Chemical Thermodynamics

Chemical thermodynamics is the study of the relation of heat and work with chemical reactions or changes of states within the confines of the law of thermodynamics.

Spontaneous process in chemical thermodynamics

Any thermodynamic process which proceeds itself by its own accord and does not require any external support is called a spontaneous process. All natural processes are spontaneous processes. Examples:

• Rusting of iron
• Mixing of gases
• Flow of heat from hot to cold body
• Combination of oxygen to haemoglobin

Characteristics of spontaneous process

• It is unidirectional in nature. So, it is an irreversible process.
• It doesn’t concern about time factors whether it is fast or slow.
• It is accompanied by an increase in randomness or disorderness.
• It proceeds without the addition of external energy.

Non-spontaneous process

Any thermodynamic process which cannot proceed itself by its own accord and require extra support is called a non- spontaneous process. Examples:

• Lifting of water from low level to high level
• Flow of heat from cold to hot body
• Separation of oxygen from atmospheric air

Enthalpy change and spontaneity

By the study of various spontaneous process, it reveals that all the process proceeds towards the state of their lower value of energy in order to gain stability. Therefore, one should assume that most spontaneous processes are accompanied by a decrease in energy at constant pressure and temperature. This concludes that spontaneous processes are those processes that are only exothermic.

\begin{align*} C + O_{2} &\rightarrow CO_{2},\Delta H =-93.4 KCal\\ N_{2} + 3H_{2} &\rightarrow 2NH_{3},\Delta H = -22.4 KCal\end{align*}

By the view of the above examples, one should try to explain spontaneity in terms of the negative value of enthalpy. Later on, there are a few thermodynamic processes that are accompanied by increase in enthalpy of the system which are:

\begin{align*} H_{2}O(s) &\rightarrow H_{2}O(l),\Delta H = +1.48KCal\\ NH_{4}Cl(aq) &\rightarrow NH_{4}^{+} + Cl^{-},\Delta H = +15.58KCal \end{align*}

The melting of ice is an endothermic process. Similarly, dissociation of aqueous NaCl is also the endothermic process.
Hence, it is concluded that to predict spontaneity in terms of enthalpy is not a suitable criteria.
Any other factor is responsible for this fact which is called entropy introduced by the second law of thermodynamics.
This leads to the necessity of the development of the second law.

Concept of entropy

It is a vital thermodynamic function that is used in the field of thermodynamic. It is derived from the Greek word trope which means heat change and the prefix en is to show its connection with energy. It is defined as:

1. The thermodynamic function which measures the degree of randomness or disorderness of the system. This means higher the value of disordered state, greater would be the value of entropy and vice versa.
2. It is recognized as the thermodynamic function which measures the unavailable energy or unavailable work of the thermodynamic system.
3. In certain case, it is signified as the grasp of unavailable energy to the temperature at which the system works.

Entropy is denoted by S. Like enthalpy and internal energy, it is also the state function. So, the absolute value of it can’t be measured but a change in value between two states is practically measured.

Let S₁ and S₂ are entropies of the thermodynamic system at its initial and final state, change in entropy between two-state is given as:

\Delta S = S_{2} - S_{1}

Mathematically, entropy is defined as the ratio of total heat contained by the system at constant pressure to the temperature at an absolute state.

\Delta S = \frac{q_{p}}{T}=\frac{\Delta H}{T}

where H is called enthalpy. Unit of entropy is JK^-1 or CalK^-1.

Standard entropy change

When entropy change of 1 mole of a substance is measured at 1 atm or 760 mm of Hg pressure and 298 K, then entropy change is called standard entropy change.

\Delta S^{o}=S^{o}_{2}-S^{o}_{1} = \frac{q_{p}}{T}=\frac{\Delta H^{o}}{T}

Entropy change in chemical reaction

The entropy change in a chemical reaction is equal to the difference in total entropy of product and total entropy of reactant.

