Thermodynamics
“It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown.”
Albert Einstein
Chemical energy stored by molecules can be released as heat during chemical reactions when a fuel like methane, cooking gas or coal burns in air. The chemical energy may also be used to do mechanical work when a fuel burns in an engine or to provide electrical energy through a galvanic cell like dry cell. Thus, various forms of energy are interrelated and under certain conditions, these may be transformed from one form into another. The study of these energy transformations forms the subject matter of thermodynamics. The laws of thermodynamics deal with energy changes of macroscopic systems involving a large number of molecules rather than microscopic systems containing a few molecules. Thermodynamics is not concerned about how and at what rate these energy transformations are carried out, but is based on initial and final states of a system undergoing the change. Laws of thermodynamics apply only when a system is in equilibrium or moves from one equilibrium state to another equilibrium state. Macroscopic properties like pressure and temperature do not change with time for a system in equilibrium state. In this unit, we would like to answer some of the important questions through thermodynamics, like:
How do we determine the energy changes involved in a chemical reaction/process? Will it occur or not?
What drives a chemical reaction/process?
To what extent do the chemical reactions proceed?
6.1 THERMODYNAMIC TERMS
We are interested in chemical reactions and the energy changes accompanying them. For this we need to know certain thermodynamic terms. These are discussed below.
6.1.1 The System and the Surroundings
A system in thermodynamics refers to that part of universe in which observations are made and remaining universe constitutes the surroundings. The surroundings include everything other than the system. System and the surroundings together constitute the universe.
The universe
However, the entire universe other than the system is not affected by the changes taking place in the system. Therefore, for all practical purposes, the surroundings are that portion of the remaining universe which can interact with the system. Usually, the region of space in the neighbourhood of the system constitutes its surroundings.
For example, if we are studying the reaction between two substances A and B kept in a beaker, the beaker containing the reaction mixture is the system and the room where the beaker is kept is the surroundings (Fig. 6.1).
Note that the system may be defined by physical boundaries, like beaker or test tube, or the system may simply be defined by a set of Cartesian coordinates specifying a particular volume in space. It is necessary to think of the system as separated from the surroundings by some sort of wall which may be real or imaginary. The wall that separates the system from the surroundings is called boundary. This is designed to allow us to control and keep track of all movements of matter and energy in or out of the system.
6.1.2 Types of the System
We, further classify the systems according to the movements of matter and energy in or out of the system.
1. Open System
In an open system, there is exchange of energy and matter between system and surroundings [Fig. 6.2 (a)]. The presence of reactants in an open beaker is an example of an open system[^0]. Here the boundary is an imaginary surface enclosing the beaker and reactants.
2. Closed System
In a closed system, there is no exchange of matter, but exchange of energy is possible between system and the surroundings [Fig. 6.2 (b)]. The presence of reactants in a closed vessel made of conducting material e.g., copper or steel is an example of a closed system.
3. Isolated System
In an isolated system, there is no exchange of energy or matter between the system and the surroundings [Fig. 6.2 (c)]. The presence of reactants in a thermos flask or any other closed insulated vessel is an example of an isolated system.
6.1.3 The State of the System
The system must be described in order to make any useful calculations by specifying quantitatively each of the properties such as its pressure
The state of a thermodynamic system is described by its measurable or macroscopic (bulk) properties. We can describe the state of a gas by quoting its pressure (
The state of the surroundings can never be completely specified; fortunately it is not necessary to do so.
6.1.4 The Internal Energy as a State Function
When we talk about our chemical system losing or gaining energy, we need to introduce a quantity which represents the total energy of the system. It may be chemical, electrical, mechanical or any other type of energy you may think of, the sum of all these is the energy of the system. In thermodynamics, we call it the internal energy,
- heat passes into or out of the system,
- work is done on or by the system,
- matter enters or leaves the system.
These systems are classified accordingly as you have already studied in section 5.1.2.
