Chemical Equilibrium PDF

60 304 Chemical Equilibrium E3 Chapter 8 Chemical Equilibrium Whenever we hear the word Equilibrium immediately a picture arises in our mind an object under the influence of two opposing forces. For chemical reactions also this is true. A reaction also can exist in a state of equilibrium balancing f...

60 304 Chemical Equilibrium E3 Chapter 8 Chemical Equilibrium Whenever we hear the word Equilibrium immediately a picture arises in our mind an object under the influence of two opposing forces. For chemical reactions also this is true. A reaction also can exist in a state of equilibrium balancing forward and backward reactions. ID (d) Esterification, e.g., (e) Evaporation of water in a closed vessel, e.g., H 2 O(l) ⇌ H 2 O(g) Q U Reversible and Irreversible reactions CH 3 COOH  C2 H 5 OH ⇌ CH 3 COOC 2 H 5  H 2 O D YG A chemical reaction is said to have taken place when the concentration of reactants decreases, and the concentration of the products increases with time. The chemical reactions are classified on the basis of the extent to which they proceed, into the following two classes; (1) Reversible reactions : Reaction in which entire amount of the reactants is not converted into products is termed as reversible reaction. (2) Irreversible reactions : Reaction in which entire amount of the reactants is converted into products is termed as irreversible reaction. (i) Characteristics of irreversible reactions (a) These reactions proceed only in one direction (forward direction), (b) These reactions can proceed to completion, (i) Characteristics of reversible reactions (a) These reactions can be started from either side, U (b) These reactions are never complete, (c) In an irreversible reaction, G < 0, (d) The arrow () is placed between reactants and products, (c) These reactions have a tendency to attain a state of equilibrium, in which Free energy change is zero (G = 0), ST (d) This sign (⇌) represents the reversibility of the reaction, (ii) Examples of reversible reactions (a) Neutralisation between an acid and a base either of which or both are weak e.g., (ii) Examples of irreversible reactions (a) Neutralisation between strong acid and strong base e.g., NaOH  HCl NaCl  H 2 O 13.7 kcal (b) Double decomposition reactions or precipitation reactions e.g., CH 3 COOH  Na OH ⇌ CH 3 COONa  H 2 O BaCl 2 (aq )  H 2 SO 4 (aq ) BaSO 4 (s)  2 HCl(aq ) (b) Salt hydrolysis, e.g., (c) Thermal decomposition, e.g., Fe Cl3  3 H 2 O ⇌ Fe OH 3  3 HCl (c) Thermal decomposition, e.g., PCl 5 ( g ) ⇌ PCl 3 ( g )  Cl 2 ( g ) Q MnO2 , 2 KClO 3 (s)   2 KCl (s)  3O2  (d) Redox reactions, e.g., SnCl 2(aq )  2 FeCl 3 (aq) SnCl 4 (aq)  2 FeCl 2(aq) Chemical Equilibrium 305 k f [ A]a [B]b  k b [C]c [D]d Equilibrium and Its dynamic nature “Equilibrium is the state at which the concentration of reactants and products do not change with time. i.e. concentrations of reactants and products become constant.” Concentration Products kf kb  Kc  [C]c [D]d [ A]a [B]b Where, K c is called equilibrium constant. In terms of partial pressures, equilibrium constant is denoted by K p and PCc PDd PAa PBb In terms of mole fraction, equilibrium constant is denoted by K x and Time Equilibrium state The important characteristics of equilibrium state are, (1) Equilibrium state can be recognised by the constancy of certain measurable properties such as pressure, density, colour, concentration etc. by changing these conditions of the system, we can control the extent to which a reaction proceeds. (2) Equilibrium state can only be achieved in close vessel. (3) Equilibrium state is reversible in nature. (5) At equilibrium state, Rate of forward reaction = Rate of backward reaction Equilibrium state Time Law of mass action and Equilibrium constant On the basis of observations of many equilibrium reactions, two Norwegian chemists Goldberg and Waage suggested (1864) a quantitative relationship between the rates of reactions and the concentration of the reacting substances. This relationship is known as law of mass action. It states that U “The rate of a chemical reaction is directly proportional to the product of the molar concentrations of the reactants at a constant temperature at any given time.” The molar concentration i.e. number of moles per litre