Chemical Equilibrium, Lecture notes of Physical Chemistry

Download Chemical Equilibrium and more Lecture notes Physical Chemistry in PDF only on Docsity! Shejuti Rahman Brishty Lecturer, Department of Pharmacy Chemical Equilibrium Reversible reaction A reaction which can go in the forward and backward direction simultaneously is called a ‘Reversible Reaction’. Such a reaction is represented by writing a pair of arrows between the teactants and products. A+B=C+D The arrow pointing the right indicates the forward reaction, while that pointing left shows the reverse reaction. Examples of reversible reactions Some common examples of reversible reactions are listed below: © =2NO> (g) = N20s4 (g) © Hp (g)+ h(g) = 2HI (g) © PCls (s) = PCls (s) + Cle (g) © CaCOs (s) = CaO (s) + COz (g) © CH3COOH (/) + C2HsOH (J) = CHsCOOC2Hs (/) + H20 (D Equilibrium Equilibrium is a state in which there are no observable changes as time goes by. Chemical equilibrium The state of a reversible reaction when the two opposing reactions occur at the same rate and the concentrations of the reactants and products do not change with time. H+ |p ==> 2HI Reaction Rate Time —————> Shejuti Rahman Brishty Lecturer, Department of Pharmacy More clearly, chemical equilibrium is achieved when: 1. the rates of the forward and reverse reactions are equal and 2. the concentrations of the reactants and products remain constant. Chemical Equilibrium is Dynamic Equilibrium A+B2C+D As this reaction attains equilibrium, the concentrations of A and B, as also of C and D remains constant with time. Apparently, it appears that the equilibrium is dead. But it is not so. The equilibrium is dynamic. Actually, the forward and the reverse reactions are taking place at equilibrium but the concentrations remain unchanged. Consider the following reversible reaction, Hp (g) + b (g) = 2HI (g) The dynamic nature of chemical equilibrium can be demonstrated by adding small amount of radioactive iodine (I2*) to the above reaction in the state of equilibrium. It is noticed after some time that a mixture contains radioactive hydrogen iodide (HI*). It indicates that the reaction is going on even at equilibrium. Ha (g) + I*2 (g) = 2HI* (g) Characteristics of chemical equilibrium 1) Constancy of concentrations. When a chemical equilibrium is established in a closed vessel at constant temperature, concentrations of the various species in the reaction mixture become constant. The reaction mixture at equilibrium is called Equilibrium mixture. The concentrations at equilibrium are called Equilibrium concentrations. The equilibrium concentrations are represented by square brackets. Thus, [A] denotes the equilibrium concentration of substance A in moles per litre (mol L”). 2) Equilibrium can be initiated from either side. The state of equilibrium of a reversible reaction can be approached whether we start with reactants or products, for example, the equilibrium H2 (g) + I: (g) = 2HI (g) is established if we start the reaction with H2 and In, or 2 HI. 3) Equilibrium cannot be attained in an open vessel. The equilibrium can be established only if the reaction vessel is closed and no part of the reactants or products is allowed to escape out. In an open vessel, the gaseous teactants and/or products may escape into the atmosphere leaving behind no possibility of attaining equilibrium. However, the equilibrium can be attained when all the reactants and products are in the same phase i.e., ethanol and ethanoic acid: CH3COOH (/) + C2HsOH (I) = CHsCOOC3Hs (I) + H20 () Shejuti Rahman Brishty Lecturer, Department of Pharmacy Consider the reaction Costtcient’” 2a = c+D ofA Here, the forward reaction is dependent on the collisions of each of twoA molecules. Therefore. for writing the equilibrium expression, each molecule is regarded as a separate entity ie., A+tA — C+D Then the equilibrium constant expression is [CHD] _ [C1001 paper equa [ATA] [A] coefficent of A As a general rule, if there are two or more molecules of the same substance in the chemical equation. its concentration is raised to the power equal to the numerical coefficient of the substance in the equation. k= Equilibrium Constant Expression for a Reaction in General Terms The general reaction may be written as aA+bB == cC+dD where a, b, c and d are numerical quotients of the substance. A, B, C and D respectively. The equilibrium constant expression is _Ic¥ (ok *~ [al [sl where K- is the Equilibrium constant. The general definition of the equilibrium constant may thus be stated as: ‘the product of the equilibrium concentrations of the products divided by the product of the equilibrium concentrations of the reactants, with each concentration term raised to a power equal to the coefficient of the substance in the balanced equation’. How to