(a) Work
Let us first examine a change in internal energy by doing work. We take a system containing some quantity of water in a thermos flask or in an insulated beaker. This would not allow exchange of heat between the system and surroundings through its boundary and we call this type of system as adiabatic. The manner in which the state of such a system may be changed will be called adiabatic process. Adiabatic process is a process in which there is no transfer of heat between the system and surroundings. Here, the wall separating the system and the surroundings is called the adiabatic wall (Fig. 6.3).
Let us bring the change in the internal energy of the system by doing some work on it. Let us call the initial state of the system as state
One way: We do some mechanical work, say
Second way: We now do an equal amount (i.e.,
In fact, the experiments in the above manner were done by J. P. Joule between 1840-50 and he was able to show that a given amount of work done on the system, no matter how it was done (irrespective of path) produced the same change of state, as measured by the change in the temperature of the system.
So, it seems appropriate to define a quantity, the internal energy
Therefore, internal energy,
By conventions of IUPAC in chemical thermodynamics. The positive sign expresses that
Can you name some other familiar state functions? Some of other familiar state functions are
(b) Heat
We can also change the internal energy of a system by transfer of heat from the surroundings to the system or vice-versa without expenditure of work. This exchange of energy, which is a result of temperature difference is called heat,
We take water at temperature,
By conventions of IUPAC in chemical thermodynamics. The
- Earlier negative sign was assigned when the work is done on the system and positive sign when the work is done by the system. This is still followed in physics books, although IUPAC has recommended the use of new sign convention.
(c) The general case
Let us consider the general case in which a change of state is brought about both by doing work and by transfer of heat. We write change in internal energy for this case as:
For a given change in state,
The equation 5.1 i.e.,
The energy of an isolated system is constant.
It is commonly stated as the law of conservation of energy i.e., energy can neither be created nor be destroyed.
Note: There is considerable difference between the character of the thermodynamic property energy and that of a mechanical property such as volume. We can specify an unambiguous (absolute) value for volume of a system in a particular state, but not the absolute value of the internal energy. However, we can measure only the changes in the internal energy,
6.2 APPLICATIONS
Many chemical reactions involve the generation of gases capable of doing mechanical work or the generation of heat. It is important for us to quantify these changes and relate them to the changes in the internal energy. Let us see how!
6.2.1 Work
First of all, let us concentrate on the nature of work a system can do. We will consider only mechanical work i.e., pressure-volume work.
For understanding pressure-volume work, let us consider a cylinder which contains one mole of an ideal gas fitted with a frictionless piston. Total volume of the gas is
inside becomes equal to
then, volume change
We also know, pressure
Therefore, force on the piston
If
The negative sign of this expression is required to obtain conventional sign for
If the pressure is not constant at every stage of compression, but changes in number of finite steps, work done on the gas will be summed over all the steps and will be equal to
If the pressure is not constant but changes during the process such that it is always infinitesimally greater than the pressure of the gas, then, at each stage of compression, the volume decreases by an infinitesimal amount,
Here,
A process or change is said to be reversible, if a change is brought out in such a way that the process could, at any moment, be reversed by an infinitesimal change. A reversible process proceeds infinitely slowly by a series of equilibrium states such that system and the surroundings are always in near equilibrium with each other.
Processes other than reversible processes are known as irreversible processes.
In chemistry, we face problems that can be solved if we relate the work term to the internal pressure of the system. We can relate work to internal pressure of the system under reversible conditions by writing equation 5.3 as follows:
Since
Now, the pressure of the gas
Therefore, at constant temperature (isothermal process),
Free expansion: Expansion of a gas in vacuum
Now, we can write equation 5.1 in number of ways depending on the type of processes.
Let us substitute
If a process is carried out at constant volume
the subscript
Isothermal and free expansion of an ideal gas
For isothermal (
Equation 5.1,
1. For isothermal irreversible change
2. For isothermal reversible change
For adiabatic change,
5.2.2 Enthalpy,
(a) A Useful New State Function
We know that the heat absorbed at constant volume is equal to change in the internal energy i.e.,
We may write equation (6.1) as
Let us represent the initial state by subscript 1 and final state by 2
We can rewrite the above equation as
On rearranging, we get
Now we can define another thermodynamic function, the enthalpy
so, equation (6.6) becomes
Although
For finite changes at constant pressure, we can write equation 5.7 as
Since
It is important to note that when heat is absorbed by the system at constant pressure, we are actually measuring changes in the enthalpy.
