Chemistry 130 Gibbs Free Energy Dr. John F. C. Turner 409 Buehler Hall [email protected] Chemistry 130 Equilibrium and energy So far in chemistry 130, and in Chemistry 120, we have described chemical reactions thermodynamically by using U - the change in internal energy, U, which involves heat transferring in or out of the system only or H - the change in enthalpy, H, which involves heat transfers in and out of the system as well as changes in work. U applies at constant volume, where as H applies at constant pressure. Chemistry 130 Equilibrium and energy When chemical systems change, either physically through melting, evaporation, freezing or some other physical process variables (V, P, T) or chemically by reaction variables (ni) they move to a point of equilibrium by either exothermic or endothermic processes. Characterizing the change as exothermic or endothermic does not tell us whether the change is spontaneous or not. Both endothermic and exothermic processes are seen to occur spontaneously. Chemistry 130 Equilibrium and energy Our descriptions of reactions and other chemical changes are on the basis of exothermicity or endothermicity ± whether H is negative or positive H is negative ± exothermic H is positive ± endothermic As a description of changes in heat content and work, these are adequate but they do not describe whether a process is spontaneous or not. There are endothermic processes that are spontaneous ± evaporation of water, the dissolution of ammonium chloride in water, the melting of ice and so on. We need a thermodynamic description of spontaneous processes in order to fully describe a chemical system Chemistry 130 Equilibrium and energy A spontaneous process is one that takes place without any influence external to the system. The opposite of a spontaneous change is a non-spontaneous change ± one where there must be an external influence to force the change. For any observed, spontaneous change, the reverse process is non-spontaneous. Chemistry 130 Equilibrium and energy If we use energy as the sole criterion of spontaneous change, we are using effectively a mechanical analogy ± systems move to the local minimum in energy as the point of equilibrium. In the example of a ball falling, we have one variable, position, in a field, the gravitational field of the earth, and there is no endothermic path. Potential energy is converted into kinetic energy in flight and then into heat and sound (q and w) at impact. Chemistry 130 Equilibrium and energy In this case, minimization of the potential energy and conversion ultimately into heat defines the point of equilibrium and appears to be linked to the direction of spontaneous change. Early theories of chemical thermodynamics rested on the evolution of heat as the ©driving force© for a reaction, which fails. Chemistry 130 Equilibrium and energy It is certainly true that many reactions that are spontaneous are accompanied by the evolution of heat: + - −1 NaOHs Naaq OHaq H = −44.51 kJ mol H2 O But some are not and are endothermic and yet are still spontaneous: + - −1 NH4 Cls NH4aq Claq H = 14.78.51 kJ mol H2 O So, in the ©mechanical© view of chemical change, in the case of ammonium chloride, we have a system that spontaneously moves to a higher state of energy. Physical changes such as melting and boiling are inherently endothermic and the same problem occurs. Chemistry 130 Equilibrium and energy Both of these examples have an associated enthalpy change: + - −1 NaOH s Naaq OHaq H = −44.51 kJ mol H2O + - −1 NH4 Cl s NH4aq Claq H = 14.78.51 kJ mol H2 O Some processes do not result in a net change of energy in the q system and are still spontaneous: T 1 ≫ T 2 In an insulated system that cannot exchange heat with the surroundings, heat will spontaneously move to equalize a temperature gradient between two bodies. T 1 = T 2 Chemistry 130 Equilibrium and energy Similarly, there are no forces between a particles of a perfect gas and the internal energy of the perfect gas is independent of volume. Yet a perfect gas will always expand to fill the volume available, with no net change in energy. Chemistry 130 Equilibrium and energy So spontaneous changes can take place endothermically, exothermically or with no exchange of energy + - −1 NaOHs Naaq OHaq H = −44.51 kJ mol H2 O + - −1 NH4 Cls NH4aq Claq H = 14.78.51 kJ mol H2 O q T 1 ≫ T 2 T 1 = T 2 Chemistry 130 Equilibrium and energy We need a description of spontaneous change that includes the direction of the change, a description of the point of equilibrium quantitatively Energy is not a good description ± chemical changes are not