Equilibrium
Chemical equilibria are important in numerous biological and environmental processes. For example, equilibria involving
When a liquid evaporates in a closed container, molecules with relatively higher kinetic energy escape the liquid surface into the vapour phase and number of liquid molecules from the vapour phase strike the liquid surface and are retained in the liquid phase. It gives rise to a constant vapour pressure because of an equilibrium in which the number of molecules leaving the liquid equals the number returning to liquid from the vapour. We say that the system has reached equilibrium state at this stage. However, this is not static equilibrium and there is a lot of activity at the boundary between the liquid and the vapour. Thus, at equilibrium, the rate of evaporation is equal to the rate of condensation. It may be represented by
The double half arrows indicate that the processes in both the directions are going on simultaneously. The mixture of reactants and products in the equilibrium state is called an equilibrium mixture.
Equilibrium can be established for both physical processes and chemical reactions. The reaction may be fast or slow depending on the experimental conditions and the nature of the reactants. When the reactants in a closed vessel at a particular temperature react to give products, the concentrations of the reactants keep on decreasing, while those of products keep on increasing for some time after which there is no change in the concentrations of either of the reactants or products. This stage of the system is the dynamic equilibrium and the rates of the forward and reverse reactions become equal. It is due to this dynamic equilibrium stage that there is no change in the concentrations of various species in the reaction mixture. Based on the extent to which the reactions proceed to reach the state of chemical equilibrium, these may be classified in three groups.
(i) The reactions that proceed nearly to completion and only negligible concentrations of the reactants are left. In some cases, it may not be even possible to detect these experimentally.
(ii) The reactions in which only small amounts of products are formed and most of the reactants remain unchanged at equilibrium stage.
(iii) The reactions in which the concentrations of the reactants and products are comparable, when the system is in equilibrium.
The extent of a reaction in equilibrium varies with the experimental conditions such as concentrations of reactants, temperature, etc. Optimisation of the operational conditions is very important in industry and laboratory so that equilibrium is favorable in the direction of the desired product. Some important aspects of equilibrium involving physical and chemical processes are dealt in this unit along with the equilibrium involving ions in aqueous solutions which is called as ionic equilibrium.
7.1 EQUILIBRIUM IN PHYSICAL PROCESSES
The characteristics of system at equilibrium are better understood if we examine some physical processes. The most familiar examples are phase transformation processes, e.g.,
7.1.1 Solid-Liquid Equilibrium
Ice and water kept in a perfectly insulated thermos flask (no exchange of heat between its contents and the surroundings) at
It is obvious that ice and water are in equilibrium only at particular temperature and pressure. For any pure substance at atmospheric pressure, the temperature at which the solid and liquid phases are at equilibrium is called the normal melting point or normal freezing point of the substance. The system here is in dynamic equilibrium and we can infer the following:
(i) Both the opposing processes occur simultaneously.
(ii) Both the processes occur at the same rate so that the amount of ice and water remains constant.
7.1.2 Liquid-Vapour Equilibrium
This equilibrium can be better understood if we consider the example of a transparent box carrying a U-tube with mercury (manometer). Drying agent like anhydrous calcium chloride (or phosphorus penta-oxide) is placed for a few hours in the box. After removing the drying agent by tilting the box on one side, a watch glass (or petri dish) containing water is quickly placed inside the box. It will be observed that the mercury level in the right limb of the manometer slowly increases and finally attains a constant value, that is, the pressure inside the box increases and reaches a constant value. Also the volume of water in the watch glass decreases (Fig. 7.1). Initially there was no water vapour (or very less) inside the box. As water evaporated the pressure in the box increased due to addition of water molecules into the gaseous phase inside the box. The rate of evaporation is constant.
However, the rate of increase in pressure decreases with time due to condensation of vapour into water. Finally it leads to an equilibrium condition when there is no net evaporation. This implies that the number of water molecules from the gaseous state into the liquid state also increases till the equilibrium is attained i.e.,
rate of evaporation= rate of condensation
At equilibrium the pressure exerted by the water molecules at a given temperature remains constant and is called the equilibrium vapour pressure of water (or just vapour pressure of water); vapour pressure of water increases with temperature. If the above experiment is repeated with methyl alcohol, acetone and ether, it is observed that different liquids have different equilibrium vapour pressures at the same temperature, and the liquid which has a higher vapour pressure is more volatile and has a lower boiling point.
If we expose three watch glasses containing separately
Water and water vapour are in equilibrium position at atmospheric pressure (1.013 bar) and at
7.1.3 Solid - Vapour Equilibrium
Let us now consider the systems where solids sublime to vapour phase. If we place solid iodine in a closed vessel, after sometime the vessel gets filled up with violet vapour and the intensity of colour increases with time. After certain time the intensity of colour becomes constant and at this stage equilibrium is attained. Hence solid iodine sublimes to give iodine vapour and the iodine vapour condenses to give solid iodine. The equilibrium can be represented as,
Other examples showing this kind of equilibrium are,
Camphor (solid)
7.1.4 Equilibrium Involving Dissolution of Solid or Gases in Liquids
Solids in liquids
We know from our experience that we can dissolve only a limited amount of salt or sugar in a given amount of water at room temperature. If we make a thick sugar syrup solution by dissolving sugar at a higher temperature, sugar crystals separate out if we cool the syrup to the room temperature. We call it a saturated solution when no more of solute can be dissolved in it at a given temperature. The concentration of the solute in a saturated solution depends upon the temperature. In a saturated solution, a dynamic equilibrium exits between the solute molecules in the solid state and in the solution:
Sugar (solution)
the rate of dissolution of sugar
Equality of the two rates and dynamic nature of equilibrium has been confirmed with the help of radioactive sugar. If we drop some radioactive sugar into saturated solution of non-radioactive sugar, then after some time radioactivity is observed both in the solution and in the solid sugar. Initially there were no radioactive sugar molecules in the solution but due to dynamic nature of equilibrium, there is exchange between the radioactive and non-radioactive sugar molecules between the two phases. The ratio of the radioactive to non-radioactive molecules in the solution increases till it attains a constant value.
