Chemical Thermodynamics

Spontaneous process: The irreversible process which proceeds by itself is called spontaneous process.A spontaneous process always tries to attain the equilibrium state. E.g. Conduction of heat in metal bar from hot end to cold end until the uniformity of the temperature is maintained. The processes which cannot proceed by themselves and needs an external agent is called non-spontaneous process. They bring the system away from the equilibrium.

Second law Chemical thermodynamics: The Second Law of Thermodynamics states that the state of entropy of the entire universe, as an isolated system, will always increase over time. The second law also states that the changes in the entropy in the universe can never be negative.

Following are the statements of second law of thermodynamics:

(i) All spontaneous process is irreversible in nature.

(ii) The net entropy of the universe in any natural process always increases and tends to acquire maximum value.

(iii) In reversible process, the sum of entropies of system and surrounding remains constant but in an irreversible the total entropy of the system and surrounding increases.

Hence, we can write:

(i) For isolated spontaneous process, the entropy change (ΔS)(ΔS) is +ve > 0.

(ii) For non – isolated spontaneous process.

Or, ΔSuniverse=ΔSsys+ΔSsurΔSuniverse=ΔSsys+ΔSsur> 0, i.e. + ve

Explanation:

We have known, entropy change (ΔS)(ΔS) in the reversible heat change divided by temperature in absolute scale.

Or, ΔS=dQrevTΔS=dQrevT…(i)

Now, for non – isolated, spontaneous process:

When a system absorbs dQ amount of heat an equal amount of heat (dQ) is lost by the surrounding.

Or, dQ_sys = – dQ_sur.

Or, dQsysT=−dQsurrTdQsysT=−dQsurrT [Dividing by T]

So, ΔSsys=−ΔSsurrΔSsys=−ΔSsurr [From eqn (i)]

From this relationship, we conclude that entropy change of the system is greater than that of surrounding.

So, ΔStotal=ΔSsystem+ΔSsurrΔStotal=ΔSsystem+ΔSsurr

= dQsysT+(−dQsurrT)dQsysT+(−dQsurrT)> 0.

= +ve [from equation (ii)]

Therefore, the total entropy of the universe [non – isolated spontaneous process] is accompanied by the increase of entropy i.e. entropy change has +ve value.

Entropy and its physical concept:  The thermal property of a system which remains constant during an adiabatic process when no heat energy is given or removed from it is called entropy.

Physical concept of Entropy:

The physical meaning of entropy is that entropy is a measure of degree of disorder (or randomness) of a system. The relation between entropy and disorder provides a suitable explanation for entropy change in various processes. The greater the disorder in a system, the higher is the entropy. Obviously, for a given substance the solid state is the state of lowest entropy (most ordered state), the gaseous state is the state of highest entropy and the liquid state, is intermediate between the two. In the case of mixing of two gases when the stopcock is opened, the gases mix to achieve more randomness or disorder. In this case, there is no exchange of matter or energy between the system and the surroundings. The change occurs from ordered state (less entropy) to disordered state (higher entropy). Thus the change in entropy is positive.

Entropy change in phase transformation:

Entropy is a thermodynamic quantity which is related to uniformity of a system being measured. Entropy is central to the second law of thermodynamics. The second law of thermodynamics determines which physical processes can occur, for example it predicts that heat will flow from high temperature to low temperature. The second law of thermodynamics can be stated as: the entropy of an isolated systemalways increases, and processes which increase entropy can occur spontaneously. Since entropy increases as uniformity increases, qualitatively the second law says that uniformity increases.

Entropy and spontaneity:

The thermodynamic entropy S, often simply called the entropy in the context of thermodynamics, can provide a measure of the amount of energy in a physical system that cannot be used to do work. trope “a turning”.

In order to find out some other factor that may be responsible for the feasibility of a process, let us examine endothermic reactions. The simplest process occurring without any energy change (where DH is almost zero) may be illustrated with the help of following experiment.

(a) – Before mixing

(b) – After mixing

Let us consider two containers connected by means of a valve. The containers are perfectly insulated so that no heat enters or leaves the system. While one container is filled with a liter of helium gas, the other is filled with a liter of neon gas. The two gases are non-reacting (being inert gases). When the valve is opened, it is observed that the two gases get mixed together spontaneously. During the mixing, there is a negligible energy change and, therefore, the criterion of decrease of energy for feasibility of process does not help. If we look closely to the final and initial states of system, we observe that in the initial state the two gases are orderly filled separately in the two containers. On the other hand, after mixing, helium and neon are distributed between both the containers. In other words, each gas occupies a large volume in the final state and, thereby, number of possible locations for the molecules of each gas is increased. This means that there is more disorder or randomness on mixing. Thus, the gases mix to achieve more randomness. Once mixed the gases cannot separate because to do so they will involve decrease in randomness due to lesser volume. Thus, it may be concluded that the process proceeds spontaneously in a direction in which the randomness or disorder of the system increases.

