Chapter 23, Problem 23.64P

(a)

Interpretation Introduction

Interpretation:

Value of $\Delta S_{rxn}^o$ has to be determined for the reaction $I_2\left(s\right)\underset{}{\to }{I}_2\left(g\right)$.

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 23.64P

Value of $\Delta S_{rxn}^o$ is $\text{144}\text{.6}\text{J}/\text{K}\cdot \text{mol}$.

Explanation of Solution

The given reaction is shown below,

  $I_2\left(s\right)\underset{}{\to }{I}_2\left(g\right)$

Standard enthalpy of formation values is given below,

  $\begin{array}{c}\text{Δ}S°\left[I_2\left(s\right)\right]\text{=}\text{116}\text{.1}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[I_2\left(g\right)\right]\text{=}\text{260}\text{.7}\text{J}/\text{K}\cdot \text{mol}\end{array}$

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,

  $\begin{array}{c}\Delta S_{rxn}^o\text{= }\left[\left(1\right)\left(\text{260}\text{.7}\text{J}/\text{K}\cdot \text{mol}\right)\right]-\left[\left(1\right)\left(\text{116}\text{.1}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ \\ =\text{ 144}\text{.6}\text{J}/\text{K}\cdot \text{mol}\end{array}$

(b)

Interpretation Introduction

Interpretation:

Value of $\Delta S_{rxn}^o$ has to be determined for the reaction ${\text{BaCO}}_{\text{3}}\left(s\right)\underset{}{\to }\text{BaO}\left(s\right)\text{ + }C{O}_2\left(g\right)$.

Concept Introduction:

Refer to (a).

Answer to Problem 23.64P

Value of $\Delta S_{rxn}^o$ is $\text{173}\text{.8}\text{J}/\text{K}\cdot \text{mol}$.

Explanation of Solution

The given reaction is shown below,

  ${\text{BaCO}}_{\text{3}}\left(s\right)\underset{}{\to }\text{BaO}\left(s\right)\text{ + }C{O}_2\left(g\right)$

Standard enthalpy of formation values is given below,

  $\begin{array}{c}\text{Δ}S°\left[{\text{BaCO}}_{\text{3}}\left(s\right)\right]\text{=}\text{112}\text{.1}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[\text{BaO}\left(s\right)\right]\text{=}\text{72}\text{.1}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[C{O}_2\left(g\right)\right]\text{=}\text{213}\text{.8}\text{J}/\text{K}\cdot \text{mol}\end{array}$

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,

  $\begin{array}{c}\Delta S_{rxn}^o\text{= }\left[\left(1\right)\left(\text{72}\text{.1}\text{J}/\text{K}\cdot \text{mol}\right)+\left(1\right)\left(\text{213}\text{.8}\text{J}/\text{K}\cdot \text{mol}\right)\right]-\left[\left(1\right)\left(\text{112}\text{.1}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ \\ =\text{ 173}\text{.8}\text{J}/\text{K}\cdot \text{mol}\end{array}$

(c)

Interpretation Introduction

Interpretation:

Value of $\Delta S_{rxn}^o$ has to be determined for the reaction ${\text{CH}}_{\text{4}}\left(g\right){\text{ + Cl}}_{\text{2}}\left(g\right)\underset{}{\to }{\text{CH}}_{\text{3}}\text{Cl}\left(g\right)\text{+ HCl}\left(g\right)$.

Concept Introduction:

Refer to (a).

Answer to Problem 23.64P

Value of $\Delta S_{rxn}^o$ is $\text{12}\text{.1}\text{J}/\text{K}\cdot \text{mol}$.

Explanation of Solution

The given reaction is shown below,

  ${\text{CH}}_{\text{4}}\left(g\right){\text{ + Cl}}_{\text{2}}\left(g\right)\underset{}{\to }{\text{CH}}_{\text{3}}\text{Cl}\left(g\right)\text{+ HCl}\left(g\right)$

Standard enthalpy of formation values is given below,

  $\begin{array}{c}\text{Δ}S°\left[{\text{CH}}_{\text{4}}\left(g\right)\right]\text{=}\text{186}\text{.3}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{Cl}}_{\text{2}}\left(g\right)\right]\text{=}\text{223}\text{.1}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{CH}}_{\text{3}}\text{Cl}\left(g\right)\right]\text{=}\text{234}\text{.6}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[\text{HCl}\left(g\right)\right]\text{=}\text{186}\text{.9}\text{J}/\text{K}\cdot \text{mol}\end{array}$

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,

  $\begin{array}{c}\Delta S_{rxn}^o\text{= }\left[\left(1\right)\left(\text{234}\text{.6}\text{J}/\text{K}\cdot \text{mol}\right)+\left(1\right)\left(\text{186}\text{.9}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ -\left[\left(1\right)\left(\text{186}\text{.3}\text{J}/\text{K}\cdot \text{mol}\right)+\left(1\right)\left(\text{223}\text{.1}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ \\ =\text{ 12}\text{.1}\text{J}/\text{K}\cdot \text{mol}\end{array}$

(d)

Interpretation Introduction

Interpretation:

Value of $\Delta S_{rxn}^o$ has to be determined for the reaction $\text{2 NaBr}\left(s\right){\text{ + Cl}}_{\text{2}}\left(g\right)\underset{}{\to }\text{2 NaCl}\left(s\right){\text{+ Br}}_{\text{2}}\left(l\right)$.

Concept Introduction:

Refer to (a).

Answer to Problem 23.64P

Value of $\Delta S_{rxn}^o$ is $-\text{100}\text{.3 }\text{J}/\text{K}\cdot \text{mol}$.

Explanation of Solution

The given reaction is shown below,

  $\text{2 NaBr}\left(s\right){\text{ + Cl}}_{\text{2}}\left(g\right)\underset{}{\to }\text{2 NaCl}\left(s\right){\text{+ Br}}_{\text{2}}\left(l\right)$

Standard enthalpy of formation values is given below,

  $\begin{array}{c}\text{Δ}S°\left[\text{NaBr}\left(s\right)\right]\text{=}\text{86}\text{.8}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{Cl}}_{\text{2}}\left(g\right)\right]\text{=}\text{223}\text{.1}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[\text{NaCl}\left(s\right)\right]\text{=}\text{72}\text{.1}\text{J}/\text{K}\cdot \text{mol}\\ \\ \text{Δ}S°\left[{\text{Br}}_{\text{2}}\left(l\right)\right]\text{=}\text{152}\text{.2}\text{J}/\text{K}\cdot \text{mol}\end{array}$

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,

  $\begin{array}{c}\Delta S_{rxn}^o\text{= }\left[\left(2\right)\left(\text{72}\text{.1}\text{J}/\text{K}\cdot \text{mol}\right)+\left(1\right)\left(\text{152}\text{.2}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ -\left[\left(2\right)\left(\text{86}\text{.8}\text{J}/\text{K}\cdot \text{mol}\right)+\left(1\right)\left(\text{223}\text{.1}\text{J}/\text{K}\cdot \text{mol}\right)\right]\\ \\ =-\text{100}\text{.3 }\text{J}/\text{K}\cdot \text{mol}\end{array}$