CHAPTER 7: Chemical EquilibriumChemical EquilibriumGas-Phase EquilibriumGas equilibrium exampleExample, cont’dGas concentrations instead of partial pressuresMore generallyExampleReaction quotientReaction quotients exampleLe Châtelier’s PrincipleLaw of Mass ActionOther forms of Châtelier’s PrincipleOther forms of Châtelier’s PrincipleHeterogeneous EquilibriumEquilibrium in ExtractionChromatographyCHAPTER 7: Chemical Equilibrium•Chemical Reactions and Equilibrium•Calculating Equilibrium Constants•The Reaction Quotient•Calculation of Gas-Phase Equilibria•The effect of External Stresses: Le Châtelier’s Principle•Heterogeneous Equilibrium•Extraction and Separation ProcessesCHEM 1310 A/B Fall 2006Chemical Equilibrium• Many reactions go to “completion”, e.g., NaClfully dissolves in water, but Ca(OH)2does not• Chemical “equilibrium” is the balance between products and reactants. Can be affected by conditions (e.g., higher solubility at higher T)• Equilibrium is “dynamic,” like phase equilibria of chapter 6 --- individual reactant and product molecules frequenly switch palaces• This chapter quantifies the chemical equilibrium conceptCHEM 1310 A/B Fall 2006Gas-Phase Equilibrium•2 NO2(g) ⇔ N2O4(g)(red-brown) (colorless)•How much NO2and N2O4will depend on conditions• Double arrow suggests reaction (“Rx”) goes in both directions• Equilibrium achieved when forward Rx happens exactly as often asreverse Rx• For any amounts of NO2 and N2O4 the pressures are always in a fixed ration equal to the “equilibrium constant” (for a given T, etc)(PN2O4/ Pref)k = ---------------------- Pref = 1 atm, only incl.(PNO2/ Pref)2to cancel units; usually dropkeep partial pressures in atmNote: k is unitlessCHEM 1310 A/B Fall 2006• Why is the denominator squared? Use coefficients from balanced chemical equations, e.g.,a A (g) +…+ b B (g) ⇔ c C (g) +…+ d D(g)for gases A, B, C, D, with coefficients a, b, c, d, gives PCcx … x PDd Product pressuresk = ------------------------PAax … x PBb Reactant pressuresnote: pressures raised to power of coefficients in balanced chemical equation!• If we measure all partial pressures PA,PB, PC, PD we can easily compute k.CHEM 1310 A/B Fall 2006Gas equilibrium exampleIf k=8.8 at 25oC for the 2NO2⇔ N2O4Rx, and we start with a partial pressure of 0.8 atm of NO2, how much NO2is converted to N2O4(in atm) at fixed T (when equilibrium is reached)?Partial Pressures: 2 NO2⇔ N2O4Initial: 0.8 0Final: ? ?(equilib) CHEM 1310 A/B Fall 2006Example, cont’dCHEM 1310 A/B Fall 2006Gas concentrations instead of partial pressures• Can also work these problem using gas concentrations, [A] = nA/ V = PA/ RT•(PN2O4/ Pref) K = ---------------- becomes(PNO2/ Pref)2K = ( [N2O4] RT / Pref) [N2O4]-------------------------- = ---------- x (RT / Pref) -1. ( [NO2] RT / Pref)2[NO2]2CHEM 1310 A/B Fall 2006More generallya A(g) + b B(g) ⇔ c C(g) + d D(g)[C]c[D]d K = ---------- x (RT/Pref)c+d-a-b[A]a[B]buseful to use R=0.08206 L atm mol-1K-1will cancel T & PrefunitsCHEM 1310 A/B Fall 2006ExampleCH4(g) + H2O(g) ⇔ CO(g) + 3H2(g)At equilibrium at 900K, the concentrations of H2, CO, and H2O are all 0.00642 mol L-1. What’s the concentration of CH4(g) if K=0.172?CHEM 1310 A/B Fall 2006Reaction quotient• Reaction keeps shifting forwards or backwards until the partial pressures or concentrations match K• a A + b B ⇔ c C + d D (all gas phase)K = [PCcPDd/ PAaPBb]eqdefined for PA, PB, PC, PDat equilibrium• What if the P’s haven’t reached equilibrium yet? Then call it Q, the “reaction quotient”Q = [PCcPDd/ PAaPBb] for any P’s• If Q<K, need more product to reach equilibrium. If Q>K, need more reactants to reach equilibrium.CHEM 1310 A/B Fall 2006Reaction quotients example• Consider N2(g) + 3H2(g) ⇔ 2NH3(g)•If PN2= 55atm, PH2= 11atm, PNH3= 22atm initially, is the final pressure of NH3greater or smaller than its initial pressure? K=1.9x10-4CHEM 1310 A/B Fall 2006Le Châtelier’s Principle• Last example shows we can make the reaction go forwards or backwards by adding more reactants or products; this is the “law of mass action”• This is an example of a more general principle: Le Châtelier’s Principle• A system in equilibrium which is subjected to a stress reacts in a way to counteract the stressCHEM 1310 A/B Fall 2006Law of Mass Action• Using Le Châtelier’s Principle to make a Rx go forward or backward by adding more of a reactant/product• Industry uses the law of mass action in the synthesis of ammoniaN2(g) + 3H2(g) ⇔ 2 NH3(g)Can drive the Rx to completion by continually removing NH3CHEM 1310 A/B Fall 2006Other forms of Châtelier’s Principle• Changing volume: If we decrease the volume of a reaction vessel, the presure goes up, and the system will try to reduce stress by reducing pressure by making fewer gas moleculesN2(g) + 3H2(g) ⇔ 2NH3(g)If P goes up, Rx shifts to the right to make pressure decrease againCHEM 1310 A/B Fall 2006Other forms of Châtelier’s Principle• Changing temperature: Some reactions require heat (endothermic). Raising the temperature supplies more heat, drives Rx forward. Opposite for exothermic. N2(g) + 3H2(g) ⇔ 2NH3(g) + heatThis is an exothermic Rx (gives off heat). Rx goes backwards if T goes up (system tries to reduce extra heat). Opposite happens if T goes down (system tries to make more heat)CHEM 1310 A/B Fall 2006Heterogeneous Equilibrium• How do we write a rate constant for a Rx likeO2(g) + 2 H2O(l) ⇔ 2 H2O2(aq) ??• Use “activities”– For gases, activity is just the partial pressure (more precisely, P/Pref)– For dissolved species, activity is concentration in mol L-1– Pure solids and liquids have activity = 1•K = [H2O2]2/ (PO2x 1)CHEM 1310 A/B Fall 2006Equilibrium in Extraction• Extraction: 2 solvents A and B, add solute C. C will dissolve in both A and B, but the amount in A vsB is determined by the equilibrium constant K = [C]A/ [C]B.• Can extract polar solutes from nonpolar solvents by washing with water or a polar solventIodine travels from the upperaqueous phase to the lower CCl4phase preferentiallyCHEM 1310 A/B Fall 2006Chromatography• Achieve equilibrium between a “stationary phase” (e.g., column of water adsorbed to silica gel) and a “mobile phase” (solution containing one