Remember
At constant volume
The difference between
Thus,
or
Here,
Substituting the value of
The equation 5.10 is useful for calculating
(b) Extensive and Intensive Properties
In thermodynamics, a distinction is made between extensive properties and intensive properties. An extensive property is a property whose value depends on the quantity or size of matter present in the system. For example, mass, volume, internal energy, enthalpy, heat capacity, etc. are extensive properties.
Those properties which do not depend on the quantity or size of matter present are known as intensive properties. For example temperature, density, pressure etc. are intensive properties. A molar property,
(c) Heat Capacity
In this sub-section, let us see how to measure heat transferred to a system. This heat appears as a rise in temperature of the system in case of heat absorbed by the system.
The increase of temperature is proportional to the heat transferred
The magnitude of the coefficient depends on the size, composition and nature of the system. We can also write it as
The coefficient,
Thus, we can measure the heat supplied by monitoring the temperature rise, provided we know the heat capacity.
When
(d) The Relationship between
At constant volume, the heat capacity,
We can write equation for heat,
at constant volume as
at constant pressure as
The difference between
For a mole of an ideal gas,
On putting the values of
6.3 MEASUREMENT OF AND : CALORIMETRY
We can measure energy changes associated with chemical or physical processes by an experimental technique called calorimetry. In calorimetry, the process is carried out in a vessel called calorimeter, which is immersed in a known volume of a liquid. Knowing the heat capacity of the liquid in which calorimeter is immersed and the heat capacity of calorimeter, it is possible to determine the heat evolved in the process by measuring temperature changes. Measurements are made under two different conditions:
i) at constant volume,
ii) at constant pressure,
(a)
For chemical reactions, heat absorbed at constant volume, is measured in a bomb calorimeter (Fig. 6.7). Here, a steel vessel (the bomb) is immersed in a water bath. The whole device is called calorimeter. The steel vessel is immersed in water bath to ensure that no heat is lost to the surroundings. A combustible
substance is burnt in pure dioxygen supplied in the steel bomb. Heat evolved during the reaction is transferred to the water around the bomb and its temperature is monitored. Since the bomb calorimeter is sealed, its volume does not change i.e., the energy changes associated with reactions are measured at constant volume. Under these conditions, no work is done as the reaction is carried out at constant volume in the bomb calorimeter. Even for reactions involving gases, there is no work done as
(B)
Measurement of heat change at constant pressure (generally under atmospheric pressure) can be done in a calorimeter shown in Fig. 6.8. We know that
In an exothermic reaction, heat is evolved, and system loses heat to the surroundings. Therefore,
6.4 ENTHALPY CHANGE, OF A REACTION - REACTION ENTHALPY
In a chemical reaction, reactants are converted into products and is represented by,
Reactants
The enthalpy change accompanying a reaction is called the reaction enthalpy. The enthalpy change of a chemical reaction, is given by the symbol
Here symbol
where
Enthalpy change is a very useful quantity. Knowledge of this quantity is required when one needs to plan the heating or cooling required to maintain an industrial chemical reaction at constant temperature. It is also required to calculate temperature dependence of equilibrium constant.
(a) Standard Enthalpy of Reactions
Enthalpy of a reaction depends on the conditions under which a reaction is carried out. It is, therefore, necessary that we must specify some standard conditions. The standard enthalpy of reaction is the enthalpy change for a reaction when all the participating substances are in their standard states.
