Title: Lesson 5 Free Energy and Equilibrium Learning Objectives: Know that the position of the equilibrium corresponds to a maximum value of entropy and minimum in the value of Gibb’s free energy Know how Gibbs free energy change and the equilibrium constant can be used to measure the position of an equilibrium reaction, using the equation ∆G= -RTlnK

Main Menu Free Energy and Equilibrium  Why do different reactions have different values for their equilibrium constant, K c ? Why do some reactions barely take place and others go near to completion?  Gibbs free energy change, ∆G, is the measure of the work that is available from the system. It’s sign is used to predict the spontaneity of the reaction.

Main Menu Compare a reaction to discharging a battery…  At the start, the total free energy of the reactants > products. A lot of work is available. (-ve ∆G  Forwards reaction)  As the battery discharges, the reaction continues converting reactants to products. Total free energy decreases for reactants, increases for products. (∆G less –ve) Less work available.  The system reaches equilibrium. Total free energies of reactants and products are equal and no work can be extracted from the system. Battery is dead. The composition of reactants and products at equilibrium is determined by the difference of free energy in the reactants and products Reaction starts with either pure reactants or pure products. Free energy decreases in both directions to a minimum value of free energy = equilibrium.

Main Menu What if the products have more free energy than the reactants?  Decrease in free energy during the reaction = work done = increase in entropy.  Highest possible value of entropy is when free energy is at a minimum (equilibrium) ∆G can be used to predict spontaneity and position of equilibrium: Large negative ∆G  spontaneous and equilibrium mixture with high proportion of products. Large positive ∆G  non spontaneous and equilibrium mixture with high proportion of reactants.

Main Menu Kc can be calculated from thermodynamic data  We have now identified two terms that relate to the position of the equilibrium: K c and ∆G   This equation is given in section 1 of the data booklet.

Main Menu Equilibrium constant can be calculated from free energy and vice versa...  Useful when equilibrium constant is difficult to measure directly... E.g. too slow, component amounts too small to measure... The value of ∆G determines the value of the equilibrium constant, K c. From chapter 5, ∆G depends on ∆H and ∆S.

Main Menu Kinetics and Equilibrium  Rusting of iron  Heterogeneous Equilibrium - Cannot derive the equilibrium expression here  K c can be calculated from knowing ∆G = 1490 x 10 6 J using  This gives K c =  Very large K c indicates thermodynamically favourable reaction  proceeds towards completion.  ∆G is large and negative, but we know rusting is a slow process.  Magnitude of equilibrium constant gives no information about rate of reaction.

Main Menu K c values for forwards and backwards step can explain some aspects of equilibria...  Rate laws for the forward and backward reaction:  The equilibrium constant expression for the reaction is:  At equilibrium:  Rearrange:

Main Menu How do equilibrium constant K c and rate constant k affect how equilibrium responds to changing conditions?  Concentration:  Increasing reactants  increase forward reaction  shifts equilibrium to the right.  Increasing products  increase backwards reaction  shifts equilibrium to the left.  Value of K c stays constant as concentration does not affect rate constant (k).

Main Menu How do equilibrium constant K c and rate constant k affect how equilibrium responds to changing conditions?  Catalyst:  Increases forwards and backwards rate constant (k) by same factor so ratio of values is still the same. So K c is not affected.  Temperature:  From Arrhenius equation:Rate constant increases with increasing temperature.  Activation energies of forward and backward reactions are different, so rate constants for forwarded and backwards are affected differently.  So ratio k/k’ = K c is temperature dependent.  For an endothermic reaction, E a forward > backwards, so increasing temperature will affect k more, so K c increases.

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