Entropy change in physical transformation

i. Entropy of fusion

It is defined as the entropy change of 1 mole of substance when it is converted from solid to its liquid phase at the melting point.

\begin{align*} \Delta S_{fusion} &= \Delta S_{(liquid)} - \Delta S_{(solid)}\\ \Delta S_{fusion} &=\frac{\Delta H_{fusion}}{T_{m}} \end{align*}

ii. Entropy of vapourization

It is defined as the entropy change of 1 mole of substance when it is converted from liquid to gas state at its boiling point.

\begin{align*} \Delta S_{vaporization} &= \Delta S_{(gas)} - \Delta S_{(liquid)}\\ &=\frac{\Delta H_{vapour}}{T_{b}} \end{align*}

iii. Entropy of sublimation

It is defined as the entropy change of 1 mole of substance when it is converted from its solid state to its gaseous state directly at its transition temperature.

\begin{align*} \Delta S_{sublimation} &= \Delta S_{(gas)} - \Delta S_{(solid)}\\ &=\frac{\Delta H_{sublimation}}{T_{t}} \end{align*}

Second law of thermodynamics

It accounts the entropy as the major factor to predict the spontaneity of the process. It states that” In all spontaneous processes, there is an increase in net entropy” or “In all irreversible process, there is an increase in total entropy” or “The total entropy of the universe is always greater than zero.”
Mathematically,

\Delta S_{total}>0

Explanation of second law of thermodynamics

This fact can be explained on the basis of the following observations:

i. In isolated system

Let us suppose the following two examples:

• Mixing of two gases (diffusion) on opening the stock cork
• Spreading of a drop of ink in a beaker containing water

These processes don’t involve any interaction in surrounding in respect of mass and energy. So, they are called isolated systems. During the progress of the process either mixing of gases or spreading of a drop of ink in water, result in the lower-order state of molecules i.e. all these processes lead to the increase in disorderness of the system. Hence, we can say there is an increase in total entropy.

ii. In open system

Let us suppose the following spontaneous process:

• Cooling down of a cup of tea
• Reaction between marble chips and dil. HCl

Those processes involve the interaction of matter as well as energy with the surrounding. So, entropy change of system as well as surrounding should be considered. During the progress of the process, either cooling down of tea or reaction between marble chips and dil. HCl results in the overall increase in total entropy.

Mathematical deduction of second law of thermodynamics

Let us suppose a thermodynamic system at its higher temperature state T₁, q quantity of heat flows irreversibly from system to surrounding which is at low-temperature state T2.
Then decrease in entropy of the system,

Then decrease in entropy of the system,
ΔS_system = -q/T₁
Increase in entropy of surrounding,
ΔS_surrounding = + q/T2
Then, the total entropy change is

\begin{align*} \Delta S_{total}&=\Delta s_{system}+\Delta S_{surrounding}\\ &=-\frac{q}{T_{1}}+\frac{q}{T_{2}}\\ &=q\left [ \frac{1}{T_{2}}-\frac{1}{T_{1}} \right ]\\ &=q\left [ \frac{T_{1}-T_{2}}{T_{1}T_{2}} \right ] \end{align*}

Since, T₁>T₂, So (T₁-T₂)/T₁T₂ > 0 or positive quantity.
Hence, ΔS_total > 0
or, ΔS_universe > 0
Thus, it verifies the second law of thermodynamics.

Gibbs free energy

Since the criteria of spontaneity in terms of total entropy change is: ΔS_total > 0
So, While dealing with the chemical reaction, it is possible to calculate the entropy change of the system practically but not possible to calculate every time the entropy change of surrounding due to its infinite size.
Therefore, the spontaneity of the process should not only be predicted on the basis of entropy change of the system but also on the entropy change of surroundings. So, a new function is been introduced which is called Gibb’s free energy.

It is defined as the amount of energy available within the thermodynamic system which can be put into useful work under constant temperature and pressure.
It is related to enthalpy and entropy by:

G = H - TS---(i)

Here, H, T and S all are state functions. So, free energy is also a function of the state. Hence, absolute value of it can’t be measured but a change in value between two states is practically measured.
Let G₁ and G₂ are free energies of two different states of a system. From (i), we get:

\begin{align*} G_{1} &= H_{1}- T_{1}S_{1}---(ii)\\ G_{2} &= H_{2}- T_{2}S_{2}---(iii) \end{align*}

Then change in free energies between two states,

\begin{align*} G_{2}-G_{1} &= \left (H_{2}-H_{1} \right )- \left (T_{2}S_{2}-T_{1}S_{1} \right )\\ if\ T_{1}&=T_{2}=T,\\ \Delta G &= \Delta H - T\Delta S---(iv) \end{align*}

where, ΔH = change in enthalpy and ΔS = change in entropy
Equation (iv) is called Gibbs free energy equation or sometimes Gibb’s Helmholtz equation.