The standard state of a substance at a specified temperature is its pure form at 1 bar. For example, the standard state of liquid ethanol at
Standard conditions are denoted by adding the superscript
(b) Enthalpy Changes during Phase Transformations
Phase transformations also involve energy changes. Ice, for example, requires heat for melting. Normally this melting takes place at constant pressure (atmospheric pressure) and during phase change, temperature remains constant (at
Here
The enthalpy change that accompanies melting of one mole of a solid substance in standard state is called standard enthalpy of fusion or molar enthalpy of fusion,
Melting of a solid is endothermic, so all enthalpies of fusion are positive. Water
Table 6.1 Standard Enthalpy Changes of Fusion and Vaporisation
Substance | ||||
---|---|---|---|---|
63.15 | 0.72 | 77.35 | 5.59 | |
195.40 | 5.65 | 239.73 | 23.35 | |
159.0 | 1.992 | 188.0 | 16.15 | |
68.0 | 6.836 | 82.0 | 6.04 | |
177.8 | 5.72 | 329.4 | 29.1 | |
250.16 | 2.5 | 349.69 | 30.0 | |
273.15 | 6.01 | 373.15 | 40.79 | |
1081.0 | 28.8 | 1665.0 | 170.0 | |
278.65 | 9.83 | 353.25 | 30.8 |
requires heat for evaporation. At constant temperature of its boiling point
Amount of heat required to vaporize one mole of a liquid at constant temperature and under standard pressure (
Sublimation is direct conversion of a solid into its vapour. Solid
Standard enthalpy of sublimation,
The magnitude of the enthalpy change depends on the strength of the intermolecular interactions in the substance undergoing the phase transfomations. For example, the strong hydrogen bonds between water molecules hold them tightly in liquid phase. For an organic liquid, such as acetone, the intermolecular dipole-dipole interactions are significantly weaker. Thus, it requires less heat to vaporise
Table 6.2 Standard Molar Enthalpies of Formation
Substance | Substance | ||
---|---|---|---|
-1675.7 | +26.48 | ||
-1216.3 | -436.75 | ||
0 | -393.8 | ||
+30.91 | MgO(s) | -601.70 | |
-1206.92 | -924.54 | ||
C (diamond) | +1.89 | -573.65 | |
C (graphite) | 0 | -411.15 | |
-635.09 | -361.06 | ||
-74.81 | -287.78 | ||
52.26 | -46.11 | ||
-238.86 | +90.25 | ||
-277.69 | +33.18 | ||
+49.0 | -319.70 | ||
-110.53 | -443.5 | ||
-393.51 | -910.94 | ||
-84.68 | -325.1 | ||
0 | -511.3 | ||
-103.85 | -296.83 | ||
-126.15 | -395.72 | ||
-58.2 | +34 | ||
0 | -657.0 | ||
-241.82 | +716.68 | ||
-285.83 | +217.97 | ||
-271.1 | +121.68 | ||
-92.31 | -824.2 | ||
-36.40 |
Therefore,
There is negligible change in the volume during the change form liquid to solid state.
Therefore,
(c) Standard Enthalpy of Formation
The standard enthalpy change for the formation of one mole of a compound from its elements in their most stable states of aggregation (also known as reference states) is called Standard Molar Enthalpy of Formation. Its symbol is
It is important to understand that a standard molar enthalpy of formation,
is not an enthalpy of formation of calcium carbonate, since calcium carbonate has been formed from other compounds, and not from its constituent elements. Also, for the reaction given below, enthalpy change is not standard enthalpy of formation,
Here two moles, instead of one mole of the product is formed from the elements, i.e.,
Therefore, by dividing all coefficients in the balanced equation by 2 , expression for enthalpy of formation of
Standard enthalpies of formation of some common substances are given in Table 6.2.
By convention, standard enthalpy for formation,
Suppose, you are a chemical engineer and want to know how much heat is required to decompose calcium carbonate to lime and carbon dioxide, with all the substances in their standard state.
Here, we can make use of standard enthalpy of formation and calculate the enthalpy change for the reaction. The following general equation can be used for the enthalpy change calculation.
where
Thus, the decomposition of
(d) Thermochemical Equations
A balanced chemical equation together with the value of its
The above equation describes the combustion of liquid ethanol at constant temperature and pressure. The negative sign of enthalpy change indicates that this is an exothermic reaction.
