\stackrel{}{\to }2N{H}_3\left(g\right)$

Put in $\left(\Delta n\right)$ in equation (1),

  $\Delta n=\left(2\right)-\left(3+1\right)=-2$

Therefore, the $\Delta H=\Delta U+\Delta nRT$ as temperature increase and $\left(\Delta H\right)$ value is decreases