Gases in liquids
When a soda water bottle is opened, some of the carbon dioxide gas dissolved in it fizzes out rapidly. The phenomenon arises due to difference in solubility of carbon dioxide at different pressures. There is equilibrium between the molecules in the gaseous state and the molecules dissolved in the liquid under pressure i.e.,
This equilibrium is governed by Henry’s law, which states that the mass of a gas dissolved in a given mass of a solvent at any temperature is proportional to the pressure of the gas above the solvent. This amount decreases with increase of temperature. The soda water bottle is sealed under pressure of gas when its solubility in water is high. As soon as the bottle is opened, some of the dissolved carbon dioxide gas escapes to reach a new equilibrium condition required for the lower pressure, namely its partial pressure in the atmosphere. This is how the soda water in bottle when left open to the air for some time, turns ‘flat’. It can be generalised that:
(i) For solid
(ii) For liquid
(iii) For dissolution of solids in liquids, the solubility is constant at a given temperature.
(iv) For dissolution of gases in liquids, the concentration of a gas in liquid is proportional to the pressure (concentration) of the gas over the liquid. These observations are summarised in Table 6.1
Table 6.1 Some Features of Physical Equilibria
Process | Conclusion |
---|---|
Liquid |
temperature |
Solid |
Melting point is fixed at constant pressure |
Solute Sugar |
Concentration of solute in solution is constant at a given temperature |
[gas constant at a given temperature constant at a given temperature |
7.1.5 General Characteristics of Equilibria Involving Physical Processes
For the physical processes discussed above, following characteristics are common to the system at equilibrium:
(i) Equilibrium is possible only in a closed system at a given temperature.
(ii) Both the opposing processes occur at the same rate and there is a dynamic but stable condition.
(iii) All measurable properties of the system remain constant.
(iv) When equilibrium is attained for a physical process, it is characterised by constant value of one of its parameters at a given temperature. Table 6.1 lists such quantities.
(v) The magnitude of such quantities at any stage indicates the extent to which the physical process has proceeded before reaching equilibrium.
7.2 EQUILIBRIUM IN CHEMICAL PROCESSES - DYNAMIC EQUILIBRIUM
Analogous to the physical systems chemical reactions also attain a state of equilibrium. These reactions can occur both in forward and backward directions. When the rates of the forward and reverse reactions become equal, the concentrations of the reactants and the products remain constant. This is the stage of chemical equilibrium. This equilibrium is dynamic in nature as it consists of a forward reaction in which the reactants give product(s) and reverse reaction in which product(s) gives the original reactants.
For a better comprehension, let us consider a general case of a reversible reaction,
With passage of time, there is accumulation of the products
Eventually, the two reactions occur at the same rate and the system reaches a state of equilibrium.
Similarly, the reaction can reach the state of equilibrium even if we start with only
The dynamic nature of chemical equilibrium can be demonstrated in the synthesis of ammonia by Haber’s process. In a series of experiments, Haber started with known amounts of dinitrogen and dihydrogen maintained at high temperature and pressure and at regular intervals determined the amount of ammonia present. He was successful in determining also the concentration of unreacted dihydrogen and dinitrogen. Fig. 7.4 (page 174) shows that after a certain time the composition of the mixture remains the same even though some of the reactants are still present. This constancy in composition indicates that the reaction has reached equilibrium. In order to understand the dynamic nature of the reaction, synthesis of ammonia is carried out with exactly the same starting conditions (of partial pressure and temperature) but using
equilibrium is attained, these two mixtures
Use of isotope (deuterium) in the formation of ammonia clearly indicates that chemical reactions reach a state of dynamic equilibrium in which the rates of forward and reverse reactions are equal and there is no net change in composition.
Equilibrium can be attained from both sides, whether we start reaction by taking,
Similarly let us consider the reaction,
Dynamic Equilibrium - A Student’s Activity
Equilibrium whether in a physical or in a chemical system, is always of dynamic nature. This can be demonstrated by the use of radioactive isotopes. This is not feasible in a school laboratory. However this concept can be easily comprehended by performing the following activity. The activity can be performed in a group of 5 or 6 students.
Take two
Put one tube in cylinder 1 and second in cylinder 2. Immerse one tube in cylinder 1 , close its upper tip with a finger and transfer the coloured water contained in its lower portion to cylinder 2. Using second tube, kept in
If you continue intertransferring coloured solution between the cylinders, there will not be any further change in the levels of coloured water in two cylinders. If we take analogy of ’level’ of coloured water with ‘concentration’ of reactants and products in the two cylinders, we can say the process of transfer, which continues even after the constancy of level, is indicative of dynamic nature of the process. If we repeat the experiment taking two tubes of different diameters we find that at equilibrium the level of coloured water in two cylinders is different. How far diameters are responsible for change in levels in two cylinders? Empty cylinder (2) is an indicator of no product in it at the beginning.
