TOPIC 17 EQUILIBRIUM

1. TOPIC 17 EQUILIBRIUM 17.1 THE EQUILIBRIUM LAW

2. ESSENTIAL IDEA The position of equilibrium can be quantified by the equilibrium law. The equilibrium constant for a particular reaction only depends on the temperature. NATURE OF SCIENCE (1.8 and 1.9) Employing quantitative reasoning – experimentally determined rate expressions for forward and backward reactions can be deduced directly from the stoichiometric equations and allow Le Chatelier’s principle to be applied.

3. THEORY OF KNOWLEDGE The equilibrium law can be deduced by assuming that the order of the forward reaction and backward reaction matches the coefficients in the chemical equation. What is the role of deductive reasoning in science? We can use mathematics successfully to model equilibrium systems. Is this because we create mathematics to mirror reality or because the reality is intrinsically mathematical? Many problems in science can only be solved when assumptions are made which simplify the mathematics. What is the role of intuition in problem solving?

4. APPLICATION/SKILLS Solution of homogeneous equilibrium problems using the expression for Kc.

5. A homogeneous system is one in which all substances are in the same phase for example all gases or all solutions.

6. Heterogeneous Equilibria The position of a heterogeneous equilibrium does not depend on the amounts of pure solids or liquids present. Liquids and solids are never a part of the K expression. Write the equilibrium expression for the reaction: PCl5(s)  PCl3(l) + Cl2(g) Pure solid Pure liquid

7. Remember the Equilibrium Constant Kc jA + kB  lC + mD Where Kc is the equilibrium constant, and is unitless. The only thing that can change Kc for a reaction is a change in temperature.

8. Solving for Equilibrium Concentration Consider this reaction at some temperature: H2O(g) + CO(g)  H2(g) + CO2(g) K = 2.0 Assume you start with 8 moles of H2O and 6 moles of CO in a 1 dm3 container. How many moles of H2O, CO, H2, and CO2 are present at equilibrium? Here, we learn about “ICE” – the most important problem solving technique in solving all equilibrium problems.

9. ICE TABLES Only molar concentrations are used in ICE tables. ICE stands for “Initial” concentrations, “Change” in concentrations, and “Equilibrium” concentrations.

10. Solving for Equilibrium Concentration H2O(g) + CO(g)  H2(g) + CO2(g) K = 2.0 Step #1:We write the K expression for the reaction. Always use concentrations in ICE tables.

11. Solving for Equilibrium Concentration Step #2:We make an ICE table using the initial concentrations. The “change” comes from the coefficients. H2O(g) + CO(g)  H2(g) + CO2(g) 8 6 0 0 -x -x +x +x 8-x 6-x x x

12. Solving for Equilibrium Concentration Step #3:We plug equilibrium concentrations into our equilibrium expression, and solve for x H2O(g) + CO(g)  H2(g) + CO2(g)

13. ADDITIONAL COMMENTS • Many equilibrium ICE tables have to be solved using the quadratic equation. • You will not be expected to use calculations involving the quadratic equation. • When Kc is very small (10-3 or smaller), you will be making an assumption that the change in concentration of the reactants is basically zero.

14. UNDERSTANDING/KEY IDEA 17.1.A Le Chatelier’s principle for changes in concentration can be explained by the equilibrium law.

15. LeChatelier’s Principle When a system at equilibrium is placed under stress, the system will undergo a change in such a way as to relieve that stress. • Translated:The system undergoes a temporary shift in order to restore equilibrium. • 1. When you add a substance or heat, the system shifts to the opposite side. • 2. When you take out a substance or heat, the system shifts to the side of the take out. • When you increase pressure, the system shifts to the side with the least number of gaseous molecules.

16. KINETICS AND EQUILIBRIUM • The equilibrium constant is the ratio of the rate constants of the forward and backward reactions. • If “k” for the forward reaction is greater than “k” for the backward reaction, then the reaction is product favored and proceeds toward completion. K is large. • If “k” for the backward reaction is greater than “k” for the forward reaction, then the reaction has barely taken place. K is small.

17. Using the relationship between k, the rate constant, and K, the equilibrium constant, we can add to our interpretation of how equilibrium responds to changing conditions.