mechanical. Chemistry 130 Reversibility and irreversibility Thermodynamically, we define a reversible change as one that takes place within an infinitesimal step from the point of equilibrium If the point of equilibrium is defined by G ni , P ,T then irreversible changes can occur via G nid ni , P ,T G ni , P ,T G ni ,Pd P ,T G n , P , T d T i Reversible changes occur infinitely slowly and maximize the amount of work that is possible from a system. They also do not occur in practice but are the theoretical limit for developing our description of spontaneous change and the point of equilibrium. Chemistry 130 Reversibility and irreversibility G n d n , P ,T i i G ni , P ,T G ni ,Pd P ,T G ni , P ,Td T In practice, the maximum amount of work is never achievable. Real changes are irreversible and the amount of work that can be extracted is always less than the maximum amount of work. Chemistry 130 Equilibrium, energy and entropy The magnitude and sign of the change in enthalpy associated with a chemical or physical change does not reflect the spontaneity of the process. It is not a good measure. However, any description of a molecular system such as a mole of a perfect gas is inherently statistical: A mole contains 6 . 0 2 3 × 1 0 2 3 particles and the number of ways that we can arrange a mole of particles is going to be of the order of 23 Number of ways = W ~ 1010 There are therefore many (!) ways of describing a chemical system while conserving the observed macroscopic properties ± internal energy, pressure, temperature etc. Chemistry 130 Equilibrium, energy and entropy If we have a large number of ways of describing the inside of the system so that the outside stays the same, then we have a large number of ways of distributing the energy of the system amongst these different configurations. There are many equivalent ways of distributing the thermal energy of a system given a certain macroscopic energy. A change is spontaneous when the number of ways of distributing the energy increases. The point of equilibrium is when this number of ways is maximized. Chemistry 130 Entropy The measure of the number of ways of distributing energy that we use to describe this is the entropy of the system. We need entropy to be a state function and we cannot use heat, q, to do this because heat is not a state function. Instead, we define the entropy, S, for a reversible change as q Entropy = S = rev T where qrev is the reversible heat transferred and T is the thermodynamic temperature. Chemistry 130 Chemistry 130 Gibbs Free Energy Dr. John F. C. Turner 409 Buehler Hall [email protected] Chemistry 130 Entropy Summary 1. A spontaneous change is one that takes place without any external action on the system and the reverse of a spontaneous change is non-spontaneous 3. Energy and the First Law of Thermodynamics does not predict the direction of spontaneous change 4. Spontaneous change occurs when the number of ways of distributing the energy associated with the change increases 5. We quantify this increase in the distribution of energy associated with a spontaneous change by the entropy of a system q 6. Entropy is a state function and is defined by Entro p y = S rev T where qrev is the reversible heat change. 7. A reversible change is one that takes place infinitesimally close to the point of equilibrium Chemistry 130 The Gibbs function In order to predict the direction of spontaneous change, we need to consider the total entropy change in the universe. We write this as SUniverse = SSurroundings SSystem q q S = Surroundings System Universe T T from our definition of entropy. We know that the heat change in the system is equivalent to the opposite of the heat change in the surroundings: q q Surroundings = − System T T and we know, that for a system that can do work, qSystem=H Chemistry 130 The Gibbs function Now we can write the change in the universe solely in terms of changes in the system. q H Surroundings = − T T This is important because the system is the part of the universe that we know enough about for an accurate description in principle. H The entropy then becomes S = − S Universe T System TSUniverse = −H TSSystem −TSUniverse = H − TSSystem We define G = H − TSSystem where G is the Gibbs function. Chemistry 130 The Gibbs function The Gibbs function is a disguised form of entropy and has the units of energy; it is not an energy term in the First Law sense (H, U etc) but is a measure of the change in entropy of the universe. For a spontaneous change, G 0 i.e. the change in the Gibbs function must be zero or less than zero for a spontaneous change.