Chapter 9, Problem 9.142SP

Interpretation Introduction

(a)

Interpretation:

The value of $\text{ΔH}°$ for the formation of metallic mercury by heating the mineral cinnabar (HgS) needs to be determined,

$\text{HgS}\left(s\right){\text{+ O}}_{\text{2}}\left(g\right)\stackrel{}{\to }\text{Hg}\left(l\right){\text{ + SO}}_2\left(g\right)$

Concept introduction:

The Gibb’s equation of thermodynamic purposed a relation between $\text{ΔS}$, $\text{ΔH}$ and $\text{ΔG}$ with Temperature. The mathematical expression of Gibb’s equation can be written as:

$\text{ΔG = ΔH - TΔS }$

With the help of this equation one can predict the change in $\text{ΔS}$, $\text{ΔH}$ and $\text{ΔG}$. For any reaction the $\text{ΔH}$ and $\text{ΔS}$ can be calculated with the help of following equations.

$\begin{array}{l}\text{ΔrS°= }\Sigma \text{ΔrS°product - }\sum \text{ΔrS°reactant}\\ \text{ΔrH°= }\Sigma \text{ΔrH°product - }\sum \text{ΔrH°reactant}\end{array}$

Interpretation Introduction

(b)

Interpretation:

The reaction needs to be classified as spontaneous or non-spontaneous at 25&degC if $\text{ΔS}°$ for the formation of metallic mercury is +36.7 J/K and $\text{ΔrH°= -238}\text{.6kJ/mol}$.

$\text{HgS}\left(s\right){\text{+ O}}_{\text{2}}\left(g\right)\stackrel{}{\to }\text{Hg}\left(l\right){\text{ + SO}}_2\left(g\right)$

Concept introduction:

The Gibb’s equation of thermodynamic purposed a relation between $\text{ΔS}$, $\text{ΔH}$ and $\text{ΔG}$ with Temperature. The mathematical expression of Gibb’s equation can be written as:

$\text{ΔG = ΔH - TΔS }$

With the help of this equation, one can predict the change in $\text{ΔS}$, $\text{ΔH}$ and $\text{ΔG}$. For any reaction the $\text{ΔH}$ and $\text{ΔS}$ can be calculated with the help of following relation:

$\begin{array}{l}\text{ΔrS°= }\Sigma \text{ΔrS°product - }\sum \text{ΔrS°reactant}\\ \text{ΔrH°= }\Sigma \text{ΔrH°product - }\sum \text{ΔrH°reactant}\end{array}$

Interpretation Introduction

(c)

Interpretation:

The condition at which the reaction will be non-spontaneous for the formation of metallic mercury if $\text{ΔS}°$ +36.7 J/K, ${\text{Δ}}_{\text{r}}\text{G}°\text{ = -249}\text{.5 kJ/mol}$ and $\text{ΔrH°= -238}\text{.6kJ/mol}$ needs to be determined.

$\text{HgS}\left(s\right){\text{+ O}}_{\text{2}}\left(g\right)\stackrel{}{\to }\text{Hg}\left(l\right){\text{ + SO}}_2\left(g\right)$

Concept introduction:

The Gibb’s equation of thermodynamic purposed a relation between $\text{ΔS}$, $\text{ΔH}$ and $\text{ΔG}$ with Temperature. The mathematical expression of Gibb’s equation can be written as:

$\text{ΔG = ΔH - TΔS }$

With the help of this equation one can predict the change in $\text{ΔS}$, $\text{ΔH}$ and $\text{ΔG}$. For any reaction the $\text{ΔH}$ and $\text{ΔS}$ can be calculated with the help of following relation:

$\begin{array}{l}\text{ΔrS°= }\Sigma \text{ΔrS°product - }\sum \text{ΔrS°reactant}\\ \text{ΔrH°= }\Sigma \text{ΔrH°product - }\sum \text{ΔrH°reactant}\end{array}$