Chemistry 123: Physical and Organic Chemistry Topic 4: Gaseous Equilibrium

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1 Topic 4: Introduction, Topic 4: Gaseous Equilibrium Text: Chapter 6 & Brief review of Kinetic theory of gasses (Chapter 6) 4.1 Concept of dynamic equilibrium 4.2 General form & properties of equilbrium const. and reaction quotient 4.3 Extent of reaction at equilibrium; degree of dissociation 4.4 Variation of equilibrium constant with temperature 4.5 Le Chatelier's Principal and it's applications Winter 2009 Page 1 Kinetic Molecular Theory Particles are point masses in constant, random, straight line motion. Particles are separated by great distances. Collisions are rapid and elastic. No force between particles. Total energy remains constant. Winter 2009 Page 2 1

2 Pressure Assessing Collision Forces Translational kinetic energy, Frequency of collisions, Impulse or momentum transfer, Pressure proportional to impulse times frequency Winter 2009 Page 3 Pressure and Molecular Speed Three dimensional systems lead to: u m is the modal speed u av is the simple average u rms Winter 2009 Page 4 2

3 Pressure Assume one mole: PV=RT so: N A m = M: Rearrange: Winter 2009 Page 5 Distribution of Molecular Speeds Winter 2009 Page 6 3

4 Temperature Modify: PV=RT so: Solve for e k : Average kinetic energy is directly proportional to temperature! Winter 2009 Page 7 Dynamic Equilibrium Equilibrium two opposing processes taking place at equal rates. H 2 O(l) NaCl(s) H 2 O(g) H 2 O NaCl(aq) CO(g) + 2 H 2 (g) CH 3 OH(g) I 2 (H 2 O) I 2 (CCl 4 ) Winter 2009 Page 8 4

5 The Equilibrium Constant Expression Methanol synthesis is a reversible reaction. CO(g) + 2 H 2 (g) CH 3 OH(g) CH 3 OH(g) CO(g) + 2 H 2 (g) CO(g) + 2 H 2 (g) CH 3 OH(g) Winter 2009 Page 9 Three Approaches to the Equilibrium Winter 2009 Page 10 5

6 Winter 2009 Page 11 CO(g) + 2 H 2 (g) CH 3 OH(g) Winter 2009 Page 12 6

7 Forward: CO(g) + 2 H 2 (g) CH 3 OH(g) Reverse: CH 3 OH(g) CO(g) + 2 H 2 (g) R fwrd = [CO][H 2 ] 2 R rvrs = [CH 3 OH] At Equilibrium: R fwrd = R rvrs CO(g) + 2 H 2 (g) [CO][H 2 ] 2 = [CH 3 OH] CH 3 OH(g) = [CH 3 OH] = K [CO][H 2 ] 2 c Winter 2009 Page 13 Activity Thermodynamic concept introduced by Lewis. Dimensionless ratio referred to a chosen reference state. a B = [B] c B 0 = γ B [B] c B 0 is a standard reference state = 1 mol L -1 (ideal conditions) Accounts for non-ideal behaviour in solutions and gases. An effective concentration. Winter 2009 Page 14 7

8 a A + b B. g G + h H. Equilibrium constant = K c = Thermodynamic Equilibrium constant = K eq = [G] g [H] h. [A] m [B] n. (a G ) g (a H ) h. (a A ) a (a B ) b. = [G] g [H] h. [A] m [B] n. ( γ G ) g (γ H ) h. (γ A ) a (γ B ) b. 1 under ideal conditions Winter 2009 Page 15 Relationships Involving the Equilibrium Constant Reversing an equation causes inversion of K. Multiplying by coefficients by a common factor raises the equilibrium constant to the corresponding power. Dividing the coefficients by a common factor causes the equilibrium constant to be taken to that root. Winter 2009 Page 16 8

9 Gases: The Equilibrium Constant, K P Mixtures of gases are solutions just as liquids are. Use K P, based upon activities of gases. Winter 2009 Page 17 Gases: The Equilibrium Constant, K C In concentration we can do another substitution Winter 2009 Page 18 9

10 Winter 2009 Page 19 CaCO 3 (s) CaO(s) + CO 2 (g) K c = [CO 2 ] K P = P CO 2 (RT) Winter 2009 Page 20 10

11 Winter 2009 Page 21 The Reaction Quotient, Q: CO(g) + 2 H 2 (g) CH 3 OH(g) Equilibrium can be approached various ways. Qualitative determination of change of initial conditions as equilibrium is approached is needed. [G] Q c = tg [H] h t [A]tm [B] n t At equilibrium Q c = K c Winter 2009 Page 22 11

12 Winter 2009 Page 23 Altering Equilibrium Conditions: Le Châtelier s Principle When an equilibrium system is subjected to a change in temperature, pressure, or concentration of a reacting species, the system responds by attaining a new equilibrium that partially offsets the impact of the change. Winter 2009 Page 24 12

13 Topic 4: Gaseous Le Equilibrium Châtelier s Principle 2 SO 2 (g) + O 2 (g) 2 SO 3 (g) K c = at 1000K Q = [SO 3 ] 2 [SO 2 ] 2 [O 2 ] = K c Q > K c Winter 2009 Page 25 Adding a gaseous reactant or product changes P gas. Adding an inert gas changes the total pressure. Relative partial pressures are unchanged. Changing the volume of the system causes a change in the equilibrium position. When the volume of an equilibrium mixture of gases is reduced, a net change occurs in the direction that produces fewer moles of gas. When the volume is increased, a net change occurs in the direction that produces more moles of gas. Winter 2009 Page 26 13

14 Effect of Temperature on Equilibrium Raising the temperature of an equilibrium mixture shifts the equilibrium in the direction of the endothermic reaction. Lowering the temperature causes a shift in the direction of the exothermic reaction. Winter 2009 Page 27 Effect of a Catalyst on Equilibrium A catalyst changes the mechanism of a reaction to one with a lower activation energy. A catalyst has no effect on the condition of equilibrium. But does affect the rate at which equilibrium is attained. Winter 2009 Page 28 14

15 Nitrogen Cycle and the Synthesis of Nitrogen Compounds. N 2 (g) + O 2 (g) NO(g) K P = at 298K and 1.3 x 10-4 at 1800K Page 29 15