Chapter 19 Chemical Thermodynamics Spontaneous Processes Entropy and the Second Law of Thermodynamics The Molecular Interpretation of Entropy Entropy Changes in Chemical Reactions Gibbs Free Energy Free Energy and Temperature Free Energy and the Equilibrium Constant
19.1 Spontaneous Processes First Law of Thermodynamics stated: Energy can not be created nor destroyed, it can be converted from one form to another or transferred from a system to surroundings (or vice versa) A Spontaneous Process is one that, when initiated, will proceed on its own without outside assistance
Reactions that are spontaneous in one direction are non-spontaneous in the reverse direction A Chemical reaction is spontaneous if once it starts it proceed on its own, regardless of how fast the reaction occurs Spontaneity does not give us any information about the speed of a reaction
Temperature has an effect on spontaneity How do we know if a reaction is going to be spontaneous or not? Need to distinguish between reversible and irreversible reactions There is no net change to the system or its surroundings
Flow of heat is irreversible, we can t make heat flow from the cold object to the hot object Consider the system and surrounding pictured, if the difference in temperature is infinitesimal ΔT, heat will flow in the direction shown But the direction of heat flow can be reversed by making an infinitesimal change ΔT in the opposite direction A chemical system at equilibrium is reversible, an infinitesimal change in the system (reactants or products) can reverse the direction
Just because the system is restored to its original condition doesn t mean that the surroundings have likewise been restored to their original condition Contrast with the expansion of a gas at constant temperature (isothermal) The system and surroundings are not BOTH returned to their original condition IRREVERSIBLE process Any spontaneous process is irreversible, if we return the system back to its original condition the surroundings will have changed
19.2 Entropy Spontaneous reactions often give out heat ( exothermic ) however some are endothermic, so enthalpy alone can t account for the direction of spontaneous change. Entropy is the other thermodynamic quantity that accounts for the direction of spontaneous change. Entropy is nature s driving force to move to a condition of maximum randomness or disorder Entropy is given the symbol S. Entropy is a state function, the change in entropy only depends of the initial and final states of the system
When the randomness or disorder increases S > 0, when randomness decreases S < 0. Melting is an Endothermic process however it involves an increase in the randomness of the system Dissolving Sodium Chloride in water increases randomness as the Na + and Cl - ions have a greater freedom of motion. In some cases the strongly ordered arrangement of hydrating water molecules results in an overall net decrease in randomness. Dissolution in these cases is unlikely eg CaSO 4
For an isothermal process (constant T) Think of this as using a reversible path between the states Sample exercise 19.2 Second Law of Thermodynamics The first Law of Thermodynamics, energy is conserved, no matter what the process, chemical or physical, the overall energy of the system and surroundings remains the same
In any spontaneous process, the total entropy of the system and surroundings always increases These facts form the basis of the second law of thermodynamics which can be stated as follows Reversible process ΔS univ = ΔS sys + ΔS surr = 0 Irreversible process ΔS univ = ΔS sys + ΔS surr > 0
Molecular interpretation of Entropy Why is greater randomness the driving consideration for spontaneity The relationship of Entropy to this disorder (randomness) or probability was studied by Boltzmann. Boltzmann was thinking about a mole of gas particles all in motion in a container, as you do, and then considered what state they would be in if you froze them all and took a picture. Their positions at that time he called a microstate To figure out the seemingly impossible problem of relating Entropy to how many different microstates there could possibly be in a system Boltzmann came up with a very simple equation
In a simple process we can think about how the Entropy of a system changes As Boltzmann demonstrated, increasing the number of microstates increases the entropy Factors that can cause an increase in the number of microstates include. Temperature Increasing the temperature The number of particles Increasing the number of particles is like increasing the number of cards in a deck
Volume Increasing the Volume gives molecules greater freedom to move around and increases the number of possible microstates Sample exercise 19.3 What happens as the Temperature of a system is lowered?