is also called active mass. It is expressed by enclosing the symbols of formulae of the substance in square brackets. For example, molar concentration of A is expressed as [A]. ST K p  K x (P)n n = number of moles of gaseous products – number of moles of gaseous reactants in chemical equation. As a general rule, the concentration of pure solids and pure liquids are not included when writing an equilibrium equation. Value of n U G= 0 D YG Rate of reaction (6) At equilibrium state, G = 0, so that H = TS. K p  Kc (RT )n ID (4) Equilibrium state is also dynamic in nature. (X C )c (X D )d (X A )a (X B )b Relation between Kp, Kc and Kx Kx  E3 Reactants 60 Kp  Consider a simple reversible reaction Relation between Kp and Kc Units of Kp Units of Kc 0 Kp = K c No unit No unit >0 Kp > K c (atm)n (mole l–1)n K. Q Kc Reactants Products QK (Reverse reaction) Types of equilibria The equilibrium between different chemical species present in the same or different phases is called chemical equilibrium. There are two types of chemical equilibrium. (1) Homogeneous equilibrium : The equilibrium reactions in which all the reactants and the products are in the same phase are called homogeneous equilibrium reactions. C 2 H 5 OH (l)  CH 3 COOH (l) ⇌ CH 3COOC 2 H5 (l)  H 2O(l) N 2 (g)  3 H 2 (g) ⇌ 2 NH 3 (g) 2SO 2 (g)  O 2 (g) ⇌ 2SO 3 (g) completion. Reaction proceeds hardly at all (ii) If Q < K, the reaction will proceed in the direction of the products (forward reaction). U 2SO 3 (g) ⇌ 2SO 2 (g)  O2 (g) and SO 3 (g) ⇌ SO 2 (g)  1 / 2O2 (g) [SO 2 ][O 2 ]1 / 2 [SO 2 ]2 [O 2 ] and K   2 [SO 3 ] [SO 3 ] (i) If Q > K, the reaction will proceed in the direction of reactants (reverse reaction). ID (7) The value of the equilibrium constant depends upon the stoichiometry of the chemical equation. It may be noted that Q becomes equal to equilibrium constant (K) when the reaction is at the equilibrium state. At equilibrium, Q  K  K c  K p. Thus, 60 (ii) When H = +ve i.e., heat is absorbed, the reaction is endothermic. The temperature T2 is higher than T1. [ X ][Y ]. [ A][B] E3 Thus, equilibrium constant remains the same at all temperatures. K (2) Predicting the direction of reaction : The concentration ratio, i.e., ratio of the product of concentrations of products to that of reactants is also known as concentration quotient and is denoted by Q. (2) Heterogeneous equilibrium : The equilibrium reactions in which the reactants and the products are present in different phases are called heterogeneous equilibrium reactions. 2 NaHCO 3 (s) ⇌ Na 2 CO 3 (s)  CO 2 (g)  H 2 O (g) Ca(OH )2 (s)  H 2 O (l) ⇌ Ca 2  (aq)  2OH  (aq) 103 Both reactants and products are present at equilibrium Reaction proceeds to completion CaCO 3 (s) ⇌ CaO (s)  CO 2 (g) H 2 O (l) ⇌ H 2 O (g) Chemical Equilibrium 307 Table : 8.1 Homogeneous equilibria and equations for equilibrium constant (Equilibrium pressure is P atm in a V L flask) Initial mole Mole at Equilibrium 1 (1–x) Total mole at equilibrium (g) 1 (1– x) 2 SO 2  O2 ⇌ 2 SO 3 N 2  3 H 2 ⇌ 2 NH 3 2 HI (g) (g) (g) 0 1 2x (1–x) 2 (g) (g) (g) 30 (3–3x) 2x (g) 2 1 (2–2x) (1–x) (4 – 2x) PCl 5 ⇌ PCl 3  Cl 2 (g) (g) (g) 1 0 0 (1–x) x x (g) 0 2x (3 – x) (1 + x) 60 ⇌ H 2 + I2 n  0; K p  Kc n  0 ; K p  Kc n  0 ; K p  Kc Active masses 1  x  1  x       V   V  2x V  1  x   1  x   2x     3    V   V   V   2  2x   1  x       V   V  Mole fraction 1  x  1  x       2   2  2x 2 x 1x 31 x    2 2  x  2  2  x  (2  x )  2  2x     3x  Partial pressure 1  x   1  x   2x   p  p  p  2   2   2   1  x   3(1  x )  Px  P   P    2(2  x ) _   2(2  x )  (2  x )  2  2x   2x  1x  P  P    P  3x  3 x 3 x P Kc 4x2 1  x  2 4 x 2V 2 27 1  x  4 x 2V 1  x  3 x2 1  x  V Kp 4x2 1  x  2 16 x 2 2  x  2 2 1  x     V  x 2 3  x  P 1  x  1 x   1 x  Px 2 1  x2  3 x   V x   V 1 x   x   x        1  x  1  x  1  x  E3  1  x   2x      3 x 3 x ID 27 1  x  P 4  2x     V   x   1 x   x   1 x  P P  Table : 8.2 Heterogeneous equilibria and equation for equilibrium constant (Equilibrium pressure is P atm) 1 0 Mole at equilibrium (1–x) x Total moles at equilibrium (solid not included) Mole fraction Partial pressure x 2x x 1  2x 2 P 2 1 2 P 2 P2 4 U Kp 0 Relationship between equilibrium constant and G° 1 1 ST G for a reaction under any condition is related with G° by the relation, G  G  2.303 RT