Chapter 16, Problem 16.65SP

(a)

Interpretation Introduction

Interpretation:

$\Delta S_{sys}$, $\Delta S_{surr}$ and $\Delta S_{total}$ for reaction of $PC{l}_3$ with $C{l}_2$  forming $PC{l}_5$ has to be calculated and spontaneity of the reaction at $25°C$ has to be ascertained.

Concept Introduction:

• Entropy refers to measurement of randomness or disorderliness in the system.  More the number of molecules in a system more will be the movement of molecules and greater will be the entropy given that weak intermolecular forces prevails between molecules.
• Entropy is denoted by ‘S’ and $\Delta S$  change in entropy.
• $\Delta S°$ refers to standard entropy of the reaction which is termed as entropy change in a reaction under standard conditions of $298K$ and $1\text{ atm}$ pressure.  It is represented as,

$\Delta S°=S°\left(products\right)-S°\left(reac\tan ts\right)$

• $\Delta S_{total}=\Delta S_{sys}+\Delta S_{surr}$

Where,

 $\begin{array}{l}\Delta S_{total}=total\text{ entropy change}\\ \Delta S_{sys}=\text{entropy change in system (reaction)}\\ \Delta S_{surr}=\text{entropy change in surroundings}\end{array}$

• $\Delta H$ refers to change in enthalpy.  Change in enthalpy in a reaction and heat of formation are related by the formula,

$\Delta H_{rxn}^{°}=\Sigma \Delta H_f^{°}(product)-\Sigma \Delta H_f^{°}(reac\tan t)$

Where,

$\begin{array}{l}\Delta H_{rxn}^{°}=\text{ enthalpy change in reaction}\\ \Delta H_f^{°}(product)=\text{ enthalpy or heat of formation of product}\\ \Delta H_f^{°}(reac\tan t)=\text{ enthalpy or heat of formation of }reac\tan t\end{array}$

• $\Delta S_{surr}$ and $\Delta H°$ are related as,

$\Delta S_{surr}=\frac{-\Delta H°}{T}$

(b)

Interpretation Introduction

Interpretation:

For reaction of $PC{l}_3$ with $C{l}_2$  forming $PC{l}_5$ the temperature at which reaction will become non-spontaneous has to be determined.

Concept Introduction:

• Entropy refers to measurement of randomness or disorderliness in the system.  More the number of molecules in a system more will be the movement of molecules and greater will be the entropy given that weak intermolecular forces prevails between molecules.
• Entropy is denoted by ‘S’ and $\Delta S$  change in entropy.
• $\Delta S°$ refers to standard entropy of the reaction which is termed as entropy change in a reaction under standard conditions of $298K$ and $1\text{ atm}$ pressure.  It is represented as,

$\Delta S°=S°\left(products\right)-S°\left(reac\tan ts\right)$

• The term free energy G, refers to energy available in the system to do work.  Change in free energy is denoted by $\Delta G$ and it is represented as,

$\Delta G=\Delta H-T\Delta S$

• The temperature at which a spontaneous reaction becomes non-spontaneous and vice-versa is termed as crossover temperature.