Chemical Equilibrium Occurs when opposing reactions are proceeding at the same rate Forward rate = reverse rate of reaction Ex: Vapor pressure: rate of vaporization = rate of condensation Saturated solution: rate of dissociation = rate of crystallization Expressing concentrations: Gases: partial pressures, PX Solutes in liquids: molarity, [X]

Reversible Reactions and Rate Forward rate Reaction Rate Time Equilibrium is established: Forward rate = Backward rate Backward rate When equilibrium is achieved: [A] ≠ [B] and kf/kr = Keq

15.2: Law of Mass Action Derived from rate laws by Guldberg and Waage (1864) For a balanced chemical reaction in equilibrium: a A + b B ↔ c C + d D Equilibrium constant expression (Keq): Cato Guldberg Peter Waage (1836-1902) (1833-1900) or But Waage and Guldberg were also related through two marriages; Guldberg married his cousin Bodil Mathea Riddervold, daughter of cabinet minister Hans Riddervold, and the couple had three daughters. Waage married Bodil's sister, Johanne Christiane Tandberg Riddervold by whom he had five children, and after her death in 1869, he became Guldberg's brother-in-law a second time, in 1870, by marrying one of Guldberg's sisters, Mathilde Sofie Guldberg, by whom he had six children. Keq is strictly based on stoichiometry of the reaction (is independent of the mechanism). Units: Keq is considered dimensionless (no units)

Relating Kc and Kp Convert [A] into PA: where Dn = = change in coefficents of products – reactants (gases only!) = (c+d) - (a+b)

Magnitude of Keq Since Keq a [products]/[reactants], the magnitude of Keq predicts which reaction direction is favored: If Keq > 1 then [products] > [reactants] and equilibrium “lies to the right” If Keq < 1 then [products] < [reactants] and equilibrium “lies to the left”

Relationship Between Q and K Reaction Quotient (Q): The particular ratio of concentration terms that we write for a particular reaction is called reaction quotient. For a reaction, A B, Q= [B]/[A] At equilibrium, Q= K Reaction Direction: Comparing Q and K Q<K, reaction proceeds to right, until equilibrium is achieved (or Q=K) Q>K, reaction proceeds to left, until Q=K

Value of K For the reference rxn, A>B, For the reverse rxn, B >A, For the reaction, 2A > 2B For the rxn, A > C C > B K(ref)= [B]/[A] K= 1/K(ref) K= K(ref)2 K (overall)= K1 X K2

15.3: Types of Equilibria Homogeneous: all components in same phase (usually g or aq) N2 (g) + H2 (g) ↔ NH3 (g) 1 3 2 Fritz Haber (1868 – 1934) German chemist, who received the Nobel Prize in Chemistry in 1918 for his development of synthetic ammonia, important for fertilizers and explosives. He is also credited as the "father of chemical warfare" for his work developing and deploying chlorine and other poison gases during World War I; this role is thought to have provoked his wife to commit suicide. Despite his contributions to the German war effort, Haber was forced to emigrate from Germany in 1933 by the Nazis because of his Jewish background; many of his relatives were killed by the Nazis in concentration camps, gassed by Zyklon B. Though he had converted from Judaism in an effort to become fully accepted, he was forced to emigrate from Germany by the Nazis in 1933 on account of his being Jewish in their eyes. He died in the process of emigration. The Haber process now produces 500 million tons of nitrogen fertilizer per year, mostly in the form of anhydrous ammonia, ammonium nitrate, and urea. 1% of the world's annual energy supply is consumed in the Haber process (Science 297(1654), Sep 2002). That fertilizer is responsible for sustaining 40% of the Earth's population, as well as various deleterious environmental consequences.

CaCO3 (s) ↔ CaO (s) + CO2 (g) Heterogeneous: different phases CaCO3 (s) ↔ CaO (s) + CO2 (g) Definition: What we use: Concentrations of pure solids and pure liquids are not included in Keq expression because their concentrations do not vary, and are “already included” in Keq (see p. 548). Even though the concentrations of the solids or liquids do not appear in the equilibrium expression, the substances must be present to achieve equilibrium.

15.4: Calculating Equilibrium Constants Steps to use “ICE” table: “I” = Tabulate known initial and equilibrium concentrations of all species in equilibrium expression “C” = Determine the concentration change for the species where initial and equilibrium are known Use stoichiometry to calculate concentration changes for all other species involved in equilibrium “E” = Calculate the equilibrium concentrations

NH3 (aq) + H2O (l) ↔ NH41+ (aq) + OH1- (aq) Ex: Enough ammonia is dissolved in 5.00 L of water at 25ºC to produce a solution that is 0.0124 M ammonia. The solution is then allowed to come to equilibrium. Analysis of the equilibrium mixture shows that [OH1-] is 4.64 x 10-4 M. Calculate Keq at 25ºC for the reaction: NH3 (aq) + H2O (l) ↔ NH41+ (aq) + OH1- (aq)

NH3 (aq) + H2O (l) ↔ NH41+ (aq) + OH1- (aq)   Initial Change Equilibrium NH3 (aq) H2O (l) NH41+ (aq) OH1- (aq) X 0.0124 M 0 M 0 M X - x + x + x X 0.0119 M 4.64 x 10-4 M 4.64 x 10-4 M x = 4.64 x 10-4 M

Equilibrium When the rate of the forward reaction equals the rate of the reverse reaction. (c) 2006, Mark Rosengarten

Examples of Equilibrium Solution Equilibrium: when a solution is saturated, the rate of dissolving equals the rate of precipitating. NaCl (s)  Na+1 (aq) + Cl-1 (aq) Vapor-Liquid Equilibrium: when a liquid is trapped with air in a container, the liquid evaporates until the rate of evaporation equals the rate of condensation. H2O (l)  H2O (g) Phase equilibrium: At the melting point, the rate of solid turning to liquid equals the rate of liquid turning back to solid. H2O (s)  H2O (l)

Le Châtelier’s Principle If a system at equilibrium is stressed, the equilibrium will shift in a direction that relieves that stress. A stress is a factor that affects reaction rate. Since catalysts affect both reaction rates equally, catalysts have no effect on a system already at equilibrium. Equilibrium will shift AWAY from what is added Equilibrium will shift TOWARDS what is removed. This is because the shift will even out the change in reaction rate and bring the system back to equilibrium NEXT

Steps to Relieving Stress 1) Equilibrium is subjected to a STRESS. 2) System SHIFTS towards what is removed from the system or away from what is added. The shift results in a CHANGE OF CONCENTRATION for both the products and the reactants. If the shift is towards the products, the concentration of the products will increase and the concentration of the reactants will decrease. If the shift is towards the reactants, the concentration of the reactants will increase and the concentration of the products will decrease. NEXT

Examples For the reaction N2(g) + 3H2(g)  2 NH3(g) + heat Adding N2 will cause the equilibrium to shift RIGHT, resulting in an increase in the concentration of NH3 and a decrease in the concentration of N2 and H2. Removing H2 will cause a shift to the LEFT, resulting in a decrease in the concentration of NH3 and an increase in the concentration of N2 and H2. Increasing the temperature will cause a shift to the LEFT, same results as the one above. Decreasing the pressure will cause a shift to the LEFT, because there is more gas on the left side, and making more gas will bring the pressure back up to its equilibrium amount. Adding a catalyst will have no effect, so no shift will happen.