7.3 LAW OF CHEMICAL EQUILIBRIUM AND EQUILIBRIUM CONSTANT
A mixture of reactants and products in the equilibrium state is called an equilibrium mixture. In this section we shall address a number of important questions about the composition of equilibrium mixtures: What is the relationship between the concentrations of reactants and products in an equilibrium mixture? How can we determine equilibrium concentrations from initial concentrations? What factors can be exploited to alter the
composition of an equilibrium mixture? The last question in particular is important when choosing conditions for synthesis of industrial chemicals such as
To answer these questions, let us consider a general reversible reaction:
where
(6.1) where
The equilibrium equation is also known as the law of mass action because in the early days of chemistry, concentration was called “active mass”. In order to appreciate their work better, let us consider reaction between gaseous
Six sets of experiments with varying initial conditions were performed, starting with only gaseous
Data obtained from all six sets of experiments are given in Table 6.2.
It is evident from the experiments 1,2 , 3 and 4 that number of moles of dihydrogen reacted
Knowing the above facts, in order to establish a relationship between concentrations of the reactants and products, several combinations can be tried. Let us consider the simple expression,
It can be seen from Table 6.3 that if we put the equilibrium concentrations of the reactants and products, the above expression
is far from constant. However, if we consider the expression,
we find that this expression gives constant value (as shown in Table 6.3) in all the six cases. It can be seen that in this expression the power of the concentration for reactants and products are actually the stoichiometric coefficients in the equation for the chemical reaction. Thus, for the reaction
Generally the subscript ’eq’ (used for equilibrium) is omitted from the concentration terms. It is taken for granted that the concentrations in the expression for
The subscript ’
At a given temperature, the product of concentrations of the reaction products raised to the respective stoichiometric coefficient in the balanced chemical equation divided by the product of concentrations of the reactants raised to their individual stoichiometric coefficients has a constant value. This is known as the Equilibrium Law or Law of Chemical Equilibrium. The equilibrium constant for a general reaction,
is expressed as,
where
Equilibrium constant for the reaction,
Molar concentration of different species is indicated by enclosing these in square bracket and, as mentioned above, it is implied that these are equilibrium concentrations. While writing expression for equilibrium constant, symbol for phases (
Let us write equilibrium constant for the reaction,
The equilibrium constant for the reverse reaction,
Equilibrium constant for the reverse reaction is the inverse of the equilibrium constant for the reaction in the forward direction.If we change the stoichiometric coefficients in a chemical equation by multiplying throughout by a factor then we must make sure that the expression for equilibrium constant also reflects that change. For example, if the reaction (6.5) is written as,
the equilibrium constant for the above reaction is given by
On multiplying the equation (7.5) by
Therefore, equilibrium constant for the reaction is equal to
Table 6.4 Relations between Equilibrium Constants for a General Reaction and its Multiples.
Chemical equation | Equilibrium constant |
---|---|
7.4 HOMOGENEOUS EQUILIBRIA
In a homogeneous system, all the reactants and products are in the same phase. For example, in the gaseous reaction,
and,
all the reactants and products are in homogeneous solution phase. We shall now consider equilibrium constant for some homogeneous reactions.
7.4.1 Equilibrium Constant in Gaseous Systems
So far we have expressed equilibrium constant of the reactions in terms of molar concentration of the reactants and products, and used symbol,
The ideal gas equation is written as,
Here,
Therefore,
If concentration
We can also write
Here,
At constant temperature, the pressure of the gas is proportional to its concentration i.e.,
For reaction in equilibrium
We can write either
or
Further, since
Therefore,
In this example,
or
Similarly, for a general reaction
where
1 pascal,
Table 6.5 Equilibrium Constants,
Reaction | Temperature |
|
---|---|---|
298 | ||
400 | 41 | |
500 | ||
298 | ||
500 | ||
700 | ||
298 | 0.98 | |
400 | 47.9 | |
500 | 1700 |
7.5 HETEROGENEOUS EQUILIBRIA
Equilibrium in a system having more than one phase is called heterogeneous equilibrium. The equilibrium between water vapour and liquid water in a closed container is an example of heterogeneous equilibrium.
In this example, there is a gas phase and a liquid phase. In the same way, equilibrium between a solid and its saturated solution,
is a heterogeneous equilibrium.
Heterogeneous equilibria often involve pure solids or liquids. We can simplify equilibrium expressions for the heterogeneous equilibria involving a pure liquid or a pure solid, as the molar concentration of a pure solid or liquid is constant (i.e., independent of the amount present). In other words if a substance ’
On the basis of the stoichiometric equation, we can write,
Since
This shows that at a particular temperature, there is a constant concentration or pressure of
Similarly, in the equilibrium between nickel, carbon monoxide and nickel carbonyl (used in the purification of nickel),
the equilibrium constant is written as
It must be remembered that for the existence of heterogeneous equilibrium pure solids or liquids must also be present (however small the amount may be) at equilibrium, but their concentrations or partial pressures do not appear in the expression of the equilibrium constant. In the reaction,
Units of Equilibrium Constant
The value of equilibrium constant
For the reactions, unit.
Equilibrium constants can also be expressed as dimensionless quantities if the standard state of reactants and products are specified. For a pure gas, the standard state is 1 bar. Therefore a pressure of 4 bar in standard state can be expressed as 4 bar
7.6 APPLICATIONS OF EQUILIBRIUM CONSTANTS
Before considering the applications of equilibrium constants, let us summarise the important features of equilibrium constants as follows:
1. Expression for equilibrium constant is applicable only when concentrations of the reactants and products have attained constant value at equilibrium state.
2. The value of equilibrium constant is independent of initial concentrations of the reactants and products.
3. Equilibrium constant is temperature dependent having one unique value for a particular reaction represented by a balanced equation at a given temperature.
4. The equilibrium constant for the reverse reaction is equal to the inverse of the equilibrium constant for the forward reaction.
