PHYSICAL CHEMISTRY-I: THERMODYNAMICS, EQUILIBRIUM AND SOLUTIONS Course Code– CHE251 Topic: Chemical Equilibrium Course Coordinator: Dr. Jagannath Roy, Associate Professor, Department of Chemistry, Central University of South Bihar Note: These materials are only for classroom teaching purpose at Central University of South Bihar. All the data/figures/materials are taken from text books, e-books, research articles, Wikipedia and other online resources. Chemical Equilibrium Chemical equilibrium is the state of a system where the concentration of both the reactant and the products do not change with time and the system does not display any further change in properties. When the rate of the forward reaction is equal to the rate of the reverse reaction, the state of chemical equilibrium is achieved by the system. When there is no further change in the concentrations of the reactants and the products due to the equal rates of the forward and reverse reactions, the system is said to be in a state of dynamic equilibrium. A graph with the concentration on the y-axis and time on the x-axis can be plotted. Once the concentration of both the reactants and the products stops showing change, chemical equilibrium is achieved. Chemical Equilibrium Chemical Equilibrium is called Dynamic Equilibrium The stage at which the rate of the forward reaction is equal to the rate of backward reaction is called an equilibrium stage. At this point, the number of reactant molecules converting into products and product molecules into reactants are the same. The same equilibrium can be carried out with the same reactants anywhere with similar conditions with continuous interchanging of molecules hence chemical equilibrium is dynamic. Types of Chemical Equilibrium There are two types of chemical equilibrium: Homogeneous Equilibrium Heterogeneous Equilibrium Homogenous Chemical Equilibrium In this type, the reactants and the products of chemical equilibrium are all in the same phase. Homogenous equilibrium can be further divided into two types: Reactions in which the number of molecules of the products is equal to the number of molecules of the reactants. For example, H2 (g) + I2 (g) ⇌ 2HI (g) N2 (g) + O2 (g) ⇌ 2NO (g) Chemical Equilibrium Reactions in which the number of molecules of the products is not equal to the total number of reactant molecules. For example, 2SO2 (g) + O2 (g) ⇌ 2SO3 (g) COCl2 (g) ⇌ CO (g) + Cl2 (g) Heterogeneous Chemical Equilibrium In this type, the reactants and the products of chemical equilibrium are present in different phases. A few examples of heterogeneous equilibrium are listed below. CO2 (g) + C (s) ⇌ 2CO (g) CaCO3 (s) ⇌ CaO (s) + CO2 (g) Thus, the different types of chemical equilibrium are based on the phase of the reactants and products. Chemical Equilibrium Recognizing a system at Chemical Equilibrium: 1. Equilibrium may only be obtained in a closed system. 2. The rate of the forward reaction is equal to the rate of the reverse reaction. 3. Catalysts have no effect on the equilibrium point. However, changes in the concentrations of either the products or reactants, temperature, volume, or pressure can offset the equilibrium point. This point illustrated in Le Chatelier's Principle. 4. The consistency of observable or physical properties such as concentration, color, pressure, and density can indicate a reaction has reached equilibrium. Real Life use of Chemical Equilibrium: Hemoglobin is the protein in an individual's blood responsible for transporting oxygen to other cells. The following equation describes how the hemoglobin protein (Hb) binds to four oxygen atoms, which your body then uses. Hb(aq) + 4O2(g) ⇋ Hb(O2)4 As long as oxygen is available, a healthy equilibrium is maintained. However, at significant altitudes where air pressure is lowered, such as the top of mountains, there is less oxygen. The equilibrium then shifts to the left, away from oxygenated hemoglobin. Therefore, someone lacking oxygen in their body's cells and tissues tend to feel light-headed. Law of Mass Action Two Norwegian chemists proposed Law of Mass Action in 1867. This law states that ‘at a constant temperature, the rate of a chemical reaction is proportional to the ‘active masses’ of the reacting substances. The law develops a quantitative relation between the amounts of the reactants and the resultants at equilibrium. Let us consider the following general reaction: Where a, b, c and d are the stoichiometric coefficients for the reacting species A, B, C and D respectively. a b Rate of forward reaction = k1 [A] [B] c d Rate of backward reaction = k2 [C] [D] At equilibrium, rate of forward reaction= rate of backward reaction Hence, where Kc(=k1/k2) is the equilibrium constant Law of Mass Action Let us consider the following reaction: 2 3 Rate of forward reaction = k1 [A] [B] 2 Rate of backward reaction = k2 [C] [D] At equilibrium, rate of forward reaction= rate of backward reaction 2 3 2 Therefore, k1 [A] [B] = k2 [C] [D] 2 2 3 Hence, equilibrium constant , Kc(=k1/k2)= [C] [D] / [A] [B] Equlibrium constant from thermodynamic consideration Let us consider the following reaction which has attained equilibrium at a temperature T. Let G denote the thermodynamic potential or free energy of the system. From Gibbs and Duhem relation, we can express the change in thermodynamic potential of the system, ∆G , by the chemical potentials μ of the components. According to Gibbs-Duhem relationship, Change in Gibbs potential, dG = μAdnA+ μBdnB + μCdnC …….. = ∑μdn where μA is the chemical potential and nA is the no of moles of component ‘A’ and so on. Let us consider a small chemical change in the system under conditions of equilibrium so that the reactants A, B, etc diminish by very small amount such as a∆x, b∆x, c∆x …… gm-moles. In consequence, the resultants D, E , et. will increase by the amounts d∆x, e∆x, f∆x, etc. Hence we have, dnA= a∆x, dnB = b∆x, dnC =c∆x , dnD= d∆x, dnE= e∆x, dnF= f∆x …… Therefore, dG = ∑μdn = μD. d∆x + μE . e∆x + μF . f∆x +…….. – μA. a∆x – μB. b∆x – μC. c∆x…….. At equilibrium, dG = 0 Equlibrium constant from thermodynamic consideration At equilibrium, dG = 0, hence μD. d∆x + μE . e∆x + μF . f∆x +…….. = μA. a∆x + μB. b∆x + μC. c∆x +…….. or, d. μD + e. μE + f. μF + …….. = a. μA + b. μB + c. μC…….. In terms of activities, chemical potential, μ = RT ln a + z, where z = chemical potential at standard state. Hence we have, d[RT ln aD+zD]+e[RT ln aE+zE]+f[RT ln aF+zF]+…=a[RT ln aA+zA]+b[RT ln aB+zB]+ c[RT ln aC +zC]+… d e f a b c or, RT ln aD +RT ln aE +RT ln aF +…- RTln aA -RTln aB - RTln aC = azA+bzB+czC+…- dzD-ezE-fzF-… = z1 (constant) d e f a b c or, ln [(aD x aE x aF x….)/(aA x aB x aC x….)]= z1 /RT = constant d e f a b c Therefore, (aD x aE x aF x ….)/(aA x aB x aC x….)= Ka Where Ka is the thermodynamic equilibrium constant. It is expressed in terms of the activities of the components and therefore it is valid for all systems, ideal or not ideal..