log Q Standard free energy change of a reaction and its equilibrium constant are related to each other at temperature T by the relation, G o  2.303 RT log K For a general reaction aA  bB ⇌ cC  dD K (aC )c (aD )d (a A )a (aB )b Where a represent the activity of the reactants and products. It is unit less. For pure solids and liquids: a  1. For gases: a  pressure of gas in atm. 0 (1–x) (1–x) D YG Initial mole C(s)  CO2 (g) ⇌ 2 CO (g) U NH 4 HS (s) ⇌ NH 3 (g) + H 2 S (g) 2x NH 2CO2 NH 4 (s) ⇌ 2 NH 3 (g)  CO2 (g) 1 0 (1–x) 2x (1+x) 0 x 3x 1  x    1  x   2x    1  x  1  x   2x  P  P  1  x  1  x  4P x2 (1  x 2 ) 1 3 2 3 2P 3 P 3 4 P3 27 For components in solution: a  molar concentration. Le-Chatelier's principle Le-Chatelier and Braun (1884), French chemists, made certain generalizations to explain the effect of changes in concentration, temperature or pressure on the state of system in equilibrium. When a system is subjected to a change in one of these factors, the equilibrium gets disturbed and the system readjusts itself until it returns to equilibrium. The generalization is known as Le-Chatelier's principle. It may be stated as : “Change in any of the factors that determine the equilibrium conditions of a system will shift the equilibrium in such a manner to reduce or to counteract the effect of the change.” 308 Chemical Equilibrium The principle is very helpful in predicting qualitatively the effect of change in concentration, pressure or temperature on a system in equilibrium. Table : 8.3 The effect of varying conditions on the equilibrium a A + b B ⇌ c C + d D, n = (c + d) – (a + b) Equilibrium position moves Equilibrium constant Any other points Conc. of A and/or B increased To right No change No change Conc. of C and /or D increased To left No change No change Pressure increased To right if (c  d )  (a  b ) , i.e. n  ve No change To left if (c  d )  (a  b ) , i.e. n  ve No change Very little effect, if any, on reactions in liquid solution. No change No change if (c  d )  (a  b ) , i.e. n  0 To left if H  ve (exothermic) Value decreased To right if H  ve (endothermic) Value increased Addition of catalyst No change No change (b) Low temperature D YG (c) Excess of N 2 and H 2 (d) Removal of NH 3 favours forward reaction. (ii) Formation of sulphur trioxide 2 SO 2  O 2 ⇌ 2SO 3  45 kcal (exothermic) 2 vol 1 vol 2 vol (a) High pressure (n  0) (b) Low temperature (c) Excess of SO 2 and O 2 , favours the reaction in U forward direction. (iii) Synthesis of nitric oxide ⇌ 2 NO  43. 2 kcal (endothermic ) 2 vol ST N 2  O2 1 vol 1 vol (a) High temperature (b) Excess of N 2 and O 2 (c) Since reaction takes place without change in volume i.e., n  0 , pressure has no effect on equilibrium. (iv) Formation of nitrogen dioxide 2 NO  O 2 ⇌ 2 NO 2  27.8 Kcal 2 vol 1 vol 2 vol (a) High pressure (b) Low temperature (c) Excess of NO and O 2 favours the reaction in forward direction. 1 vol 1 vol 1 vol (a) Low pressure or high volume of the container, n  0 (b) High temperature (c) Excess of PCl 5. (2) Applications to the physical equilibrium (i) Melting of ice (Ice – water system) U ⇌ 2 NH 3  23 kcal (exothermic) (a) High pressure (n  0) PCl 5 ⇌ PCl 3  Cl 2  15 kcal ID The Le-Chateliers principle has a great significance for the chemical, physical systems and in every day life in a state of equilibrium. (1) Applications to the chemical equilibrium (i) Synthesis of ammonia (Haber’s process) 2 vol Equilibrium achieved faster (v) Dissociation of phosphours pentachloride Application of Le-Chatelier's principle N 2  3H 2 1 vol 3 vol Equilibrium achieved faster E3 Temperature increased 60 Change imposed on the system in equilibrium Ice (Greater Volume) ⇌ Water  x kcal (Lesser Volume) (In this reaction volume is decreased from 1.09 c.c. to 1.01 c.c. per gm.) (a) At high temperature more water is formed as it absorbs heat. (b) At high pressure more water is formed as it is accompanied by decrease in volume. (c) At higher pressure, melting point of ice is lowered, while boiling point of water is increased. (ii) Melting of sulphur : S (s) ⇌ S (l)  x kcal (This reaction accompanies increase in volume.) (a) At high temperature, more liquid sulphur is formed. (b) At higher pressure, less sulphur will melt as melting increases volume. (c) At higher