Some common examples of processes which occur in the direction of increased randomness are given below:

(i) Conversion of solids into liquids. The melting of solids into liquids (DH, +ve) results in the increase of randomness.

H₂ O (s)  à H₂ O (l) ΔH = +ve

(ii) Evaporation of water. The evaporation of water also results in the increase of randomness because the molecules in the vapor state have more randomness than in the liquid state.

H₂ O (l)  à H₂ O (g) ΔH = +ve

(iii) Dissolution of ammonium chloride in water. Solid ammonium chloride has less randomness while in solution ammonium chloride particles move freely as NH₄⁺ and Cl^– ions and hence, randomness increases.

NH₄Cl_(s)  + water   à NH₄⁺ _(aq) + Cl^–_(aq)

Thus, in all the above endothermic processes, there is always increase in randomness. Since the above reactions are spontaneous, the tendency to achieve maximum randomness is another factor which determines the spontaneity of a process.

Entropy changes and their calculation:

Even without knowing the actual values for the entropy (S^o) of substances, it is possible to predict the sign of ΔS^o for a reaction or phase change. It is useful to remember that the entropy of a system will increase when:

1. A reaction in which a molecule is broken into two or more smaller molecules.

2. A reaction in which there is an increase in moles of gas.

3. A process in which a solid changes to a liquid or gas or a liquid changes to a gas.

Let’s take the following example:

2 NaHCO₃ (s) à Na₂CO₃ (s) + H₂O (g) + CO₂ (g)

Looking at this reaction we see that two molecules of sodium bicarbonate (NaHCO₃) combine to form three molecules, Na₂CO₃, H₂O, and CO₂. Two of these molecules are gases. Therefore, rules 1 and 2 apply. The sodium bicarbonate is broken up into three smaller molecules and two of those are gases. We should suspect that the sign of ΔS^o will be positive. To confirm this, we can calculate the actual value of ΔS^o. We find the following data:

S^o (NaHCO₃) = 102 J/K

S^o (Na₂CO₃) = 139 J/K

S^o (H₂O) = 188.7 J/K

S^o (CO₂) = 213.7 J/K

Before we proceed, it is important that we take into account the physical state of the substance for which we want to obtain is value of S^o In the case of water, there are two values in the table. We must choose the value of H₂O (g), which is the physical state of the water in this reaction. If we choose the value for H₂O (l) we will be calculating the wrong change in S^o, since that is not the state of the water in the chemical reaction.

We know that ΔS^o = ΣS^o (products) – ΣS^o (reactants);

∴ Δ S^o = [(S^o Na₂CO₃) + (S^o H₂O) + S^o (CO₂)] – 2(S^o NaHCO₃),

Substituting we obtain:

Δ S^o = ([139+ 188.7 + 213.7] – 2[102]) J/K. When we do the math, we obtain a value of Δ S^o of

+337 J/K, which agrees with our prediction.

Of course, if the reaction is reversed, that is, we write it like:

Na₂CO₃ (s) + H₂O (g) + CO₂ (g) à 2 NaHCO₃ (s)

We can see that know three molecules are combining to form two molecules and that of these molecules are solids, while we started with two gases and a solid. Obviously, the value of Δ S^o has to be negative. Since we calculated the value of Δ S^o for the opposite reaction, we know that when we reverse a chemical reaction, we must also reverse the sign of ΔS^o, which in this case will be -337 J/K.

Gibbs free energy:   Gibb’s free energy is defined as the difference of enthalpy and entropy of a system at a particular temperature.It is denoted by G or F,

Free energy change for predicting feasibility of a reaction:

Free energy change is the amount of free energy released or absorbed in a process or in a chemical reaction occurring at constant temperature

It has already been seen that the total entropy change, ΔS_total determines the spontaneity of a process. The total entropy change during a process is given by

ΔS_total = ΔS_system + ΔS_surroundings ….(2)

If the reaction is carried out at constant temperature and pressure, heat involved is equal to enthalpy change,

Q _system = ΔH_system

Now, if a reaction is conducted at constant temperature and pressure, and heat (q) is given out to the surroundings reversibly, then,

(q) _Surroundings = – q_system = – ΔH_system

The entropy change of the surroundings is:

(q) _Surroundings – ΔH_system …. (3)

Δ S_surroundings = T

Substituting equation 3 in equation 2, we get

ΔS_{total  =}ΔS_system  – ΔHsystemTΔHsystemT

Multiplying both sides by T,

T Δ S_total = T Δ S_system – Δ H_system

– T ΔS_total = ΔH_system – T ΔS_system

From Equation1, Δ H – T Δ S = Δ G

ΔG_system = – T ΔS_total

It has been shown that for spontaneous chemical changes, Δ S_total is positive so that ΔG = -ve for spontaneous chemical changes.

