Chapter 3 Chemical Equilibrium Atkins: Chapters 9,10,11 Silberberg: Chapters 17, 18 & 19

At equilibrium: rateforward = ratereverse Equilibrium applies to the extent of a reaction, the concentration of product that has appeared after an unlimited time, or once no further change occurs. At equilibrium: rateforward = ratereverse A system at equilibrium is dynamic on the molecular level; no further net change is observed because changes in one direction are balanced by changes in the other. Kinetics applies to the speed of a reaction, the concentration of product that appears (or of reactant that disappears) per unit time.

Reversible reactions can proceed in either the forward or reverse direction. Equilibrium is a state in which there are no observable changes as time goes by. Chemical equilibrium is achieved when: the rates of the forward and reverse reactions are equal and the concentrations of the reactants and products remain constant Physical equilibrium H2O (l) H2O (g) Chemical equilibrium N2O4 (g) 2NO2 (g)

N2O4 (g) 2NO2 (g) equilibrium equilibrium equilibrium Start with NO2 Start with NO2 & N2O4

constant

Law of Mass Action N2O4 (g) 2NO2 (g) [NO2]2 K = = 4.63 x 10-3 [N2O4] aA + bB cC + dD ai is called the activity of component i. Law of mass action: for a reversible reaction at equilibrium and at a constant temperature, a certain ratio of reactant and product concentrations has a constant value K (called the equilibrium constant).

Activity The activity (a) of a species in a reaction is generally a complex function of the pressures and concentrations of all the components present in the reaction mixture. Ideal gases: Solutes in dilute solution: Pure solids and liquids:

Significance of the Magnitude of K [C]c[D]d [A]a[B]b aA + bB cC + dD any number greater than 10 Equilibrium Will K >> 1 Lie to the right Favor products K << 1 Lie to the left Favor reactants any number less than 0.1

Homogenous equilibrium applies to reactions in which all reacting species are in the same phase.

K using Partial Pressures gas activities as partial pressures, = moles of gaseous products - moles of gaseous reactants concentration equilibrium constant except when

Heterogenous equilibrium applies to reactions in which reactants and products are in different phases. pure solids

Equilibrium pressure - independent of the amount of either solid. PCO 2 = Kp

Multiple Equilibria K1 = PcPd PAPB A + B C + D K1 K2 = PEPF PCPD C + D E + F K2 K12 = PEPF PAPB A + B E + F K12 If a reaction can be expressed as the sum of two or more reactions, the equilibrium constant for the overall reaction is given by the product of the equilibrium constants of the individual reactions.

Form of K and the Equilibrium Expression When the equation for a reversible reaction is written in the opposite direction, the equilibrium constant becomes the reciprocal of the original equilibrium constant. 2. The value of K also depends upon how the equilibrium equation is balanced.

Predicting the Direction of a Reaction The reaction quotient (Qc ) is calculated by substituting the initial concentrations of the reactants and products into the equilibrium constant (Kc) expression. IF Qc > Kc system proceeds from right to left to reach equilibrium Qc = Kc the system is at equilibrium Qc < Kc system proceeds from left to right to reach equilibrium

Calculating Equilibrium Concentrations Express the equilibrium concentrations of all species in terms of the initial concentrations and a single unknown x, which represents the change in concentration. Write the equilibrium constant expression in terms of the equilibrium concentrations. Knowing the value of the equilibrium constant, solve for x. 3. Having solved for x, calculate the equilibrium concentrations of all species.

Gibbs Free Energy and Chemical Equilibrium DG = DG0 + RT lnQ R is the gas constant (8.314 J/K•mol) T is the absolute temperature (K) Q is the reaction quotient At Equilibrium DG = 0 Q = K 0 = DG0 + RT lnK DG0 = - RT lnK

Free Energy Versus Extent of Reaction DG0 < 0 DG0 > 0

DG0 = - RT lnK

Le Châtelier’s Principle If an external stress is applied to a system at equilibrium, the system adjusts in such a way that the stress is partially offset as the system reaches a new equilibrium position. Changes in Concentration N2 (g) + 3H2 (g) 2NH3 (g) Add NH3 Equilibrium shifts left to offset stress

Le Châtelier’s Principle Changes in Concentration (continued) aA + bB cC + dD Change Shifts the Equilibrium Increase concentration of product(s) left Decrease concentration of product(s) right Increase concentration of reactant(s) right Decrease concentration of reactant(s) left

Le Châtelier’s Principle Changes in Volume and Pressure general ideal gas reaction, in terms of mole fractions.

Reaction shifts forward – toward products Reaction shifts in reverse – toward reactants No net change

Le Châtelier’s Principle Changes in Volume and Pressure: Summary A (g) + B (g) C (g) Change Shifts the Equilibrium Increase pressure Side with fewest moles of gas Decrease pressure Side with most moles of gas Increase volume Side with most moles of gas Decrease volume Side with fewest moles of gas

Changes in Temperature endothermic colorless red-brown exothermic colder hotter

Quantifying Changes in Temperature DHo and DSo are approximately constant between T1 and T2 van’t Hoff equation

Le Châtelier’s Principle Changes in Temperature: Qualitative Summary Change Exothermic Endothermic Increase temperature K decreases K increases Decrease temperature K increases K decreases

Le Châtelier’s Principle Summary Change Equilibrium Constant Change Shift Equilibrium Concentration yes no Pressure yes no Volume yes no Temperature yes yes

Life at High Altitudes and Hemoglobin Production Hb (aq) + O2 (aq) HbO2 (aq)