18. CHANGING CONCENTRATION • If you increase the concentration of the reactant(s), you will increase the rate of the forward reaction thus shifting equilibrium to the right. • If you increase the concentration of the product(s), you will increase the rate of the backward reaction thus shifting equilibrium to the left. • The value of the equilibrium constant, K, stays constant since only temperature affects K.

19. ADDING A CATALYST • Adding a catalyst increases the rate constants, k, of both the forward and reverse reactions by the same amount so the equilibrium constant is not affected.

20. CHANGING TEMPERATURE • We know from kinetics and our studies of the Arrhenius equation, k = Ae-Ea/RT,that as temperature increases, the rate constant “k” increases. • From the potential energy diagrams, we know that the activation energies of the forward and backward reactions are different so their rate constants would be different and are affected differently by temperature.

21. The ratio of the rate constants of the forward and backward reactions is temperature dependent. • For an endothermic reaction, where Ea of the forward reaction is greater than that of the backward reaction, the increase in temperature has a greater effect on increasing “k” for the forward reaction so Kc increases as temperature increases.

22. HOW DO YOU PROVE IT? • Take the time with your partner and prove the previous statement using the potential energy diagrams and the Arrhenius equation k = Ae-Ea/RT.

23. UNDERSTANDING/KEY IDEA 17.1.B The position of equilibrium corresponds to a maximum value of entropy and a minimum value of the Gibbs free energy.

24. Different reactions have very different Kc values reflecting a wide range of the directions and extents of these reactions. • Some reactions go almost all the way to completion and others barely react at all. • Gibbs free energy can help determine these differences in reactions.

25. ΔG◦ = negative • Spontaneous • Reaction proceeds in the forward direction • ΔG◦ = positive • Non-spontaneous • Reaction proceeds in the backward direction • ΔG◦ = zero • Reaction is at equilibrium

26. A reaction with a value of ΔG◦ that is large and negative appears to occur spontaneously and has an equilibrium mixture with a high proportion of products. • A reaction with a value of ΔG◦ that is large and positive appears to be non-spontaneous and has an equilibrium mixture with a high proportion of reactants.

27. pixshark.com ΔG neg ΔG neg ΔG pos Non-spontaneous ΔG pos Non-spontaneous

28. The position of equilibrium corresponds to a maximum value of entropy for the system. In other words, any system has the highest possible value of entropy when free energy is at a minimum (equilibrium).

29. UNDERSTANDING/KEY IDEA 17.1.C The Gibb’s free energy change of a reaction and the equilibrium constant can both be used to measure the position of an equilibrium reaction and are related by the equation, ΔG◦ = -RTlnK.

30. APPLICATION/SKILLS Understand the relationship between ΔG and the equilibrium constant.

31. APPLICATION/SKILLS Be able to do calculations with the equation ΔG◦ = -RTlnK.

32. Kc AND THERMO DATA • We now have 2 terms which relate to the position of equilibrium. • Kc, the equilibrium constant • ΔG◦, the change in free energy • From the equation, ΔG◦ = -RTlnK, we can deduce relationships between the two values, Kc and ΔG◦.

33. ΔG◦ negative ln K positive K>1 mostly products ΔG◦ positive ln K negative K<1 mostly reactants ΔG◦ = 0 ln K = 0 K=1 mixture of both The equation ΔG◦ = -RTlnK can be used to solve for either Gibb’s free energy or the equilibrium constant. It is useful in situations where the K is difficult to measure directly such as if the reaction is too slow to reach equilibrium or when the component amounts are too small to measure. The value of Gibb’s free energy is the reason that different reactions have such different values for K. Remember that Gibb’s free energy is also dependent upon the change in enthalpy and change in entropy ΔG◦ = ΔH – TΔS.

34. Citations International Baccalaureate Organization. Chemistry Guide, First assessment 2016. Updated 2015. Brown, Catrin, and Mike Ford. Higher Level Chemistry. 2nd ed. N.p.: Pearson Baccalaureate, 2014. Print. Most of the information found in this power point comes directly from this textbook. The power point has been made to directly complement the Higher Level Chemistry textbook by Catrin and Brown and is used for direct instructional purposes only.