Chemical Equilibrium

The Concept of Equilibrium No chemical reaction occurs in a single direction To a certain point, every reaction is reversible, i.e., the products react to reform the reactants When the speeds of the forward and reverse reactions are equal, and the concentrations of reactants and products no longer change over time, chemical equilibrium is established Chemical equilibrium is a dynamic process in that the forward and reverse reactions continue, but at identical ratess

The Concept of Equilibrium A physical equilibrium is an equilibrium that involves a single substance ex.; A chemical equilibrium is an equilibrium that involves two or more substances

The Equilibrium Constant The equilibrium constant, K, defines the concentrations/pressures of the reactants and products at equilibrium The equilibrium constant does not have units For the reaction Where ax = 1 for a solid or a liquid ax = Px (in atm) for a gas ax = [X] (in mol/L, or M) for a solute This definition of K is the only one that is always valid with DGo = -RT ln K

The Equilibrium Constant Because ax= 1 for solids and liquids, we can say that ax (the activity) of a solid or liquid does not appear in the expression for K

The Equilibrium Constant When giving an equilibrium constant, it must be accompanied by the corresponding balanced equation, for example The value of K varies with temperature, so we must also specify the temperature If K > 1, the equilibrium favours the products (i.e., towards the right) If K < 1, the equilibrium favours the reactants (i.e., towards the left)

The Equilibrium Constant Example: The equilibrium constant, K, for the reaction is 158 at 1000 K. Calculate PO2 if PNO2 = 0.400 atm ant PNO = 0.270 atm. Solution:

Predicting the direction of a reaction The reaction quotient, Q, is the value obtained when using the actual (non-equilibrium) activities (pressures/concentrations) within the formula of the equilibrium constant If Q > K, there is too much of the products, so a certain amount of the products must be converted back to reactants; the reaction will shift to the left If Q < K, there is too much of the reactants, so a certain amount of the reactants must be converted to products; the reaction will shift to the right If Q = K, the system is at equilibrium; the system does not shift in either direction

The Calculation of Concentrations at Equilibrium If we know the equilibrium constant for a given reaction, one can calculate the concentrations in the equilibrium mixture from the initial concentrations ex.; Consider the reaction (in an organic solvent, at 200oC, K = 24.0): cis-stilbene trans-stilbene What are the concentrations of the reactants and products if at the beginning we have 0.850 mol/L of cis-stilbene (and no trans-stilbene)?

The Calculation of Concentrations at Equilibrium According to the reaction’s stoichiometry, at equilibrium, [trans-stilbene] = x mol/L and [cis-stilbene] = (0.850-x) mol/L i.e., for each molecule of trans-stilbene produced, we must lose one molecule of cis-stilbene At equilibrium,

The Calculation of Concentrations at Equilibrium In general: Express the equilibrium concentrations of all species using the initial concentrations and a single unknown (x) which represents a change in the concentration of one of the species Express the equilibrium constant in terms of the equilibrium concentrations The value of the equilibrium constant is known, solve for x After determining the value of x, compute the equilibrium concentrations of all species

The Calculation of Concentrations at Equilibrium Example: We are mixing H2(g) and I2(g) in a container. The partial pressures are 0.500 atm and 0.100 atm, respectively. For the reaction H2(g) + I2(g)  2 HI(g) K = 54.3 at 430oC. At equilibrium, what are the partial pressures of H2(g), I2(g), and HI(g)?

The Calculation of Concentrations at Equilibrium We start with pure A(s) and establish an equilibrium: A(s) ↔ 2 B(g) + 3 C(g). If the pressure of B(g) at equilibrium is 0.180 atm, calculate the value of ΔGo for this reaction.

Le Chatelier’s Principle Any change in the conditions can shift the equilibrium to the left (reactants) or to the right (products) Le Chatelier’s principle says that if a system at equilibrium is disturbed, the system reacts to counteract this disturbance A disturbance may be a change in the concentration of a reactant or product, pressure, volume, temperature, …

Le Chatelier’s Principle: Changes in Pressure and Volume Example: Consider the reaction 2 NOCl(g) 2 NO(g) + Cl2(g). Predict in which direction the net reaction will proceed if there is a decrease in pressure (resulting from an increase in volume) of the system at constant temperature. Solution: If the pressure is reduced, Le Chatelier’s principle says the system will try to combat this effect by increasing the pressure. It can do this by increasing the total number of moles of gas by shifting the equilibrium towards the products. N.B. An increase of the total pressure which is accomplished by adding a spectator gas (i.e., one that is not involved in the reaction) has no effect on the partial pressures of reactants and products. It has no effect on the equilibrium position.

Le Chatelier’s Principle: Changes in Temperature Changes in concentrations and pressures do not have an effect on the value of K However, when temperature changes, the value of K changes To predict the effect of temperature on the equilibrium position, consider the heat as a reactant or product For an endothermic reaction, heat is a “reactant” For an exothermic reaction, heat is a “product”

Le Chatelier’s Principle: Changes in Temperature According to Le Chatelier’s Principle For an endothermic reaction: An increase in temperature will move the position of equilibrium towards the products A decrease in temperature will move the equilibrium position towards the reactants For an exothermic reaction: An increase in temperature will move the position of equilibrium towards the reactants A decrease in temperature will move the equilibrium position towards the products

Le Chatelier’s Principle: Catalysts A catalyst increases the rate of both the forward and inverse reactions by lowering the energetic barrier between the reactants and products (we will learn more about this in the section on chemical kinetics) A catalyst does not have an influence on the composition of the system at equilibrium A catalyst merely helps the system reach equilibrium faster

Le Chatelier’s Principle Example: Consider the reaction What would be the effect on the system if: (a) Pressure was increased by a decrease in volume? (b) Pressure was increased by the addition of O2(g)? (c) Temperature was decreased? (d) A catalyst was added? Solution: (a) Equilibrium would be displaced towards the products (b) Equilibrium would be displaced towards the products (c) Equilibrium would be displaced towards the reactants (d) No effect on the equilibrium position