5. The equilibrium constant
Let us consider applications of equilibrium constant to:
-
predict the extent of a reaction on the basis of its magnitude,
-
predict the direction of the reaction, and
-
calculate equilibrium concentrations.
7.6.1 Predicting the Extent of a Reaction
The numerical value of the equilibrium constant for a reaction indicates the extent of the reaction. But it is important to note that an equilibrium constant does not give any information about the rate at which the equilibrium is reached. The magnitude of
We can make the following generalisations concerning the composition of equilibrium mixtures:
- If
, products predominate over reactants, i.e., if is very large, the reaction proceeds nearly to completion. Consider the following examples:
- If
, reactants predominate over products, i.e., if is very small, the reaction proceeds rarely. Consider the following examples: (a) The decomposition of into and at has a very small equilibrium constant,
- If
is in the range of to , appreciable concentrations of both reactants and products are present. Consider the following examples:
These generarlisations are illustrated in Fig. 7.6
7.6.2 Predicting the Direction of the Reaction
The equilibrium constant helps in predicting the direction in which a given reaction will proceed at any stage. For this purpose, we calculate the reaction quotient
Then,
If
If
Consider the gaseous reaction of
Suppose we have molar concentrations
Thus, the reaction quotient,
Now, in this case,
The reaction quotient,
Thus, we can make the following generalisations concerning the direction of the reaction (Fig. 7.7) :
- If
, net reaction goes from left to right - If
, net reaction goes from right to left. - If
, no net reaction occurs.
7.6.3 Calculating Equilibrium Concentrations
In case of a problem in which we know the initial concentrations but do not know any of the equilibrium concentrations, the following three steps shall be followed:
Step 1. Write the balanced equation for the reaction.
Step 2. Under the balanced equation, make a table that lists for each substance involved in the reaction:
(a) the initial concentration,
(b) the change in concentration on going to equilibrium, and
(c) the equilibrium concentration.
In constructing the table, define
Step 3. Substitute the equilibrium concentrations into the equilibrium equation for the reaction and solve for
Step 4. Calculate the equilibrium concentrations from the calculated value of
Step 5. Check your results by substituting them into the equilibrium equation.
7.7 RELATIONSHIP BETWEEN EQUILIBRIUM CONSTANT , REACTION QUOTIENT AND GIBBS ENERGY
The value of
is negative, then the reaction is spontaneous and proceeds in the forward direction. is positive, then reaction is considered non-spontaneous. Instead, as reverse reaction would have a negative , the products of the forward reaction shall be converted to the reactants. is 0 , reaction has achieved equilibrium; at this point, there is no longer any free energy left to drive the reaction.
A mathematical expression of this thermodynamic view of equilibrium can be described by the following equation:
where,
At equilibrium, when
Hence, using the equation (7.23), the reaction spontaneity can be interpreted in terms of the value of
-
If
, then is positive, and , making , which implies a spontaneous reaction or the reaction which proceeds in the forward direction to such an extent that the products are present predominantly. -
If
, then is negative, and , that is , , which implies a non-spontaneous reaction or a reaction which proceeds in the forward direction to such a small degree that only a very minute quantity of product is formed.
7.8 FACTORS AFFECTING EQUILIBRIA
One of the principal goals of chemical synthesis is to maximise the conversion of the
reactants to products while minimising the expenditure of energy. This implies maximum yield of products at mild temperature and pressure conditions. If it does not happen, then the experimental conditions need to be adjusted. For example, in the Haber process for the synthesis of ammonia from
Equilibrium constant,
We shall now be discussing factors which can influence the equilibrium.
7.8.1 Effect of Concentration Change
In general, when equilibrium is disturbed by the addition/removal of any reactant/ products, Le Chatelier’s principle predicts that:
- The concentration stress of an added reactant/product is relieved by net reaction in the direction that consumes the added substance.
- The concentration stress of a removed reactant/product is relieved by net reaction in the direction that replenishes the removed substance. or in other words, “When the concentration of any of the reactants or products in a reaction at equilibrium is changed, the composition of the equilibrium mixture changes so as to minimize the effect of concentration changes”.
Let us take the reaction,
If
The same point can be explained in terms of the reaction quotient,
Addition of hydrogen at equilibrium results in value of
Effect of Concentration - An experiment
This can be demonstrated by the following reaction:
yellow deep red
A reddish colour appears on adding two drops of
Addition of aq.
7.8.2 Effect of Pressure Change
A pressure change obtained by changing the volume can affect the yield of products in case of a gaseous reaction where the total number of moles of gaseous reactants and total number of moles of gaseous products are different. In applying Le Chatelier’s principle to a heterogeneous equilibrium the effect of pressure changes on solids and liquids can be ignored because the volume (and concentration) of a solution/liquid is nearly independent of pressure.
Consider the reaction,
Here,
As
In reaction
7.8.3 Effect of Inert Gas Addition
If the volume is kept constant and an inert gas such as argon is added which does not take part in the reaction, the equilibrium remains undisturbed. It is because the addition of an inert gas at constant volume does not change the partial pressures or the molar reaction. The reaction quotient changes only if the added gas is a reactant or product involved in the reaction.
7.8.4 Effect of Temperature Change
Whenever an equilibrium is disturbed by a change in the concentration, pressure or volume, the composition of the equilibrium mixture changes because the reaction quotient,
In general, the temperature dependence of the equilibrium constant depends on the sign of
- The equilibrium constant for an exothermic reaction (negative
) decreases as the temperature increases. - The equilibrium constant for an endothermic reaction (positive
) increases as the temperature increases.