It would be necessary to remember the following conventions regarding thermochemical equations.
1. The coefficients in a balanced thermochemical equation refer to the number of moles (never molecules) of reactants and products involved in the reaction.
2. The numerical value of
To illustrate the concept, let us consider the calculation of heat of reaction for the following reaction :
From the Table (6.2) of standard enthalpy of formation
Also
Then,
Note that the coefficients used in these calculations are pure numbers, which are equal to the respective stoichiometric coefficients. The unit for
then this amount of reaction would be one mole of reaction and
It shows that enthalpy is an extensive quantity.
3. When a chemical equation is reversed, the value of
(e) Hess’s Law of Constant Heat Summation
We know that enthalpy is a state function, therefore the change in enthalpy is independent of the path between initial state (reactants) and final state (products). In other words, enthalpy change for a reaction is the same whether it occurs in one step or in a series of steps. This may be stated as follows in the form of Hess’s Law.
If a reaction takes place in several steps then its standard reaction enthalpy is the sum of the standard enthalpies of the intermediate reactions into which the overall reaction may be divided at the same temperature.
Let us understand the importance of this law with the help of an example.
Consider the enthalpy change for the reaction
Although
Let us consider the following reactions:
We can combine the above two reactions in such a way so as to obtain the desired reaction. To get one mole of
Adding equation (i) and (iii), we get the desired equation,
for which
In general, if enthalpy of an overall reaction
It can be represented as:
6.5 ENTHALPIES FOR DIFFERENT TYPES OF REACTIONS
It is convenient to give name to enthalpies specifying the types of reactions.
(a) Standard Enthalpy of Combustion (symbol :
Combustion reactions are exothermic in nature. These are important in industry, rocketry, and other walks of life. Standard enthalpy of combustion is defined as the enthalpy change per mole (or per unit amount) of a substance, when it undergoes combustion and all the reactants and products being in their standard states at the specified temperature.
Cooking gas in cylinders contains mostly butane
Similarly, combustion of glucose gives out
Our body also generates energy from food by the same overall process as combustion, although the final products are produced after a series of complex bio-chemical reactions involving enzymes.
(b) Enthalpy of Atomization (symbol:
Consider the following example of atomization of dihydrogen
You can see that
In case of diatomic molecules, like dihydrogen (given above), the enthalpy of atomization is also the bond dissociation enthalpy. The other examples of enthalpy of atomization can be
Note that the products are only atoms of
In this case, the enthalpy of atomization is same as the enthalpy of sublimation.
(c) Bond Enthalpy (symbol:
Chemical reactions involve the breaking and making of chemical bonds. Energy is required to break a bond and energy is released when a bond is formed. It is possible to relate heat of reaction to changes in energy associated with breaking and making of chemical bonds. With reference to the enthalpy changes associated with chemical bonds, two different terms are used in thermodynamics.
(i) Bond dissociation enthalpy
(ii) Mean bond enthalpy
Let us discuss these terms with reference to diatomic and polyatomic molecules.
Diatomic Molecules: Consider the following process in which the bonds in one mole of dihydrogen gas
The enthalpy change involved in this process is the bond dissociation enthalpy of
Note that it is the same as the enthalpy of atomization of dihydrogen. This is true for all diatomic molecules. For example:
In the case of polyatomic molecules, bond dissociation enthalpy is different for different bonds within the same molecule.
Polyatomic Molecules: Let us now consider a polyatomic molecule like methane,
In methane, all the four
Therefore,
In such cases we use mean bond enthalpy of
For example in
We find that mean
[^2]This relationship is particularly more useful when the required values of
Table 6.3(a) Some Mean Single Bond Enthalpies in
435.8 | 414 | 389 | 464 | 569 | 293 | 318 | 339 | 431 | 368 | 297 | ||
347 | 293 | 351 | 439 | 289 | 264 | 259 | 330 | 276 | 238 | |||
159 | 201 | 272 | - | 209 | - | 201 | 243 | - | ||||
138 | 184 | 368 | 351 | - | 205 | - | 201 | |||||
155 | 540 | 490 | 327 | 255 | 197 | - | ||||||
176 | 213 | 226 | 360 | 289 | 213 | |||||||
213 | 230 | 331 | 272 | 213 | ||||||||
213 | 251 | 213 | - | |||||||||
243 | 218 | 209 | ||||||||||
192 | 180 | |||||||||||
151 |
Table 6.3(b) Some Mean Multiple Bond Enthalpies in
418 | 611 | ||||
946 | 837 | ||||
615 | 741 | ||||
891 | 1070 |
(reactants and products) in the reaction are in gaseous state.
