Chapter 23, Problem 23.16P

(a)

Interpretation Introduction

Interpretation:

Value of $\Delta S_{rxn}^o$ has to be determined for the reaction $2{\text{ H}}_{\text{2}}{\text{O}}_{\text{2}}\left(l\right){\text{ + N}}_{\text{2}}{\text{H}}_{\text{4}}\left(l\right)\underset{}{\to }{\text{N}}_{\text{2}}\left(g\right){\text{+ 4 H}}_{2}O\left(g\right)$.

Concept Introduction:

Entropy$\left(S\right)$: it is used to describe the disorder. It is the amount of arrangements possible in a system at a particular state.

Value of $\Delta S_{rxn}^o$ can be calculated by the equation:

  $\Delta S_{rxn}^o\text{= }S°\left[\text{products}\right]-S°\left[\text{reactants}\right]$

Answer to Problem 23.16P

Value of $\Delta S_{rxn}^o$ is $\text{606}\text{.4}\text{J}/\text{K}\cdot \text{mol}$.

Explanation of Solution

The given reaction is shown below,

  $2{\text{ H}}_{\text{2}}{\text{O}}_{\text{2}}\left(l\right){\text{ + N}}_{\text{2}}{\text{H}}_{\text{4}}\left(l\right)\underset{}{\to }{\text{N}}_{\text{2}}\left(g\right){\text{+ 4 H}}_{2}O\left(g\right)$

Standard entropy of formation values is given below,

  $\begin{array}{c}\text{Δ}S°\left[{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\left(l\right)\right]\text{=}\text{109}\text{.6}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{N}}_{\text{2}}{\text{H}}_{\text{4}}\left(l\right)\right]\text{=}\text{121}\text{.2}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{N}}_{\text{2}}\left(g\right)\right]\text{=}\text{191}\text{.6}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{H}}_{2}O\left(g\right)\right]\text{=}\text{188}\text{.8}\text{J}/\text{K}\cdot \text{mol}\end{array}$

Value of $\Delta S_{rxn}^o$ can be calculated by the equation:

  $\Delta S_{rxn}^o\text{= }S°\left[\text{products}\right]-S°\left[\text{reactants}\right]$

Substitute the values as follows,

  $\begin{array}{c}\Delta S_{rxn}^o\text{= }\left[\left(1\right)\left(\text{191}\text{.6}\text{J}/\text{K}\cdot \text{mol}\right)+\left(4\right)\left(\text{188}\text{.8}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ -\left[\left(2\right)\left(\text{109}\text{.6}\text{J}/\text{K}\cdot \text{mol}\right)+\left(1\right)\left(\text{121}\text{.2}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ \\ =\text{ 606}\text{.4}\text{J}/\text{K}\cdot \text{mol}\end{array}$

(b)

Interpretation Introduction

Interpretation:

Value of $\Delta S_{rxn}^o$ has to be determined for the reaction ${\text{N}}_{\text{2}}\left(g\right){\text{ + O}}_{\text{2}}\left(g\right)\underset{}{\to }\text{2 }NO\left(g\right)$.

Concept Introduction:

Refer to (a).

Answer to Problem 23.16P

Value of $\Delta S_{rxn}^o$ is $\text{24}\text{.8}\text{J}/\text{K}\cdot \text{mol}$.

Explanation of Solution

The given reaction is shown below,

  ${\text{N}}_{\text{2}}\left(g\right){\text{ + O}}_{\text{2}}\left(g\right)\underset{}{\to }\text{2 }NO\left(g\right)$

Standard entropy of formation values is given below,

  $\begin{array}{c}\text{Δ}S°\left[\text{NO}\left(g\right)\right]\text{=}\text{210}\text{.8}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{N}}_{\text{2}}\left(g\right)\right]\text{=}\text{191}\text{.6}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{O}}_{\text{2}}\left(g\right)\right]\text{=}\text{205}\text{.2}\text{J}/\text{K}\cdot \text{mol}\end{array}$

Value of $\Delta S_{rxn}^o$ can be calculated by the equation:

  $\Delta S_{rxn}^o\text{= }S°\left[\text{products}\right]-S°\left[\text{reactants}\right]$

