Chemical Equilibria (Gaseous Systems) Physical Chemistry Presented by Gabriel Harewood, PhD.

Course Content Definition of Chemical Equilibria Dynamic and Static Equilibrium Equilibrium Constant, Kc, Kp Le Chatelier’s Principle Effect of temperature on K

Definition of Chemical Equilibrium Chemical equilibrium applies to reactions that can occur in both directions. The following reaction can happen both ways: CH4(g) + H2O(g)  CO(g) + 3H2(g) After some of the products are formed, the products begin to react to form the reactants – reversible reaction.

Definition of Chemical Equilibrium At the beginning of the reaction, the rate of the forward reaction is higher than the rate of the reverse reaction. Therefore, the net change is more products. When the net change of products and reactants are zero – opposing processes occur at the same rate – the reaction has reached equilibrium. For equilibrium to occur, the system must be a closed.

Static vs. Dynamic Equilibrium Static Equilibrium: occurs when the sum of the forces and torque acting on the particles in an object is zero – applies to stationary objects. For example, a stick balancing on a fulcrum or a paperweight on a desk.

Static vs. Dynamic Equilibrium occurs when two reversible processes (e.g., reactions) occur at the same rate – no net change. You can show dynamic equilibrium in an equation by using special arrows: At equilibrium, the concentrations of the reactants and products are constant.

Chemical Equilibrium & Equilibrium Constant Consider the Haber Process: N2 and H2 are combined in a high-pressure tank at high P and T, in the presence of a catalyst to produce ammonia, NH3. Not all of the reactants are converted. The reaction achieves an equilibrium where all three compounds are present.

Chemical Equilibrium & Equilibrium Constant According to the Rate Law (see Unit 5: Chemical Kinetics): Rate of forward rxn = kf [N2] [H2]3 and Rate of reverse rxn = kr [NH3]2 At equilibrium: Rate of the forward process = Rate of the reverse process Therefore: kf [N2] [H2]3 = kr [NH3]2 Rearranging this equation: kf / kr = [NH3]2 = Kc [N2] [H2]3 equilibrium constant

Equilibrium Constant Expression For a reaction: aA + bB  cC + dD The equilibrium-constant expression is Kc = [C]c [D]d (Products) [A]a [B]b (Reactants) Also, for gaseous systems: Kp = PCc PDd P – partial pressures PAa PBb So for the Haber process: Kp = P(NH3)2 P(N2) P(H2)3 What are the units for Kc?

Equilibrium Constants Example: Write the equilibrium expression for Kc for the following reaction: Answer: Kc = [HI]2 [H2] [I2] When Kc >> 1: equilibrium lies to the right; mostly products When Kc << 1: equilibrium lies to the left; mostly reactants

Equilibrium Constants The equilibrium constant for a reaction in one direction is the reciprocal of the one for the reverse reaction, e.g., Kp = P(NO2)2 = 6.46 P(N2O4) Kp = P(N2O4) = 0.155 P(NO2)2 (at 100C) (at 100C)

Example A mixture of hydrogen and nitrogen in a reaction vessel are allowed to attain equilibrium at 472C. The equilibrium mixture was analysed and found to contain 7.38 atm H2, 2.46 atm N2 and 0.166 NH3. Calculate the equilibrium constant, Kp, for: Solution: Kp = P(NH3)2 = (0.166)2 P(N2) P(H2)3 (2.46) (7.38)3 Kp = 2.79 x 10-5

Note The equation used to determine the equilibrium expression must be balanced! Use the stoichiometric amounts in the equation to write the equilibrium expression. Remember that the initial concentrations of a reaction are not equal to the equilibrium concentrations.

Relationship Between Kc and Kp For gases, the pressure is proportional to concentration PV = nRT  P = nRT/V = [ ]RT  [ ] = P/RT Consider this system at equilibrium:

Relationship Between Kc and Kp Recall: [ ] = P/RT

Relationship Between Kc and Kp Therefore, the relationship between Kp and Kc is:

Le Châtelier’s Principle In developing the production of ammonia, Haber experimented with various factors to try to improve the production of ammonia. He calculated the equilibrium constant for the reaction under different conditions and noticed that: As T increased, [NH3] decreased As P increased, [NH3] increased

Le Châtelier’s Principle These observations can be explained using Le Châtelier’s principle: If a system at equilibrium is disturbed by a change in temperature, pressure, or the concentration of one of the components, the system will shift its equilibrium position in order to counteract the disturbance. Le Châtelier’s principle can be used to make qualitative predictions about the response of a system to these changes.

Le Châtelier’s Principle Change in Reactant or Product Concentrations A system at equilibrium is in a dynamic state: system is in balance. Therefore, if a system is at equilibrium and we add a reactant or product, the reaction will shift in order to reestablish equilibrium by consuming some of the added substance.

Le Châtelier’s Principle Change in Pressure and Volume If the volume of a gaseous system at equilibrium is decreased, (increasing its total pressure), Le Châtelier’s principle suggests that the equilibrium will shift to reduce the pressure. Avogadro’s law applies: Number of moles of gas on the left = 4 moles Number of moles of gas on the right = 2 moles

Le Châtelier’s Principle Will pressure or volume changes affect the following reaction? Note: concentration, pressure or volume changes do no change the equilibrium constant if temperature remains constant.

Le Châtelier’s Principle Change in Temperature When temperature is increased, it is as if we have added a reactant, or a product, to the system at equilibrium, The equilibrium shifts in the direction that consumes the excess reactant (or product), namely heat. Endothermic rxn: Reactants + heat  products Exothermic rxn: Reactants  products + heat For an endothermic rxn,  T leads to  Kc For an exothermic rxn,  T leads to  Kc.

Le Châtelier’s Principle Effects of Catalysts The addition of a catalyst to a reaction decreases the activation energy of a reaction. A catalyst thereby increases the rates of both the forward and reverse reactions. A catalyst increases the rate at which equilibrium is achieved but does not change the composition of the equilibrium mixture.

Le Châtelier’s Principle Application to Haber Process: -ve enthalpy means low T favoured

Summary Chemical Equilibria Static and dynamic equilibrium Equilibrium expression and constants Le Châtelier’s principle, effects of the following on equilibria: Concentration changes Volume or pressure changes Temperature changes Addition of a catalyst Haber Process

Next Aqueous Equilibria / Acids and Bases Solubility product and Common ion effect Dissociation of acids and bases, Ka, Kb Ionic Product, Kw pH, pOH Buffers Back titration