Name Chem 163 Sectin: Team Number: ALE 21. Gibbs Free Energy (Reference: 20.3 Silberberg 5 th editin) At what temperature des the spntaneity f a reactin change? The Mdel: The Definitin f Free Energy S far in ur study f thermdynamics, we have seen that in rder t determine if a reactin is spntaneus we must cnsider the entrpy change (S) and the enthalpy change (H) assciated with the reactin. An equatin that describes the quantitative relatinship between entrpy and the enthalpy was develped by J. Willard Gibbs, a prfessr f mathematical physics at Yale in the nineteenth century. He defined a new quantity, nw called the Gibbs free energy (G), a single quantity that cmbines bth f these ideas (eqn 1). Because enthalpy is a state functin (i.e., H is the same between tw states, regardless f the path taken getting frm the initial t the final state) and entrpy is a state functin, Gibbs Free Energy is a state functin, t. Just as it was fr enthalpies, we ften cannt determine the abslute value f the amunt f Gibbs free energy that a system has. But that is kay, because we are principally interested in hw much wrk we can btain frm a spntaneus reactin. G H T S (1) The maximum amunt f nn-expansin wrk btainable is equal t G rxn, and the change in Gibbs free energy fr a chemical reactin is smething that can be determined. G H - TS (2) Key Questins 1 a. Explain why the Gibbs free energy functin (eqn 1) is a state functin. T is the temperature in Kelvin H is H reactin (in Jules r kiljules) S is S reactin (in Jules r kiljules) Nte: H reactin and S reactin must either bth be in J r bth in kj b. Since enthalpy is a state functin, the standard enthalpy change f a chemical reactin ( be calculated frm the standard heats f frmatin ( H f H rxn ) can ) f the reactants and prducts. Likewise, since Gibbs free energy is a state functin, there s a similar relatinship that allws us calculate ( ) frm tabulated values f standard mlar Gibbs free energies f frmatin ( ). Write this G rxn relatinship by cmpleting the equatin belw. G f G rxn Page 1 f 5
2. The abslute temperature is always psitive. But the signs f H rxn and S rxn may be either negative r psitive. Therefre, the sign f G rxn may be either psitive r negative. Use eqn 2,G H - TS, t cmplete the table by filling in each blank with a < r a >, indicating what the sign f G rxn will be in each case. S rxn < 0 S rxn > 0 H rxn < 0 H rxn > 0 G rxn 0 at lw T G rxn 0 at lw T G rxn 0 at high T G rxn 0 at high T G rxn 0 at lw T G rxn 0 at lw T G rxn 0 at high T G rxn 0 at high T 3 a. Frm the previus questin and what we learned in the last ALE, it wuld seem that G rxn has t d with the spntaneity f a chemical reactin. Explain hw the sign f G rxn can be used t tell whether a chemical reactin is spntaneus r nt. b. What des it mean if G rxn 0? (Hint: Recall that mst chemical reactins are reversible.) Exercises 4. The standard heats f frmatin and entrpies f diamnd and graphite at 25 C are given in the table t the right. H f (kj/ml) S (J ml -1 K -1 ) C(diamnd) 1.9 2.4 C(graphite) 0 5.7 Calculate H rxn, S rxn and G rxn fr the cnversin f diamnd t graphite (eqn 3) at 25 C. Shw yur wrk using units and sig. figs. Circle yur answers. C(diamnd) C(graphite) (3) a. H rxn b. S rxn c. G rxn d. What can yu say abut the slgan a diamnd is frever? Page 2 f 5
5. Even at 25 C, slid idine sublimes. Gaseus idine reacts with excess flurine t frm idine pentafluride accrding t the thermchemical equatin 4. I 2 (g) + 5 F 2 (g) 2 IF 5 (g) H -1743.1 kj (4) The standard Gibbs free energies f frmatin and standard mlar entrpies f the reactants and prducts are prvided in the table t the right Frm this infrmatin, determine the standard mlar entrpy f gaseus idine at 25 C. (Hint: Yu will need t use the versin f Hess s law fr bth G f (kj/ml) S (J ml -1 K -1 ) I 2 (g) 19.4??? F 2 (g) 0 203.3 IF 5 (g) -771.6 334.5 and.) G rxn S rxn Key Questins 6. Unless H rxn and S rxn have different signs, the spntaneity f a reactin is temperature dependent. The spntaneity f a chemical reactin changes when G rxn 0. Hence, if we knw H rxn and S rxn we can use the fllwing equatin t determine the apprximate temperature at which the spntaneity f a reactin changes (either frm spntaneus t nn-spntaneus, r frm nn-spntaneus t spntaneus). G rxn H rxn T S rxn Starting with the abve equatin, slve fr T (in terms f H rxn and S rxn ) when G rxn 0. Page 3 f 5
Exercises 7. The standard heats f frmatin and entrpies f liquid water and water vapr at 25 C are given in the fllwing table t the right a. Frm this data (which are valid at 25 C), estimate the temperature at which water spntaneusly bils at a pressure f 1 atm. H f (kj/ml) S (J ml -1 K -1 ) H 2 O(l) -285.8 69.9 H 2 O(g) -241.8 188.7 b. Nte that the value yu calculated in part a is nly an estimatin. Briefly explain the surce f errr in the calculatin. Fr the next tw Questins: Refer t thermdynamic data n pages A5 - A7 f Appendix B f yur textbk. 8. The U.S. gvernment nw requires autmbile fuels t cntain a renewable cmpnent. The fermentatin f glucse frm crn t prduce ethanl fr additin t gasline is a key prcess fulfilling this requirement: C 6 H 12 O 6 (s) 2 C 2 H 5 OH (l) + 2 CO 2(g) Calculate H, S and G fr the reactin at 25 C. Is the spntaneity f the reactin dependent n temperature? Explain. Page 4 f 5
9. Cnsider the fllwing cmbustin f butane gas: a.) Predict the signs f S and H. Explain C 4 H 10 (g) + 6.5 O 2 (g) 4 CO 2(g) + 5 H 2 O (g) b.) Calculate G by tw different methds. Methd #1: Using G f Methd #2: Using S and H 10. Is an endthermic reactin mre likely t be spntaneus at higher temperatures r lwer temperatures? Explain. Page 5 f 5