(d) Lattice Enthalpy
The lattice enthalpy of an ionic compound is the enthalpy change which occurs when one mole of an ionic compound dissociates into its ions in gaseous state.
Since it is impossible to determine lattice enthalpies directly by experiment, we use an indirect method where we construct an enthalpy diagram called a Born-Haber Cycle (Fig. 6.9).
Let us now calculate the lattice enthalpy of
1.
2.
3.
4.
You have learnt about ionization enthalpy and electron gain enthalpy in Unit 3. In fact, these terms have been taken from thermodynamics. Earlier terms, ionization energy and electron affinity were in practice in place of the above terms (see the box for justification).
Ionization Energy and Electron Affinity
Ionization energy and electron affinity are defined at absolute zero. At any other temperature, heat capacities for the reactants and the products have to be taken into account. Enthalpies of reactions for
at temperature,
The value of
So,
Therefore,
6.
The sequence of steps is shown in Fig. 6.9, and is known as a Born-Haber cycle. The importance of the cycle is that, the sum of the enthalpy changes round a cycle is zero. Applying Hess’s law, we get,
for
Internal energy is smaller by 2RT (because
Now we use the value of lattice enthalpy to calculate enthalpy of solution from the expression:
For one mole of
lattice enthalpy
The dissolution of
(e) Enthalpy of Solution (symbol :
Enthalpy of solution of a substance is the enthalpy change when one mole of it dissolves in a specified amount of solvent. The enthalpy of solution at infinite dilution is the enthalpy change observed on dissolving the substance in an infinite amount of solvent when the interactions between the ions (or solute molecules) are negligible.
When an ionic compound dissolves in a solvent, the ions leave their ordered positions on the crystal lattice. These are now more free in solution. But solvation of these ions (hydration in case solvent is water) also occurs at the same time. This is shown diagrammatically, for an ionic compound,
The enthalpy of solution of
For most of the ionic compounds,
(f) Enthalpy of Dilution
It is known that enthalpy of solution is the enthalpy change associated with the addition of a specified amount of solute to the specified amount of solvent at a constant temperature and pressure. This argument can be applied to any solvent with slight modification. Enthalpy change for dissolving one mole of gaseous hydrogen chloride in
Let us consider the following set of enthalpy changes:
(S-1)
(S-2)
(S-3)
The values of
If we subtract the first equation (equation
This value
6.6 SPONTANEITY
The first law of thermodynamics tells us about the relationship between the heat absorbed and the work performed on or by a system. It puts no restrictions on the direction of heat flow. However, the flow of heat is unidirectional from higher temperature to lower temperature. In fact, all naturally occurring processes whether chemical or physical will tend to proceed spontaneously in one direction only. For example, a gas expanding to fill the available volume, burning carbon in dioxygen giving carbon dioxide.
But heat will not flow from colder body to warmer body on its own, the gas in a container will not spontaneously contract into one corner or carbon dioxide will not form carbon and dioxygen spontaneously. These and many other spontaneously occurring changes show unidirectional change. We may ask ‘what is the driving force of spontaneously occurring changes? What determines the direction of a spontaneous change? In this section, we shall establish some criterion for these processes whether these will take place or not.
