Chapter 8, Problem 8.27CP

The following reaction is exothermic:

1. (a) Write a balanced equation for the reaction (red spheres represent A atoms and ivory spheres represent B atoms).
2. (b) What are the signs ( + or − ) of ΔH and ΔS for the reaction?
3. (c) Is the reaction likely to be spontaneous at lower temperatures only, at higher temperatures only, or at all temperatures?

Interpretation Introduction

Interpretation:

Balanced equation for the following reaction has to be written.

Concept Introduction:

• Every chemical reaction obliges Law for conversion of mass which states the mass of total amount of the product should be equal to the total mass of the reactants.
• The concept of writing a balanced chemical reaction is depends on conversion of reactants into products.
• First write the reaction from the given information.
• Then count the number of atoms of each element in reactants as well as products.
• Finally obtained values could place it as coefficients of reactants as well as products.

Explanation of Solution

The given picture illustrates a chemical reaction in which a hetero-atomic triatomic molecule dissociates into two different diatomic molecules.  Let the molecules in reactant side be assumed as $A_{2}B$ and the molecules in the product be $A_2$ and $B_2.$  Balanced equation for this reaction is written as

$2A_{2}B\stackrel{}{\to }2A_2+B_2$

Interpretation Introduction

Interpretation:

The signs of $\Delta H,\Delta S$ have to be written.

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 $\Delta S°$ refers to change in entropy of the system.  $\Delta S°$ value positive for a phenomenon indicates the process is spontaneous  which proceeds without any external influence.  $\Delta S°$ value negative for a phenomenon indicates the process is non–spontaneous which proceeds upon some external influence.
• The heat content of the system is represented by ‘H’ and it is the sum of internal energy ‘E’ and product of volume and pressure,

$H=E+PV$

•  $\Delta H$ refers to change in enthalpy of the system,

$\Delta H=\Delta E+P\Delta V$

Answer to Problem 8.27CP

$\Delta H$ is in negative sign and $\Delta S$ is in positive sign for the given reaction.

Explanation of Solution

The given reaction is exothermic.  Hence $\Delta H$ must be negative.  From the given figure which illustrates the reaction we could see the number of molecules increasing as the reaction proceeds.  Number of molecules are more in product side that randomness increases as the reaction proceeds.  Increase in randomness increases entropy therefore $\Delta S$ has positive sign.

Interpretation Introduction

Interpretation:

The spontaneity of the reaction with respect to temperature has to be explained.

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 $\Delta S°$ refers to change in entropy of the system.  $\Delta S°$ value positive for a phenomenon indicates the process is spontaneous which proceeds without any external influence.  $\Delta S°$ value negative for a phenomenon indicates the process is non-spontaneous which proceeds upon some external influence.
• The heat content of the system is represented by ‘H’ and it is the sum of internal energy ‘E’ and product of volume and pressure,

$H=E+PV$

•  $\Delta H$ refers to change in enthalpy of the system,

$\Delta H=\Delta E+P\Delta V$

• The term free energy G, refers to energy available in the system to do work and enthalpy H,  refers to heat content of the system.
• Spontaneous process has positive entropy value and negative free energy, enthalpy value.
• Non-spontaneous process tends to proceed with negative entropy value and positive free energy and enthalpy.

Answer to Problem 8.27CP

The reaction tends to be spontaneous at lower temperature and non-spontaneous at higher temperature.

Explanation of Solution

Free energy change is written as,

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

Rewriting the above equation,

$T=\frac{\Delta H-\Delta G}{\Delta S}$

Since the reaction is exothermic $\Delta H$ value tends to be negative.  Spontaneous process proceeds with increase in entropy. Thus positive entropy and negative enthalpy decreases the temperature and makes the reaction spontaneous. Besides, from the above expression $\Delta S$ and temperature are inversely proportional to each other.  Thus entropy decreases with increase in temperature and increases with decreases in temperature.  Thus low temperature favors spontaneous reaction.