2/18/2013. Spontaneity, Entropy & Free Energy Chapter 16

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1 Spontaneity, Entropy & Chapter 16 G = H T S G is Gibbs free energy H is enthalpy T is temperture in Kelvin S is entropy Refers to the system Proved on p. 760 from S = H/T S univ = - G T at constant T & P Goldfish are Held with Tartar Sauce The process will be spontaneous if G is negative (because S univ is positive) used to be named available energy or energy available to do work. H Ball rolling down a slide The total energy of the system, H, decreases (potential to kinetic) in a spontaneous process. Any method involving the notion of entropy, the very existence of which depends on the second law of thermodynamics, will doubtless seem to many farfetched, and may repel beginners as obscure and difficult of comprehension. - Willard Gibbs S Diffusion The total entropy of the system, S increases in this spontaneous process T Firecrackers Will the process be more likely to occur if the temperature is higher or lower? In this example, it is more likely. 1

2 H Ball rolling down a slide The total energy of the system, H, decreases in a spontaneous process. Look at the effect of the change in H, S and T on G G = H - T S S Diffusion The total entropy of the system, S increases in this spontaneous process Look at the effect of the change in H, S and T on G G = H - T S T Firecracker Will the process be more likely to occur if the temperature is higher or lower? In this example more likely. Look at the effect of the change in H, S and T on G G = H - T S 2

3 ΔH and ΔS and the Dependence of Spontaneity on Temperature G Spontaneity G < 0 Spontaneous Exergonic G > 0 Non spontaneous Endergonic G = 0 Equilibrium ΔS univ and ΔG for H 2 O (s) H 2 O (l) Is the melting of ice spontaneous? Sample Exercise At what temperature is the folloiwng process spontaneous at 1 atm? Br 2 (l) Br 2 (g) H = 31.0 kj/mol and S = 93.0 kj/mol What is the normal boiling point of liquid Br 2? 3

4 Exercise #29 Ethanethiol (C 2 H 5 SH; also called ethyl mercaptan) is commonly added to natural gas to provide the rotten egg smell of a gas leak. The boiling point of ethanethiol is 35 C and its heat of vaporization is 27.5 kj/mol. What is the entropy of vaporization for this substance? Exercise #30 For mercury, the enthalpy of vaporization is kj/mol and the entropy of vaporization is J/k-mol. What is the normal boiling point of mercury? Entropy Changes in Chemical Reactions Predicting the Sign of S 4NH 3 (g) + 5O 2 (g) 4NO (g) + 6H 2 O (g) Fewer molecules means fewer possible configurations so positional entropy increases. The change in positional entropy is dominated by the relative numbers of molecules. H determines if a reaction is endothermic or exothermic G determines if a reaction is spontaneous (at constant T & P) 4

5 Entropy Changes in Chemical Reactions Absolute entropy values can be assigned Third Law of Thermodynamics The entropy of a perfect crystal at 0 K is zero. Because S is a state function, its value can be summation S reaction = n p S products - n p S reactants However S for elements is not zero Sample Exercises 16.8 Calculate the S for the reduction of aluminum oxide by hydrogen gas: Al 2 O 3 (s) + 3H 2 (g) 2Al (s) + 3H 2 O (g) Will S be positive or negative? 3:3 gas Look closely at the form H 2 vs. H 2 O H 2 O has not just positional entropy but vibrational and rotational The more complex the molecule, the higher the standard entropy value. 3 Things to Look For State of matter Coefficients Complexity of substance 179 J/K Substance S (J/K-mol) Al 2 O 3 (s) 51 H 2 (g) 131 Al (s) 28 H 2 O (g) Exercise #47 For the reaction at 298 K, 2NO 2 (g) N 2 O 4 (g) The values of H and S are kj/mol and kj/mol, respectively. What is the value of G at 298 K? Assuming that H and S do not depend on temperature, at what temperature is G = 0? Is G negative above or below this temperature 5

6 16.6 in Chemical Reactions Calculating G Because G is a state function, its value can be calculated by summation The standard free energy of formation of an element in tis standard state is 0. G reaction = n p G products - n p G reactants or using equations as with H or Calculate H and S then use G = H - T S 6