Criteria of spontaneity in terms of free energy change

Total entropy change for process is given by:

\Delta S_{total}=\Delta S_{system}+\Delta S_{surrounding}---(i)

Let us suppose q quantity of heat is lost by surrounding to the system at constant temperature and pressure. Then, decrease in entropy of surrounding:

\Delta S_{surrounding} =-\frac{q_{p}}{T}

Since, we have heat stored within the system at constant pressure is enthalpy change.

q_{p} =\Delta S_{system}\\ \Delta S_{surrounding} = -\frac{\Delta H_{system}}{T}\\ Substituting\ in\ (i),\ we\ get,\\ \Delta S_{total}=\Delta S_{system}-\frac{\Delta H_{system}}{T}

Since whole term represent system only. So, subscript system on RHS has been dropped.

\begin{align*} \Delta S_{total}&=\Delta S-\frac{\Delta H}{T}\\ or,\ T\Delta S_{total} &= T\Delta S -\Delta H\\ or,\ -T\Delta S_{total} &=\Delta H-T\Delta S\\ or,\ -T\Delta S_{total} = \Delta G \ &(\Delta G = \Delta H - T\Delta S)\\ or,\ T\Delta S_{total} &= -\Delta G \end{align*}

This shows that decrease in free energy is increase in total entropy for process is the main criteria of spontaneity of process.
Therefore, criteria of spontaneity in terms of free energy is summarized as:

• If ΔG = -ve and ΔS_total = +ve, the process is spontaneous.
• If ΔG = 0 and ΔS_total = 0, the process is in equilibrium
• If ΔG = +ve and ΔS_total = -ve, the process is non-spontaneous.

Standard free energy change and equilibrium constant

The free energy change of a reaction in which the reactants are converted into products under
standard state is called standard free energy change. It is given by:
ΔG° = ΔH° – TΔS°

The standard free energy change is related with equilibrium constant by following relation:
ΔG° = – RT ln K
ΔG° = – 2.303RT log K

where R = molar gas constant
T = temperature in kelvin
K = equilibrium constant

Cases

• If K=1, then G° = 0, the process is in equilibrium
• If K>1, then G° < 1, the process is spontaneous
• If K<1, then G° > 1, the process is non spontaneous

Free energy change and useful work

As we know that free energy is signified as the function which measures the tendency of doing useful work.
From first law of thermodynamics:

q =\Delta E + W---(i)

There are two types of work done in a system. One is mechanical work i.e. expansion or contraction work while the other is useful work. i.e.

\begin{align*} W &= W_{mechanical} + W_{useful}\\ or, W &= P\Delta V + W_{useful}\\ or, q &=\Delta E + P\Delta V + W_{useful}\\ or, q =\Delta H + &W_{useful}\ (\Delta H =\Delta E + P\Delta V)--(ii) \end{align*}

From second law of thermodynamics,

\begin{align*} \Delta S &= \frac{q}{T}---(iii)\\ or,\ q &= T\Delta S\\ Substituting\ &(iii)\ in\ (ii),\ we\ get\\ T\Delta S &=\Delta H + W_{useful}\\ or,\ \Delta H - T&\Delta S = - W_{useful}\\ or,\ \Delta G &= - W_{useful} \end{align*}

This shows that decrease in free energy is equal to useful work.

Effect of temperature on spontaneous process

The spontaneity of a process is explained on the basis of enthalpy, entropy and free energy change. These are related to each other by means of Gibbs Helmholtz equation. i.e.

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

The value of ΔG at any temperature is calculated from the values of ΔH and ΔS, which in turn is used to explain the spontaneity of a process. Depending upon the sign of ΔH and ΔS, the effect of temperature on spontaneity of a process is explained as follows:

1. If ΔH is negative and ΔS is positive:
   The free energy change is always negative. Hence the process is spontaneous at any temperature. All these three thermodynamic properties are in favor of spontaneity. Such process are highly spontaneous.
2. If both ΔH and ΔS are positive (endothermic):
   a. At low temperature, TΔS is less than ΔH. So, G will be positive. The process will be non spontaneous.
   b. At high temperature, TΔS is greater than ΔH. So, ΔG will be negative. The process will be spontaneous.
3. When both ΔH and ΔS are negative (exothermic):
   a. At low temperature, TΔS is less than ΔH. So, ΔG will be negative. The process will be spontaneous.
   b. At high temperature, TΔS is greater than ΔH. So, ΔG will be positive. The process will be non-spontaneous.
4. If ΔH is positive and ΔS is negative:
   Then, ΔG is positive and the process will be non-spontaneous.
5. If ΔH = TΔS, then G = 0, the reaction is at equilibrium state.