write Equilibrium Constant Expression? (steps 1-4 from Bahl & Tuli book) Step 1. Write the balanced chemical equation for the equilibrium reaction. By convention, the substances on the left of the equation are called ‘reactants’ _and those on the right are called ‘products. Step 2. Write the product of concentrations of the ‘products’ and raise the concentrations of each substance to the power ofits numerical quotient in the balanced equation. Step 3. Write the product of concentrations of the ‘reactants’ and raise the concentrations of each substance to the power ofits numerical quotient in the balanced equation. Example: N> (g) + 3H2 (g) = 2NHs (g) This is a balanced chemical equation. For this equation, * The Numerical quotient of N2 is 1, H2 is 3 and NH3 is 2. Shejuti Rahman Brishty Lecturer, Department of Pharmacy * The concentration of the ‘product’ NH3 is [NHs3]? * The product of the concentrations of the ‘reactants’ is [N2] [H2]° Step 4. Write the equilibrium expression by placing the product concentrations in the numerator and reactant concentrations in the denominator. _ Product of concentrations of ‘products’ form Step (2) “Product of concentrations of ‘reactants' form Step (3) So, for the above equation, the equilibrium constant expression will be: __ [sf * w]e) Mathematical problems: 1) From Bahl and Tuli, Chapter 17: SOLVED PROBLEM: 1, 2, 3 (page no. 628-629) 2) From Huque and Mollah, Chapter 10: Example 10.1, 10.2, 10.3 (page no. 258-259) Equilibrium Constant Expression in terms of Partial Pressure (Source: Essentials of Physical Chemistry by Bahl and Tuli, Chapter 17, page 629 of e-book) When all the reactants and products are gases. we can also formulate the equilibrium constant expression in terms of partial pressure. The relationship between the partial pressure (p) of any one gas in the equilibrium mixture and the molar concentration follows from the general ideal gas equation pV =nRT or p The quantity 7 is the number of moles of the gas per unit volume and is simply the molar concentration. Thus, p = (Molar concentration) x RT e., the partial pressure of a gas in the equilibrium mixture is directly proportional to its molar concentration at a given temperature. So, we can write the equilibrium constant expression in terms of partial pressure instead of molar concentrations. For a general reaction: IL(g)+mM(g) == yY(g)+2Z(g) the equilibrium law or the equilibrium constant may be written as _ (Py) (zy (PLY (Pu) P Shejuti Rahman Brishty Lecturer, Department of Pharmacy Here, Kp is the equilibrium constant. The subscript p is referring to partial pressure. Partial pressures are expressed in atmospheres (atm). Mathematical problems: 1) From Bahl and Tuli, Chapter 17: SOLVED PROBLEM: 1, 2, 3 (page no. 629-630) 2) From Huque and Mollah, Chapter 10: Example 10.5 (page no. 260-261) How are K- and K; related? (Source: Essentials of Physical Chemistry by Bahl and Tuli, Chapter 17, page 630 of e-book) Let us considera general reaction JA+kB == IC+mD where all reactants and products are gases. We can write the equilibrium constant expression in terms of partial pressures as = (Pe ) (pp)" ne oa) “ Assuming that all these gases constituting the equilibrium mixture obey the ideal gas equation. the partial pressure (p) of a gas is r-( n Where y is the molar concentration. Thus the partial pressures of individual gases. A. B.C and Dare: P, = [A] RT; py = [BJRT; py, = [C] RT; py = (D] RT Substituting these values in equation (1), we have xc, ~ lel (er)! Dol" Cer)" Tal Crry [BF (rr i a i+ om [AV IBF Crry* Ky = K, « (ar) om) Ky = K.*(RT)™ (2) where An = (/+m)—(j +), the difference in the sums of the coefficients for the gaseous products and reactants. From the expression (2) it is clear that when An = 0, K, =K, Shejuti Rahman Brishty Lecturer, Department of Pharmacy Le Chatelier’s Principle In 1884, the French Chemist Henry Le Chatelier proposed a general principle which applies to all systems in equilibrium. This important principle called the Le Chatelier’s principle may be stated as: ‘when a stress is applied on a system in equilibrium, the system tends to adjust itself so as to reduce the stress.’ There are three ways in which the stress can be caused on a chemical equilibrium: (1) Changing the concentration of a reactant or product. (2) Changing the pressure (or volume) of the system. (3) Changing the temperature. Thus, when applied to a chemical reaction in equilibrium, Le Chatelier’s principle can be stated as: ‘if a change in concentration, pressure or temperature is caused to a chemical reaction in equilibrium, the equilibrium will shift to the right or the left so as to minimize the change.’ Effect of a Change in Concentration When concentration of any of the reactants or products is changed, the equilibrium shifts in a direction so as to reduce the change in concentration that was made. N2(g) + 3H2(g) = 2NH3 (g) When N2 (or Hz) is added to the equilibrium already in existence (equilibrium I), the equilibrium will shift to the right so as to reduce the concentration of N2 (Le Chatelier’s principle). The concentration of NH3 at the equilibrium II is more than at equilibrium I. Obviously, the addition of Nz (a reactant) increases the concentration of NH3, while the concentration of H2 decreases. Thus, to have a better yield of NH3, one of the reactants should be added in excess. A change in the concentration of a reactant or product can be affected by the addition or temoval of that species. Let us consider a general reaction, A+BSc When a reactant A is added at equilibrium, its concentration is increased. The forward reaction alone occurs momentarily. According to Le Chatelier’s principle, a new equilibrium will be established so as to reduce the concentration of A. Thus, the addition of A causes the equilibrium to shift to nght. This increases the concentration (yield) of the product C. Following the same line of argument, a decrease in the concentration of A by its removal from the equilibrium mixture, will be undone by shift to the equilibrium position to the left. This teduces the concentration (yield) of the product C. Addition Removal a a “x A+B Cc A+ B =e Equilibrium shift Equilibrium shift 10 Shejuti Rahman Brishty Lecturer, Department of Pharmacy The addition of an inert gas has no effect on the position of the equilibrium. The addition of an inert gas, without changing the volume of the vessel, increases the total pressure but the partial pressures of the reactants and products are not changed. Figure 17.11 Illustratation of Le Chatelier's principle. (a) System at equilibrium with 10H,, 5N>, and 3NH;, for a total of 18 molecules. (b) The same molecules are forced into a smaller volume, creating a stress on the system. (c) Six H, and 2N, have been converted to 4NH. A new equilibrium has been established with 4H,, 3N,, and 7NH;, a total of 14 molecules. The stress is partially relieved by the reduction in the total number of molecules. Effect of a Change in Pressure To predict the effect of a change of pressure, Le Chatelier’s principle may be stated as: when pressure is increased on a gaseous equilibrium reaction, the equilibrium will shift in a direction which tends to decrease the pressure. The pressure of a gaseous reaction at equilibrium is determined by the total number of molecules it contains. If the forward reaction proceeds by the reduction of molecules, it will be accompanied by a decrease of pressure of the system and vice versa. Let us consider a reaction, A+BScC The combination of A and B produces a decrease of number of molecules while the decomposition of C into A and B results in the increase of molecules. Therefore, by the increase of pressure on the equilibrium it will shift to right and give more C. A decrease in pressure will cause the opposite effect. The equilibrium will shift to the left when C will decompose to form more of A and B. Molecules decrease Molecules increase A+B => A+B => > < Equilibrium shift on Equilibrium shift on increase of P decrease of P 11 Shejuti Rahman Brishty Lecturer, Department of Pharmacy The reactions in which the number of product molecules is equal to the number of reactant molecules, are unaffected by pressure changes. H2(g) + 1b (g) = 2HI (g) In such a case the system is unable to undo the increase or decrease of pressure. In light of the above discussion, we can state a general rule to predict the effect of pressure changes on chemical equilibria: ‘The increase of pressure on a chemical equilibrium shifts it in that direction in which the number of molecules decreases and vice-versa.’ Effect of Change of Temperature ‘When temperature of a reaction is increased, the equilibrium shifts in a direction in which heat is absorbed.’ Let us consider an exothermic reaction A+B=C t+ heat When the temperature of the system is increased, heat is supplied to it from outside. According to Le Chatelier’s principle, the equilibrium will shift to the left which involves the absorption of heat. This would result in the increase of the concentration of the reactants A and B. Temperature increased | (Heat added) A+B C + Heat ——— Equilibrium shift In an endothermic reaction the increase of temperature will shift the equilibrium to the right as it involves the absorption of heat. X+Ytheat=Z This increases the concentration of the product Z. Temperature increased (Heat added) | X+Y+Heatt == Z ee Equilibrium Shift In general, we can say that the increase of temperature favours the reverse change in an exothermic reaction and the forward change in an endothermic reaction. 12