Let us first understand what do we mean by spontaneous reaction or change ? You may think by your common observation that spontaneous reaction is one which occurs immediately when contact is made between the reactants. Take the case of combination of hydrogen and oxygen. These gases may be mixed at room temperature and left for many years without observing any perceptible change. Although the reaction is taking place between them, it is at an extremely slow rate. It is still called spontaneous reaction. So spontaneity means ‘having the potential to proceed without the assistance of external agency’. However, it does not tell about the rate of the reaction or process. Another aspect of spontaneous reaction or process, as we see is that these cannot reverse their direction on their own. We may summarise it as follows:
A spontaneous process is an irreversible process and may only be reversed by some external agency.
(a) Is Decrease in Enthalpy a Criterion for Spontaneity?
If we examine the phenomenon like flow of water down hill or fall of a stone on to the ground, we find that there is a net decrease in potential energy in the direction of change. By analogy, we may be tempted to state that a chemical reaction is spontaneous in a given direction, because decrease in energy has taken place, as in the case of exothermic reactions. For example:
The decrease in enthalpy in passing from reactants to products may be shown for any exothermic reaction on an enthalpy diagram as shown in Fig. 6.10(a).
Thus, the postulate that driving force for a chemical reaction may be due to decrease in energy sounds ‘reasonable’ as the basis of evidence so far!
Now let us examine the following reactions:
Fig. 6.10 (a) Enthalpy diagram for exothermic reactions
These reactions though endothermic, are spontaneous. The increase in enthalpy may be represented on an enthalpy diagram as shown in Fig. 6.10(b).
Fig. 6.10 (b) Enthalpy diagram for endothermic reactions
Therefore, it becomes obvious that while decrease in enthalpy may be a contributory factor for spontaneity, but it is not true for all cases.
(b) Entropy and Spontaneity
Then, what drives the spontaneous process in a given direction ? Let us examine such a case in which
Let us consider diffusion of two gases into each other in a closed container which is isolated from the surroundings as shown in Fig. 6.11.
The two gases, say, gas A and gas B are represented by black dots and white dots
respectively and separated by a movable partition [Fig. 6.11 (a)]. When the partition is withdrawn [Fig. 6.11(b)], the gases begin to diffuse into each other and after a period of time, diffusion will be complete.
Let us examine the process. Before partition, if we were to pick up the gas molecules from left container, we would be sure that these will be molecules of gas A and similarly if we were to pick up the gas molecules from right container, we would be sure that these will be molecules of gas B. But, if we were to pick up molecules from container when partition is removed, we are not sure whether the molecules picked are of gas A or gas B. We say that the system has become less predictable or more chaotic.
We may now formulate another postulate: in an isolated system, there is always a tendency for the systems’ energy to become more disordered or chaotic and this could be a criterion for spontaneous change!
At this point, we introduce another thermodynamic function, entropy denoted as
Now let us try to quantify entropy. One way to calculate the degree of disorder or chaotic distribution of energy among molecules would be through statistical method which is beyond the scope of this treatment. Other way would be to relate this process to the heat involved in a process which would make entropy a thermodynamic concept. Entropy, like any other thermodynamic property such as internal energy
Whenever heat is added to the system, it increases molecular motions causing increased randomness in the system. Thus heat
The total entropy change
When a system is in equilibrium, the entropy is maximum, and the change in entropy,
We can say that entropy for a spontaneous process increases till it reaches maximum and at equilibrium the change in entropy is zero. Since entropy is a state property, we can calculate the change in entropy of a reversible process by
We find that both for reversible and irreversible expansion for an ideal gas, under isothermal conditions,
(c) Gibbs Energy and Spontaneity
We have seen that for a system, it is the total entropy change,
For this purpose, we define a new thermodynamic function the Gibbs energy or Gibbs function,
Gibbs function,
The change in Gibbs energy for the system,
At constant temperature,
Usually the subscript ‘system’ is dropped and we simply write this equation as
Thus, Gibbs energy change
Now let us consider how
We know,
If the system is in thermal equilibrium with the surrounding, then the temperature of the surrounding is same as that of the system. Also, increase in enthalpy of the surrounding is equal to decrease in the enthalpy of the system.