pressure, melting point of sulphur is increased. (iii) Boiling of water (water- water vapour system) Water ⇌ Water Vapours  x kcal (Low volume) (Higher volume) (It is accompanied by absorption of heat and increase in volume.) (a) At high temperature more vapours are formed. (b) At higher pressure, vapours will be converted to liquid as it decreases volume. (c) At higher pressure, boiling point of water is increased (principle of pressure cooker). (iv) Solubility of salts : If solubility of a salt is accompanied by absorption of heat, its solubility increases with rise in temperature; e.g., NH 4 Cl, K2 SO 4 , KNO 3 etc. Chemical Equilibrium 309 KNO 3(s)  (aq)  KNO 3(aq)  x kcal On the other hand if it is accompanied by evolution of heat, solubility decreases with increase in temperature; e.g., CaCl 2 , Ca(OH )2 , NaOH , KOH etc.    Ca(OH )2( s)  (aq)  Ca(OH )2 (aq)  x kcal decreased and dissolved CO2 gas escapes out with a fizze. Increase in pressure favours melting of ice into water Flash evaporation is a technique generally used for concentrating certain aqueous solutions which cannot be concentrated by normal boiling. Freeze drying is a technique where water is made to sublime off at a temperature below 0°C. (II) N 2 O 4 (g) ⇌ 2 NO 2(g) , y  2 ST U 1 (III) 2NO 2 ⇌ N 2 O 4 , y  2 2(d  D) Dd  x (for I and II) and x  (for III) d d Also D  2  Molecular weight (theoretical value) d  2  Molecular weight (abnormal value) of the mixture.  Pure ice can be made to melt at a temperature slightly    A reversible reaction is one which [MP PET 1986] E3 2. D YG Where M  Initial molecular mass, m  molecular mass at equilibrium Thus for the equilibria (I) PCl 5(g) ⇌ PCl 3(g)  Cl 2(g) , y  2 1. (a) Proceeds in one direction (b) Proceeds in both directions (c) Proceeds spontaneously (d) All the statements are wrong Which of the following is a characteristic of a reversible reaction [AFMC 1993] (a) Number of moles of reactants and products are equal (b) It can be influenced by a catalyst (c) It can never proceed to completion (d) None of the above The reaction CaCO 3 ⇌ CaO  CO 2 (g) goes to completion in lime kiln because 3. U D is also called Van’t Hoff factor. d M m In terms of molecular mass, x  (y  1) m reactant. Reversible and Irreversible reaction ID In the following reversible chemical equation. A ⇌ yB Initial mol 1 0 At equilibrium (1–x) yx x = degree of dissociation Number of moles of A and B at equilibrium  1  x  yx  1  x (y  1) If initial volume of 1 mole of A is V, then volume of equilibrium mixture of A and B is,  [1  x (y  1)]V Molar density before dissociation, molecular weight m D  volume V Molar density after dissociation, D m Dd ;  [1  x (y  1)] ; x  d [1  x (y  1)]V d d(y  1) y is the number of moles of products from one mole of 60 Relation between vapour density and Degree of dissociation below 0°C by increasing the pressure. As the water so obtained on melting is below 0°C, it refreezes when pressure is reduced. It is called regelation of ice. Increase in external pressure always increases the boiling point and vice-versa. If the reaction is multipled by 2, the equilibrium constant is squared. When a bottle of coca or beer is opened, the pressure is [MP PMT/PET 1988; CPMT 1990] (a) Of the high temperature (b) CaO is more stable than CaCO 3 (c) CaO is not dissociated (d) CO 2 escapes continuously 4. 5. In the given reaction N 2  O 2 ⇌ 2 NO , equilibrium means that (a) Concentration of reactants is changing where as concentration of products is constant (b) Concentration of all substances is constant (c) Concentration of reactants is constant where as concentration of products is changing (d) Concentration of all substances is changing Which of the following reactions is reversible [MADT Bihar 1980] (a) H 2  I 2  2 HI (b) H 2 SO 4  Ba (OH )2  BaSO 4  2 H 2 O (c) NaCl  AgNO 3  NaNO 3  AgCl 6. (d) Fe  S  FeS All reactions which have chemical disintegration [MP PMT 1990] (a) (b) (c) (d) 7. Is reversible Is reversible and endothermic Is exothermic Is reversible or irreversible and endothermic or exothermic Amongst the following chemical reactions the irreversible reaction is [MP PMT 1999] [ 310 Chemical Equilibrium (a) H 2  I 2 ⇌ HI (b) AgNO 3  NaCl ⇌ AgCl  NaNO 3 (c) CaCO 3 ⇌ CaO  CO 2 ST U D YG U ID E3 60 (d) O2  2SO 2 ⇌ 2SO 3