Temperature changes affect the equilibrium constant and rates of reactions. Production of ammonia according to the reaction,
is an exothermic process. According to Le Chatelier’s principle, raising the temperature shifts the equilibrium to left and decreases the equilibrium concentration of ammonia. In other words, low temperature is favourable for high yield of ammonia, but practically very low temperatures slow down the reaction and thus a catalyst is used.
Effect of Temperature - An experiment
Effect of temperature on equilibrium can be demonstrated by taking
formation of
Effect of temperature can also be seen in an endothermic reaction,
At room temperature, the equilibrium mixture is blue due to
7.8.5 Effect of a Catalyst
A catalyst increases the rate of the chemical reaction by making available a new low energy pathway for the conversion of reactants to products. It increases the rate of forward and reverse reactions that pass through the same transition state and does not affect equilibrium. Catalyst lowers the activation energy for the forward and reverse reactions by exactly the same amount. Catalyst does not affect the equilibrium composition of a reaction mixture. It does not appear in the balanced chemical equation or in the equilibrium constant expression.
Let us consider the formation of
German chemist, Fritz Haber discovered that a catalyst consisting of iron catalyse the reaction to occur at a satisfactory rate at temperatures, where the equilibrium concentration of
Optimum conditions of temperature and pressure for the synthesis of
though the value of
Note: If a reaction has an exceedingly small
7.9 IONIC EQUILIBRIUM IN SOLUTION
Under the effect of change of concentration on the direction of equilibrium, you have incidently come across with the following equilibrium which involves ions:
There are numerous equilibria that involve ions only. In the following sections we will study the equilibria involving ions. It is well known that the aqueous solution of sugar does not conduct electricity. However, when common salt (sodium chloride) is added to water it conducts electricity. Also, the conductance of electricity increases with an increase in concentration of common salt. Michael Faraday classified the substances into two categories based on their ability to conduct electricity. One category of substances conduct electricity in their aqueous solutions and are called electrolytes while the other do not and are thus, referred to as non-electrolytes. Faraday further classified electrolytes into strong and weak electrolytes. Strong electrolytes on dissolution in water are ionized almost completely, while the weak electrolytes are only partially dissociated. For example, an aqueous solution of sodium chloride is comprised entirely of sodium ions and chloride ions, while that of acetic acid mainly contains unionized acetic acid molecules and only some acetate ions and hydronium ions. This is because there is almost
7.10 ACIDS, BASES AND SALTS
Acids, bases and salts find widespread occurrence in nature. Hydrochloric acid present in the gastric juice is secreted by the lining of our stomach in a significant amount of 1.2-1.5 L/day and is essential for digestive processes. Acetic acid is known to be the main constituent of vinegar. Lemon and orange juices contain citric and ascorbic acids, and tartaric acid is found in tamarind paste. As most of the acids taste sour, the word “acid” has been derived from a latin word “acidus” meaning sour. Acids are known to turn blue litmus paper into red and liberate dihydrogen on reacting with some metals. Similarly, bases are known to turn red litmus paper blue, taste bitter and feel soapy. A common example of a base is washing soda used for washing purposes. When acids and bases are mixed in the right proportion they react with each other to give salts. Some commonly known examples of salts are sodium chloride, barium sulphate, sodium nitrate. Sodium chloride (common salt) is an important component of our diet and is formed by reaction between hydrochloric acid and sodium hydroxide. It exists in solid state as a cluster of positively charged sodium ions and negatively charged chloride ions which are held together due to electrostatic interactions between oppositely charged species (Fig.6.10). The electrostatic forces between two charges are inversely proportional to dielectric constant of the medium. Water, a universal solvent, possesses a very high dielectric constant of 80 . Thus, when sodium chloride is dissolved in water, the electrostatic interactions are reduced by a factor of 80 and this facilitates the ions to move freely in the solution. Also, they are well-separated due to hydration with water molecules.
Comparing, the ionization of hydrochloric acid with that of acetic acid in water we find that though both of them are polar covalent
molecules, former is completely ionized into its constituent ions, while the latter is only partially ionized
Faraday was born near London into a family of very limited means. At the age of 14 he was an apprentice to a kind bookbinder who allowed Faraday to read the books he was binding. Through a fortunate chance he became laboratory assistant to Davy, and during 1813-4, Faraday accompanied him to the Continent. During this trip he gained much from the experience of coming into contact with many of the leading scientists of the time. In 1825, he succeeded Davy as Director of the Royal Institution laboratories, and in 1833 he also became the first Fullerian Professor of Chemistry. Faraday’s first important work was on analytical chemistry. After 1821 much of his work was on electricity and magnetism and different electromagnetic phenomena. His ideas have led to the establishment of modern field theory. He discovered his two laws of electrolysis in 1834. Faraday was a very modest and kind hearted person. He declined all honours and avoided scientific controversies. He preferred to work alone and never had any assistant. He disseminated science in a variety of ways including his Friday evening discourses, which he founded at the Royal Institution. He has been very famous for his Christmas lecture on the ‘Chemical History of a Candle’. He published nearly 450 scientific papers.
7.10.1 Arrhenius Concept of Acids and Bases
According to Arrhenius theory, acids are substances that dissociates in water to give hydrogen ions
A bare proton,
Thus, it bonds to the oxygen atom of a solvent water molecule to give trigonal pyramidal hydronium ion,
Similarly, a base molecule like
The hydroxyl ion also exists in the hydrated form in the aqueous solution. Arrhenius concept of acid and base, however, suffers from the limitation of being applicable only to aqueous solutions and also, does not account for the basicity of substances like, ammonia which do not possess a hydroxyl group.