The Third Law Of Thermodynamics At 0K, all the units in the lattice have no thermal energy, no motion, 1 Microstate S = k lnw W = 1 lnw = 0 So S = 0
What happens to Entropy as we continue to heat
19.4 Entropy Changes in Chemical Reactions We can measure ΔH of a reaction by using calorimetry, however there is no such easy method for determining ΔS for a reaction Absolute values for Entropies, S, can be obtained Standard Molar Entropy S o is defined for pure substances at 1 atm pressure and 298K
The Entropy change for a reaction can be calculated from the Standard Molar Entropies ΔS o = Σ ns o (products) - Σ ms o (reactants) Sample Exercise 19.5 Entropy Changes in the Surroundings The Entropy change of the surroundings depends on the how much heat is absorbed or given off by the system For a constant pressure reaction (usual) then q p (heat exchanged at constant pressure) = ΔH so the entropy change of the surroundings can be written as
Because S o univ is positive (increases) for any spontaneous reaction we can put together the equations for calculating ΔS sys with ΔS surr to predict whether a reaction will be spontaneous For the reaction CO(g) + 2H 2 (g) CH 3 OH (l) at 298K
Prediction of Spontaneity depends on The sign of ΔH and ΔS And the magnitude of ΔH, ΔS and the temperature (in KELVIN) A spontaneous reaction can be exothermic or endothermic
19.5 Gibbs Free Energy From the calculation previous using ΔS o univ = ΔS o sys + ΔS o surr the spontaneity of a reaction was seen to involve enthalpy H and Entropy S J W Gibbs came up with a new state function G, that connected entropy and enthalpy to predict whether a reaction occurring at a constant temperature would be spontaneous
From the definition of ΔS univ, we can relate the state function G to spontaneity ΔS univ = ΔS sys + ΔS surr = ΔS sys + (ΔH sys /T) Multiply both sides by T gives TΔS univ = ΔH sys - TΔS sys = ΔG sys ΔG sys = - TΔS univ at constant temperature and pressure So the value of ΔG should predict whether a reaction will be spontaneous In any spontaneous process occurring at constant temperature and pressure the free energy always decreases
This can be explained in the diagram for the formation of ammonia The expression for Q is the same as the Equilibrium Constant except that the reactants and products need not be in equilibrium Q < K concentration of products less than reactants, (Q > K vice versa)
Standard Free Energy The standard free Energy ΔG o is defined as the change in the free energy when reactants in their standard states are converted to products in their standard states Standard Free Energy of Formation Sample exercise 19.6 From these values we can calculate the standard free energy change of reactions G is a State Function, so: Sample exercise 19.7
19.6 Free Energy and Temperature We can calculate ΔG o from ΔG o f, but this value is for 298K The entropy term (TΔS) is dependant on the absolute temperature and as such ΔG will also vary with temperature. It is possible that the temperature could change the sign of ΔG and a reaction that is non spontaneous at one temperature could become spontaneous at another temperature The table indicates how temperature effects the spontaneity of reactions Sample exercise 19.8
Sample Exercise 19.9 A substance at its melting point and boiling point exists in equilibrium, ΔH fus = TΔS and ΔH vap = TΔS Sample Exercise 19.10
19.7 Free Energy and the equilibrium constant At equilibrium ΔG = 0 ΔG o can be calculated at standard conditions using the tabulated data for ΔG fo But most reactions DO NOT occurs at standard conditions A method is required that can calculate ΔG using the value of ΔG o under non standard conditions The expression for Q is the same as the Equilibrium Constant except that the reactants and products need not be in equilibrium Q < K concentration of products less than reactants, (Q > K vice versa)
A t standard state, When Q = 1, the concentrations of all reactants and products is 1M (ln Q = 0) and ΔG = ΔG o Q is useful in predicting the direction of reaction At equilibrium ΔG = 0 and Q = K therefore
The expression for ΔG o at equilibrium ΔG o = -RT ln K is often re-arranged to solve for K This relationship expresses the relationship between the equilibrium constant and the Temperature Remember units ΔG o = kj/mol T = K Gas Pressures in atm Solution concentration in M For gas phase reaction the equilibrium constant is K p For reactions in solution the equilibrium constant is K c Sample Exercise 19.12
In many situations we need to drive non-spontaneous reactions This is done by coupling the non-spontaneous reaction with a spontaneous reaction eg. Cu 2 S(s) 2Cu(s) + S(s) ΔG o = +86.2kJ S(s) + O2(g) SO2(g) ΔG o = -300.4kJ So the overall coupled reaction would be: The standard free energy change ΔG o for this reaction would be: