Chapter 23, Problem 23.15P

(a)

Interpretation Introduction

Interpretation:

Value of $\Delta S_{rxn}^o$ has to be determined for the reaction $4{\text{ NH}}_{\text{3}}\left(g\right){\text{ + 7 O}}_2\left(g\right)\underset{}{\to }4{\text{NO}}_{\text{2}}\left(g\right){\text{+ 6 H}}_{2}O\left(g\right)$.

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 23.15P

Value of $\Delta S_{rxn}^o$ is $-114.4\text{J}/\text{K}\cdot \text{mol}$.

Explanation of Solution

The given reaction is shown below,

  $4{\text{ NH}}_{\text{3}}\left(g\right){\text{ + 7 O}}_2\left(g\right)\underset{}{\to }4{\text{NO}}_{\text{2}}\left(g\right){\text{+ 6 H}}_{2}O\left(g\right)$

Standard entropy of formation values is given below,

  $\begin{array}{c}\text{Δ}S°\left[{\text{NH}}_{\text{3}}\left(g\right)\right]\text{=}\text{192}\text{.8}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{O}}_2\left(g\right)\right]\text{=}\text{205}\text{.2}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{NO}}_{\text{2}}\left(g\right)\right]\text{=}\text{240}\text{.1}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{H}}_{2}O\left(g\right)\right]\text{=}\text{188}\text{.8}\text{J}/\text{K}\cdot \text{mol}\end{array}$

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,

  $\begin{array}{c}\Delta S_{rxn}^o\text{= }\left[\left(4\right)\left(\text{240}\text{.1}\text{J}/\text{K}\cdot \text{mol}\right)+\left(6\right)\left(\text{188}\text{.8}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ -\left[\left(4\right)\left(\text{192}\text{.8}\text{J}/\text{K}\cdot \text{mol}\right)+\left(7\right)\left(\text{205}\text{.2}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ \\ =-114.4\text{J}/\text{K}\cdot \text{mol}\end{array}$

(b)

Interpretation Introduction

Interpretation:

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

Concept Introduction:

Refer to (a).

Answer to Problem 23.15P

Value of $\Delta S_{rxn}^o$ is $-\text{332}\text{.3}\text{J}/\text{K}\cdot \text{mol}$.

Explanation of Solution

The given reaction is shown below,

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

Standard entropy of formation values is given below,

  $\begin{array}{c}\text{Δ}S°\left[C{H}_{3}OH\left(l\right)\right]\text{=}\text{126}\text{.8}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{H}}_{\text{2}}\left(g\right)\right]\text{=}\text{130}\text{.7}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[\text{CO}\left(g\right)\right]\text{=}\text{197}\text{.7}\text{J}/\text{K}\cdot \text{mol}\end{array}$

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,

  $\begin{array}{c}\Delta S_{rxn}^o\text{= }\left[\left(1\right)\left(\text{126}\text{.8}\text{J}/\text{K}\cdot \text{mol}\right)\right]-\left[\left(1\right)\left(\text{197}\text{.7}\text{J}/\text{K}\cdot \text{mol}\right)+\left(2\right)\left(\text{130}\text{.7}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ \\ =-\text{332}\text{.3}\text{J}/\text{K}\cdot \text{mol}\end{array}$

(c)

Interpretation Introduction

Interpretation:

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

Concept Introduction:

Refer to (a).

Answer to Problem 23.15P

Value of $\Delta S_{rxn}^o$ is $133.9\text{J}/\text{K}\cdot \text{mol}$.

Explanation of Solution

The given reaction is shown below,

  $C\left(s,\text{ graphite}\right){\text{ + H}}_{\text{2}}O\left(g\right)\underset{}{\to }CO\left(g\right){\text{ + H}}_2\left(g\right)$

Standard entropy of formation values is given below,

  $\begin{array}{c}\text{Δ}S°\left[C\left(s,\text{ graphite}\right)\right]\text{=}\text{5}\text{.7}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{H}}_{\text{2}}O\left(g\right)\right]\text{=}\text{188}\text{.8}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[CO\left(g\right)\right]\text{=}\text{197}\text{.7}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{H}}_2\left(g\right)\right]\text{=}\text{130}\text{.7}\text{J}/\text{K}\cdot \text{mol}\end{array}$

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,

  $\begin{array}{c}\Delta S_{rxn}^o\text{= }\left[\left(1\right)\left(\text{197}\text{.7}\text{J}/\text{K}\cdot \text{mol}\right)+\left(1\right)\left(\text{130}\text{.7}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ -\left[\left(1\right)\left(\text{5}\text{.7}\text{J}/\text{K}\cdot \text{mol}\right)+\left(1\right)\left(\text{188}\text{.8}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ \\ =133.9\text{J}/\text{K}\cdot \text{mol}\end{array}$

(d)

Interpretation Introduction

Interpretation:

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

Concept Introduction:

Refer to (a).

Answer to Problem 23.15P

Value of $\Delta S_{rxn}^o$ is $-\text{173}\text{J}/\text{K}\cdot \text{mol}$.

Explanation of Solution

The given reaction is shown below,

  $2\text{ CO}\left(g\right){\text{ + O}}_{\text{2}}\left(g\right)\underset{}{\to }2{\text{ CO}}_2\left(g\right)$

Standard entropy of formation values is given below,

  $\begin{array}{c}\text{Δ}S°\left[\text{CO}\left(g\right)\right]\text{= 197}\text{.7}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{O}}_{\text{2}}\left(g\right)\right]\text{=}\text{205}\text{.2}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{CO}}_2\left(g\right)\right]\text{=}\text{213}\text{.8}\text{J}/\text{K}\cdot \text{mol}\end{array}$

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,

  $\begin{array}{c}\Delta S_{rxn}^o\text{= }\left[\left(2\right)\left(\text{213}\text{.8}\text{J}/\text{K}\cdot \text{mol}\right)\right]-\left[\left(2\right)\left(\text{197}\text{.7}\text{J}/\text{K}\cdot \text{mol}\right)+\left(1\right)\left(\text{205}\text{.2}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ \\ =-\text{173}\text{J}/\text{K}\cdot \text{mol}\end{array}$