Hydronium and Hydroxyl Ions
Hydrogen ion by itself is a bare proton with very small size (
7.10.2 The Brönsted-Lowry Acids and Bases
The Danish chemist, Johannes Brönsted and the English chemist, Thomas M. Lowry gave a more general definition of acids and bases. According to Brönsted-Lowry theory, acid is a substance that is capable of donating a hydrogen ion
Consider the example of dissolution of
The basic solution is formed due to the presence of hydroxyl ions. In this reaction, water molecule acts as proton donor and ammonia molecule acts as proton acceptor and are thus, called Lowry-Brönsted acid and base, respectively. In the reverse reaction,
Consider the example of ionization of hydrochloric acid in water.
It can be seen in the above equation, that water acts as a base because it accepts the proton. The species
It is interesting to observe the dual role of water as an acid and a base. In case of reaction with
Arrhenius was born near Uppsala, Sweden. He presented his thesis, on the conductivities of electrolyte solutions, to the University of Uppsala in 1884. For the next five years he travelled extensively and visited a number of research centers in Europe. In 1895 he was appointed professor of physics at the newly formed University of Stockholm, serving its rector from 1897 to 1902. From 1905 until his death he was Director of physical chemistry at the Nobel Institute in Stockholm. He continued to work for many years on electrolytic solutions. In 1899 he discussed the temperature dependence of reaction rates on the basis of an equation, now usually known as Arrhenius equation.
He worked in a variety of fields, and made important contributions to immunochemistry, cosmology, the origin of life, and the causes of ice age. He was Nobel Prize in Chemistry in 1903 for his theory of electrolytic dissociation and its use in the development of chemistry.
7.10.3 Lewis Acids and Bases
G.N. Lewis in 1923 defined an acid as a species which accepts electron pair and base which donates an electron pair. As far as bases are concerned, there is not much difference between Brönsted-Lowry and Lewis concepts, as the base provides a lone pair in both the cases. However, in Lewis concept many acids do not have proton. A typical example is reaction of electron deficient species
Electron deficient species like
7.11 IONIZATION OF ACIDS AND BASES
Arrhenius concept of acids and bases becomes useful in case of ionization of acids and bases as mostly ionizations in chemical and biological systems occur in aqueous medium. Strong acids like perchloric acid
In section 7.10 .2 we saw that acid (or base) dissociation equilibrium is dynamic involving a transfer of proton in forward and reverse directions. Now, the question arises that if the equilibrium is dynamic then with passage of time which direction is favoured? What is the driving force behind it? In order to answer these questions we shall deal into the issue of comparing the strengths of the two acids (or bases) involved in the dissociation equilibrium. Consider the two acids
It follows that as a strong acid dissociates completely in water, the resulting base formed would be very weak i.e., strong acids have very weak conjugate bases. Strong acids like perchloric acid
Certain water soluble organic compounds like phenolphthalein and bromothymol blue behave as weak acids and exhibit different colours in their acid (HIn) and conjugate base (In
Such compounds are useful as indicators in acid-base titrations, and finding out
7.11.1 The Ionization Constant of Water and its Ionic Product
Some substances like water are unique in their ability of acting both as an acid and a base. We have seen this in case of water in section 6.10.2. In presence of an acid, HA it accepts a proton and acts as the base while in the presence of a base,
The dissociation constant is represented by,
The concentration of water is omitted from the denominator as water is a pure liquid and its concentration remains constant.
The concentration of
The value of
The density of pure water is
We can distinguish acidic, neutral and basic aqueous solutions by the relative values of the
7.11.2 The pH Scale
Hydronium ion concentration in molarity is more conveniently expressed on a logarithmic scale known as the
From the definition of
Thus, an acidic solution of
Acidic solutions possess a concentration of hydrogen ions,
Acidic solution has
Basic solution has
Neutral solution has
Now again, consider the equation (7.28) at
Taking negative logarithm on both sides of equation, we obtain
Note that although
Measurement of
For greater accuracy pH meters are used. pH meter is a device that measures the pH-dependent electrical potential of the test solution within 0.001 precision. pH meters of the size of a writing pen are now available in the market. The pH of some very common substances are given in Table 7.5 (page 212).
Table 6.5 The pH of Some Common Substances
Name of the Fluid | pH | Name of the Fluid | pH |
---|---|---|---|
Saturated solution of NaOH | Black Coffee | 5.0 | |
O.1 M NaOH solution | 13 | Tomato juice | |
Lime water | 10.5 | Soft drinks and vinegar | |
Milk of magnesia | 10 | Lemon juice | |
Egg white, sea water | 7.8 | Gastric juice | |
Human blood | 7.4 | 1 M HCl solution | |
Milk | 6.8 | Concentrated HCl | |
Human Saliva | 6.4 |
7.11.3 Ionization Constants of Weak Acids
Consider a weak acid HX that is partially ionized in the aqueous solution. The equilibrium can be expressed by:
Let
Change (M)
Equilibrium concentration (M)
Here,
At a given temperature
The values of the ionization constants of some selected weak acids are given in Table 6.6.
Table 6.6 The Ionization Constants of Some Selected Weak Acids (at 298K)
Acid | Ionization Constant, |
---|---|
Hydrofluoric Acid |
|
Nitrous Acid |
|
Formic Acid |
|
Niacin |
|
Acetic Acid |
|
Benzoic Acid |
|
Hypochlorous Acid |
|
Hydrocyanic Acid |
|
Phenol |
The
Knowing the ionization constant,
A general step-wise approach can be adopted to evaluate the
Step 1. The species present before dissociation are identified as Brönsted-Lowry acids/bases.
Step 2. Balanced equations for all possible reactions i.e., with a species acting both as acid as well as base are written.