Therefore, entropy change of surroundings,
Rearranging the above equation:
For spontaneous process,
Using equation 5.21, the above equation can be written as
(i) If
(ii) If
Note : If a reaction has a positive enthalpy change and positive entropy change, it can be spontaneous when
(d) Entropy and Second Law of Thermodynamics
We know that for an isolated system the change in energy remains constant. Therefore, increase in entropy in such systems is the natural direction of a spontaneous change. This, in fact is the second law of thermodynamics. Like first law of thermodynamics, second law can also be stated in several ways. The second law of thermodynamics explains why spontaneous exothermic reactions are so common. In exothermic reactions heat released by the reaction increases the disorder of the surroundings and overall entropy change is positive which makes the reaction spontaneous.
(e) Absolute Entropy and Third Law of Thermodynamics
Molecules of a substance may move in a straight line in any direction, they may spin like a top and the bonds in the molecules may stretch and compress. These motions of the molecule are called translational, rotational and vibrational motion respectively. When temperature of the system rises, these motions become more vigorous and entropy increases. On the other hand when temperature is lowered, the entropy decreases. The entropy of any pure crystalline substance approaches zero as the temperature approaches absolute zero. This is called third law of thermodynamics. This is so because there is perfect order in a crystal at absolute zero. The statement is confined to pure crystalline solids because theoretical arguments and practical evidences have shown that entropy of solutions and super cooled liquids is not zero at
6.7 GIBBS ENERGY CHANGE AND EQUILIBRIUM
We have seen how a knowledge of the sign and magnitude of the free energy change of a chemical reaction allows:
(i) Prediction of the spontaneity of the chemical reaction.
(ii) Prediction of the useful work that could be extracted from it.
So far we have considered free energy changes in irreversible reactions. Let us now examine the free energy changes in reversible reactions.
‘Reversible’ under strict thermodynamic sense is a special way of carrying out a process such that system is at all times in perfect equilibrium with its surroundings. When applied to a chemical reaction, the term ‘reversible’ indicates that a given reaction can proceed in either direction simultaneously, so that a dynamic equilibrium is set up. This means that the reactions in both the directions should proceed with a decrease in free energy, which seems impossible. It is possible only if at equilibrium the free energy of the system is minimum. If it is not, the system would spontaneously change to configuration of lower free energy.
So, the criterion for equilibrium
Gibbs energy for a reaction in which all reactants and products are in standard state,
or
We also know that
For strongly endothermic reactions, the value of
Using equation (6.24),
Table 6.4 Effect of Temperature on Spontaneity of Reactions
Description |
|||
---|---|---|---|
- | + | - | Reaction spontaneous at all temperatures |
- | - | Reaction spontaneous at low temperature | |
- | - | Reaction nonspontaneous at high temperature | |
+ | + | Reaction nonspontaneous at low temperature | |
+ | + | Reaction spontaneous at high temperature | |
+ | - | Reaction nonspontaneous at all temperatures |
- The term low temperature and high temperature are relative. For a particular reaction, high temperature could even mean room temperature.
(i) It is possible to obtain an estimate of
(ii) If
Using equation (6.24),
Summary
Thermodynamics deals with energy changes in chemical or physical processes and enables us to study these changes quantitatively and to make useful predictions. For these purposes, we divide the universe into the system and the surroundings. Chemical or physical processes lead to evolution or absorption of heat (q), part of which may be converted into work (w). These quantities are related through the first law of thermodynamics via
At constant volume,
There are varieties of enthalpy changes. Changes of phase such as melting, vaporization and sublimation usually occur at constant temperature and can be characterized by enthalpy changes which are always positive. Enthalpy of formation, combustion and other enthalpy changes can be calculated using Hess’s law. Enthalpy change for chemical reactions can be determined by
and in gaseous state by
First law of thermodynamics does not guide us about the direction of chemical reactions i.e., what is the driving force of a chemical reaction. For isolated systems,
Chemical reactions are generally carried at constant pressure, so we define another state function Gibbs energy,
For a spontaneous change,
Standard Gibbs energy change is related to equilibrium constant by