Thus, the spontaneity of a chemical change can be predicted either by

(i) T ΔS system = +ve or

(ii) ΔG = -ve.

The use of Gibbs free energy change has the advantage because it refers to system only whereas in considering entropy criteria, the system as well as the surroundings is to be considered.

Free energy change with work:

Initial and final state of the system is given by

Or, G₁ = H₁ – T₁S₁… (i)

Or, G₂ = H₂ – T₂S₂… (ii)

The, change of free energy is given by:

Or, G₂ – G₁ = (H₂ – H₁) – T₂S₂ + T₁S₁.

So, ΔG=ΔF−TΔSΔG=ΔF−TΔS….(iii)

So, Equation (iii) is Gibb’s equation and is very useful in describing the spontaneity of a process.

We have,

Or, ΔG=ΔH−TΔSΔG=ΔH−TΔS ….(iii)

We also have, ΔH=ΔE+PΔV.ΔH=ΔE+PΔV.

So, ΔG=ΔE+pΔV−TΔSΔG=ΔE+pΔV−TΔS(iv)

From 1^st law of thermodynamics,

Or, ΔQ=ΔE+ΔwΔQ=ΔE+Δw

So, ΔE=ΔQ−ΔwΔE=ΔQ−Δw

Substituting, the value in equation (I v), we get,

Or, ΔG=ΔQ−ΔW+pΔV−TΔSΔG=ΔQ−ΔW+pΔV−TΔS….(v)

From definition of entropy change,

Or, ΔS=ΔQrevTΔS=ΔQrevT

So, ΔQ=TΔSΔQ=TΔS

Again, on substituting the value of ΔQΔQ in equation (v),

Or, ΔG=TΔS−ΔW+pΔV−TΔSΔG=TΔS−ΔW+pΔV−TΔS

Or, ΔG=−ΔW+pΔVΔG=−ΔW+pΔV

Or, ΔG=−(ΔW−pΔV)ΔG=−(ΔW−pΔV)

Or, ΔG=−WnetΔG=−Wnet

Or, −ΔG=Wnet−ΔG=Wnet…. (vi

Therefore, this is the required relation.

Differences between internal energy and enthalpy

Differences between exothermic reaction and endothermic reaction

Standard free energy change and equilibrium constant:

The standard free energy change is defined as the free energy change for a process at 298 K and 1 atmospheric pressure in which the reactants in their standard states are converted to the products in their standard states. Like the standard enthalpy of formation of an element, the standard free energy of formation of an element in its standard state is assumed to be zero. Thus,

Δ G° = Σ Δ G _f° (products) – Σ Δ G ­_f° (reactants)

=[sum of the standard free energy in the formation of products ] – [ sum of standard energy in the formation of reactants]

The standard free energy change, Δ G^o is related to the equilibrium constant K by the relation,

Δ G^o = – RT ln K

or ΔG^o = –2.303 RT log K (since,since,ln X = 2.303 log X)

This relation helps us to calculate the value of Δ G^o if K is known or vice-versa.

Influence of temperature on spontaneous process:

A spontaneous process is a chemical reaction in which a system releases free energy (most often as heat) and moves to a lower, more thermodynamically stable, energy state. The sign convention of changes in free energy follows the general convention for thermodynamic measurements, in which a release of free energy from the system corresponds to a negative change in free energy, but a positive change for the surroundings.

Thus, for a reaction at constant temperature and pressure where

ΔG = ΔH – TΔS

A negative ΔG would depend on the sign of the changes in enthalpy (ΔH), entropy (ΔS), and the magnitude of theabsolutetemperature (in kelvins). Changes in the sign of ΔG cannot be changed directly by temperature, because it can never be less than zero.

When ΔS is positive and ΔH is negative, a process is spontaneous.

When ΔS is positive and ΔH is positive, a process is spontaneous at high temperatures, where exothermicity plays a small role in the balance.

When ΔS is negative and ΔH is negative, a process is spontaneous at low temperatures, where exothermic city isimportant.

When ΔS is negative and ΔH is positive, a process is not spontaneous at any temperature, but the reverse process is spontaneous.