Step 3. The reaction with the higher
Step 4. Enlist in a tabular form the following values for each of the species in the primary reaction
(a) Initial concentration, c.
(b) Change in concentration on proceeding to equilibrium in terms of
(c) Equilibrium concentration.
Step 5. Substitute equilibrium concentrations into equilibrium constant equation for principal reaction and solve for
Step 6. Calculate the concentration of species in principal reaction.
Step 7. Calculate
The above mentioned methodology has been elucidated in the following examples.
7.11.4 Ionization of Weak Bases
The ionization of base
In a weak base there is partial ionization of
Alternatively, if
The values of the ionization constants of some selected weak bases,
Table 6.7 The Values of the Ionization Constant of Some Weak Bases at
Base | |
---|---|
Dimethylamine, |
|
Triethylamine, |
|
Ammonia, |
|
Quinine, |
|
Pyridine, |
|
Aniline, |
|
Urea, |
Many organic compounds like amines are weak bases. Amines are derivatives of ammonia in which one or more hydrogen atoms are replaced by another group. For example, methylamine, codeine, quinine and
nicotine all behave as very weak bases due to their very small
The
7.11.5 Relation between and
As seen earlier in this chapter,
Where,
It can be seen from the net reaction that the equilibrium constant is equal to the product of equilibrium constants
This can be extended to make a generalisation. The equilibrium constant for a net reaction obtained after adding two (or more) reactions equals the product of the equilibrium constants for individual reactions:
Similarly, in case of a conjugate acid-base pair,
Knowing one, the other can be obtained. It should be noted that a strong acid will have a weak conjugate base and vice-versa.
Alternatively, the above expression
As the concentration of water remains constant it has been omitted from the denominator and incorporated within the dissociation constant. Then multiplying and dividing the above expression by
It may be noted that if we take negative logarithm of both sides of the equation, then
7.11.6 Di- and Polybasic Acids and Di- and Polyacidic Bases
Some of the acids like oxalic acid, sulphuric acid and phosphoric acids have more than one ionizable proton per molecule of the acid. Such acids are known as polybasic or polyprotic acids.
The ionization reactions for example for a dibasic acid
And the corresponding equilibrium constants are given below:
Here,
Table 6.8 The Ionization Constants of Some Common Polyprotic Acids (298K)
Acid | |||
---|---|---|---|
Oxalic Acid | |||
Ascorbic Acid | |||
Sulphurous Acid | |||
Sulphuric Acid | Very large | ||
Carbonic Acid | |||
Citric Acid | |||
Phosphoric Acid |
It can be seen that higher order ionization constants
Polyprotic acid solutions contain a mixture of acids like
7.11.7 Factors Affecting Acid Strength
Having discussed quantitatively the strengths of acids and bases, we come to a stage where we can calculate the
But it should be noted that while comparing elements in the same group of the periodic table,
Similarly,
But, when we discuss elements in the same row of the periodic table, H-A bond polarity becomes the deciding factor for determining the acid strength. As the electronegativity of A increases, the strength of the acid also increases. For example,
7.11.8 Common Ion Effect in the Ionization of Acids and Bases
Consider an example of acetic acid dissociation equilibrium represented as:
or
Addition of acetate ions to an acetic acid solution results in decreasing the concentration of hydrogen ions,
In order to evaluate the
Initial concentration
Let
Change in concentration (M)
Equilibrium concentration (M)
Therefore,
As
Hence,
Thus,
7.11.9 Hydrolysis of Salts and the pH of their Solutions
Salts formed by the reactions between acids and bases in definite proportions, undergo ionization in water. The cations/anions
formed on ionization of salts either exist as hydrated ions in aqueous solutions or interact with water to reform corresponding acids/ bases depending upon the nature of salts. The later process of interaction between water and cations/anions or both of salts is called hydrolysis. The
We now consider the hydrolysis of the salts of the following types :
(i) salts of weak acid and strong base e.g.,
(ii) salts of strong acid and weak base e.g.,
(iii) salts of weak acid and weak base, e.g.,
In the first case,
Acetate ion thus formed undergoes hydrolysis in water to give acetic acid and
Acetic acid being a weak acid
Similarly,
Ammonium ions undergo hydrolysis with water to form
Ammonium hydroxide is a weak base
Consider the hydrolysis of
Without going into detailed calculation, it can be said that degree of hydrolysis is independent of concentration of solution, and
The
7.12 BUFFER SOLUTIONS
Many body fluids e.g., blood or urine have definite
7.12.1 Designing Buffer Solution
Knowledge of
Preparation of Acidic Buffer
To prepare a buffer of acidic
For which we can write the expression
Rearranging the expression we have,
Taking logarithm on both the sides and rearranging the terms we get -
The expression (7.40) is known as Henderson-Hasselbalch equation. The quantity
In the equation (6.39), if the concentration of
A similar analysis of a buffer made with a weak base and its conjugate acid leads to the result,
We know that
or
If molar concentration of base and its conjugate acid (cation) is same then
7.13 SOLUBILITY EQUILIBRIA OF SPARINGLY SOLUBLE SALTS
We have already known that the solubility of ionic solids in water varies a great deal. Some of these (like calcium chloride) are so soluble that they are hygroscopic in nature and even absorb water vapour from atmosphere. Others (such as lithium fluoride) have so little solubility that they are commonly termed as insoluble. The solubility depends on a number of factors important amongst which are the lattice enthalpy of the salt and the solvation enthalpy of the ions in a solution. For a salt to dissolve in a solvent the strong forces of attraction between its ions (lattice enthalpy) must be overcome by the ion-solvent interactions. The solvation enthalpy of ions is referred to in terms of solvation which is always negative i.e. energy is released in the process of solvation. The amount of solvation enthalpy depends on the nature of the solvent. In case of a nonpolar (covalent) solvent, solvation enthalpy is small and hence, not sufficient to overcome lattice enthalpy of the salt. Consequently, the salt does not dissolve in non-polar solvent. As a general rule, for a salt to be able to dissolve in a particular solvent its solvation enthalpy must be greater than its lattice enthalpy so that the latter may be overcome by former. Each salt has its characteristic solubility which depends on temperature. We classify salts on the basis of their solubility in the following three categories.