Substitute the values as follows,

  $\begin{array}{c}\Delta S_{rxn}^o\text{= }\left[\left(2\right)\left(\text{210}\text{.8}\text{J}/\text{K}\cdot \text{mol}\right)\right]-\left[\left(1\right)\left(\text{191}\text{.6}\text{J}/\text{K}\cdot \text{mol}\right)+\left(1\right)\left(\text{205}\text{.2}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ \\ =\text{ 24}\text{.8}\text{J}/\text{K}\cdot \text{mol}\end{array}$

(c)

Interpretation Introduction

Interpretation:

Value of $\Delta S_{rxn}^o$ has to be determined for the reaction ${\text{2 CH}}_4\left(g\right){\text{ + O}}_{\text{2}}\left(g\right)\underset{}{\to }\text{2 }C{H}_{3}OH\left(l\right)$.

Concept Introduction:

Refer to (a).

Answer to Problem 23.16P

Value of $\Delta S_{rxn}^o$ is $-\text{324}\text{.2}\text{J}/\text{K}\cdot \text{mol}$.

Explanation of Solution

The given reaction is shown below,

  ${\text{2 CH}}_4\left(g\right){\text{ + O}}_{\text{2}}\left(g\right)\underset{}{\to }\text{2 }C{H}_{3}OH\left(l\right)$

Standard entropy of formation values is given below,

  $\begin{array}{c}\text{Δ}S°\left[C{H}_{3}OH\left(l\right)\right]\text{=}\text{126}\text{.8}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{CH}}_4\left(g\right)\right]\text{=}\text{186}\text{.3}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{O}}_{\text{2}}\left(g\right)\right]\text{=}\text{205}\text{.2}\text{J}/\text{K}\cdot \text{mol}\end{array}$

Value of $\Delta S_{rxn}^o$ can be calculated by the equation:

  $\Delta S_{rxn}^o\text{= }S°\left[\text{products}\right]-S°\left[\text{reactants}\right]$

Substitute the values as follows,

  $\begin{array}{c}\Delta S_{rxn}^o\text{= }\left[\left(2\right)\left(\text{126}\text{.8}\text{J}/\text{K}\cdot \text{mol}\right)\right]-\left[\left(2\right)\left(\text{186}\text{.3}\text{J}/\text{K}\cdot \text{mol}\right)+\left(1\right)\left(\text{205}\text{.2}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ \\ =-\text{324}\text{.2}\text{J}/\text{K}\cdot \text{mol}\end{array}$

(d)

Interpretation Introduction

Interpretation:

Value of $\Delta S_{rxn}^o$ has to be determined for the reaction ${\text{C}}_2{\text{H}}_4\left(g\right){\text{ + H}}_{\text{2}}\left(g\right)\underset{}{\to }{C}_2{H}_6\left(g\right)$.

Concept Introduction:

Refer to (a).

Answer to Problem 23.16P

Value of $\Delta S_{rxn}^o$ is $-\text{120}\text{.8}\text{J}/\text{K}\cdot \text{mol}$.

Explanation of Solution

The given reaction is shown below,

  ${\text{C}}_2{\text{H}}_4\left(g\right){\text{ + H}}_{\text{2}}\left(g\right)\underset{}{\to }{C}_2{H}_6\left(g\right)$

Standard entropy of formation values is given below,

  $\begin{array}{c}\text{Δ}S°\left[C_2{H}_6\left(g\right)\right]\text{= }\text{229}\text{.2}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{C}}_2{\text{H}}_4\left(g\right)\right]\text{=}\text{219}\text{.3}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{H}}_{\text{2}}\left(g\right)\right]\text{=}\text{130}\text{.7}\text{J}/\text{K}\cdot \text{mol}\end{array}$

Value of $\Delta S_{rxn}^o$ can be calculated by the equation:

  $\Delta S_{rxn}^o\text{= }S°\left[\text{products}\right]-S°\left[\text{reactants}\right]$

Substitute the values as follows,

  $\begin{array}{c}\Delta S_{rxn}^o\text{= }\left[\left(1\right)\left(\text{229}\text{.2}\text{J}/\text{K}\cdot \text{mol}\right)\right]-\left[\left(1\right)\left(\text{219}\text{.3}\text{J}/\text{K}\cdot \text{mol}\right)+\left(1\right)\left(\text{130}\text{.7}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ \\ =-\text{120}\text{.8}\text{J}/\text{K}\cdot \text{mol}\end{array}$