Category I | Soluble | Solubility |
Category II | Slightly Soluble |
|
Category III | Sparingly Soluble |
Solubility |
We shall now consider the equilibrium between the sparingly soluble ionic salt and its saturated aqueous solution.
7.13.1 Solubility Product Constant
Let us now have a solid like barium sulphate in contact with its saturated aqueous solution. The equilibrium between the undisolved solid and the ions in a saturated solution can be represented by the equation:
The equilibrium constant is given by the equation:
For a pure solid substance the concentration remains constant and we can write
We call
Thus, molar solubility of barium sulphate will be equal to
A salt may give on dissociation two or more than two anions and cations carrying different charges. For example, consider a salt like zirconium phosphate of molecular formula
A solid salt of the general formula
And its solubility product constant is given by:
The term
Name of the Salt | Formula | |
---|---|---|
Silver Bromide | ||
Silver Carbonate | ||
Silver Chromate | ||
Silver Chloride | ||
Silver Iodide | AgI | |
Silver Sulphate | ||
Aluminium Hydroxide | ||
Barium Chromate | ||
Barium Fluoride | ||
Barium Sulphate | ||
Calcium Carbonate | ||
Calcium Fluoride | ||
Calcium Hydroxide | ||
Calcium Oxalate | ||
Calcium Sulphate | ||
Cadmium Hydroxide | ||
Cadmium Sulphide | ||
Chromic Hydroxide | ||
Cuprous Bromide | ||
Cupric Carbonate | ||
Cuprous Chloride | ||
Cupric Hydroxide | ||
Cuprous Iodide | CuI | |
Cupric Sulphide | CuS | |
Ferrous Carbonate | ||
Ferrous Hydroxide | ||
Ferric Hydroxide | ||
Ferrous Sulphide | ||
Mercurous Bromide | ||
Mercurous Chloride | ||
Mercurous Iodide | ||
Mercurous Sulphate | ||
Mercuric Sulphide | HgS | |
Magnesium Carbonate | ||
Magnesium Fluoride | ||
Magnesium Hydroxide | ||
Magnesium Oxalate | ||
Manganese Carbonate | ||
Manganese Sulphide | ||
Nickel Hydroxide | ||
Nickel Sulphide | NiS | |
Lead Bromide | ||
Lead Carbonate | ||
Lead Chloride | ||
Lead Fluoride | ||
Lead Hydroxide | ||
Lead Iodide | ||
Lead Sulphate | ||
Lead Sulphide | ||
Stannous Hydroxide | ||
Stannous Sulphide | ||
Strontium Carbonate | ||
Strontium Fluoride | ||
Strontium Sulphate | ||
Thallous Bromide | ||
Thallous Chloride | ||
Thallous Iodide | TII | |
Zinc Carbonate | ||
Zinc Hydroxide | ||
Zinc Sulphide |
7.13.2 Common Ion Effect on Solubility of Ionic Salts
It is expected from Le Chatelier’s principle that if we increase the concentration of any one of the ions, it should combine with the ion of its opposite charge and some of the salt will be precipitated till once again
The solubility of salts of weak acids like phosphates increases at lower
Taking inverse of both side and adding 1 we get
Now, again taking inverse, we get
Thus solubility
Summary
When the number of molecules leaving the liquid to vapour equals the number of molecules returning to the liquid from vapour, equilibrium is said to be attained and is dynamic in nature. Equilibrium can be established for both physical and chemical processes and at this stage rate of forward and reverse reactions are equal. Equilibrium constant,
Equilibrium constant has constant value at a fixed temperature and at this stage all the macroscopic properties such as concentration, pressure, etc. become constant. For a gaseous reaction equilibrium constant is expressed as
All substances that conduct electricity in aqueous solutions are called electrolytes. Acids, bases and salts are electrolytes and the conduction of electricity by their aqueous solutions is due to anions and cations produced by the dissociation or ionization of electrolytes in aqueous solution. The strong electrolytes are completely dissociated. In weak electrolytes there is equilibrium between the ions and the unionized electrolyte molecules. According to Arrhenius, acids give hydrogen ions while bases produce hydroxyl ions in their aqueous solutions. Brönsted-Lowry on the other hand, defined an acid as a proton donor and a base as a proton acceptor. When a Brönsted-Lowry acid reacts with a base, it produces its conjugate base and a conjugate acid corresponding to the base with which it reacts. Thus a conjugate pair of acid-base differs only by one proton. Lewis further generalised the definition of an acid as an electron pair acceptor and a base as an electron pair donor. The expressions for ionization (equilibrium) constants of weak acids
SUGGESTED ACTIVITIES FOR STUDENTS REGARDING THIS UNIT
(a) The student may use
(b) The
(c) They may prepare some buffer solutions by mixing the solutions of sodium acetate and acetic acid and determine their
(d) They may be provided with different indicators to observe their colours in solutions of varying
(e) They may perform some acid-base titrations using indicators.
(f) They may observe common ion effect on the solubility of sparingly soluble salts.
(g) If