Gibbs Free Energy and Chemical Equilibrium (or how to predict chemical reactions without doing experiments)

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1 Gbbs Free Energy and Chemcal Equlbrum (or how to predct chemcal reactons wthout dong experments) OCN 623 Chemcal Oceanography Readng: Frst half of Chapter 3, Snoeynk and Jenkns (1980)

2 Introducton We want to answer these questons: Wll ths reacton go? If so, how far can t proceed? We wll do ths by usng thermodynamcs. Ths lecture wll be restrcted to a small subset of thermodynamcs the soluton of chemcal equlbrum problems

3 Chemcal Equlbrum Consder a reversble reacton takng place at constant temperature: aa + bb cc + dd The reactants A and B combne to form products C and D. The concentratons of A and B decrease untl they reach values that do not change wth tme:

4 The tme-nvarant concentratons of reactants and products are called equlbrum concentratons The rato of these concentratons (or actvtes actve concentratons) s characterstc for each reacton, and s called the equlbrum constant, K: K { C} { A} c a { D} { B} d b Note that at equlbrum, the forward and reverse reactons proceed at the same, stable rate.

5 Free Energy A crteron for equlbrum s that the total free energy (Gbbs free energy, G r ) of the reacton s at a mnmum: If we add more reactant or more product, the reacton wll proceed spontaneously (wthout external help) as long as the value for G r decreases Thus, a reacton n the drecton of decreasng G r s spontaneous. A reacton n the drecton of ncreasng G r s not spontaneous, and wll not occur n a closed system.

6 As any reacton proceeds an ncremental amount, the change n G r can be calculated as: G r = υg f products υg f reactants where ν s the stochometrc coeffcent (a,b,c,d) for speces, and G f s the free energy of formaton per mole of speces 1. If G r < 0, (.e., G r s negatve and thus G r decreases as the reacton proceeds), then the reacton proceeds spontaneously as wrtten 2. If G r > 0, (.e., G r s postve and thus G r ncreases as the reacton proceeds), then the reacton proceeds spontaneously n the opposte drecton as wrtten 3. If G r = 0, (.e., G r s at a mnmum), then the reacton s at equlbrum and wll not proceeds spontaneously n ether drecton

7 Values for G for a reacton gve us a powerful tool to predct f a reacton s possble. We calculate n-stu G r usng ths equaton: where In-stu G r = G r + Std. state RT { C} ln { A} c a { D} { B} d b G r = υg f products υg f reactants The the superscrpt zero ( ) ndcates standard state: 25 C (298 K),1 atm pressure, and actvty = 1 G f s the standard-state free energy of formaton per mole of speces { } = actvty (actve concentraton) R = the deal gas constant = cal K -1 mol -1 = 8.31 J K -1 mol -1 T = K

8 Standard free energy of formaton ( G f ): G f = 0 at standard state for all pure elements (sold reference) G f = 0 for H + at a concentraton of 1 mole/lter at standard state (soluton reference) Allows the measure of the energy change nvolved n formng compounds at standard state from ther component elements at standard state Measured values are lsted n tables. Unts are: kj/mol (SI unts) kcal/mol

9 Table n readng (handout)

10 See complete table n handout

11 Sample Calculaton #1 Consder the dssoluton of CaCO 3 (calcte) n aqueous soluton: CaCO 3 Ca 2+ + CO 3 2- Does the reacton proceed spontaneously as wrtten? Calculate the free energy of reacton at standard state (products and reactants at actvty = 1, P = 1 atm, T = 25 C): G r = υg f products υg f reactants G r = (1(-132) + 1(-126) (1(-270)) kcal/mol = ( ) kcal/mol = +12 kcal/mol Therefore, at standard state, the reacton spontaneously proceeds n the opposte drecton to what s wrtten (.e., calcte precptates)

12

13 Actvtes How to Calculate Actvty of water = 1

14 Equlbrum at In-Stu Condtons We have already seem that: In-stu G = G + Std. state RT ln { C } { A} c a { D} { B} d b We can defne a reacton quotent, Q, usng n-stu condtons: Q { C} { A} Thus: G = G + RT ln Q c a { D} { B} d b In the case of equlbrum, Q = K and G = 0: Thus: 0 = G + RT ln K G = -RT ln K Substtutng (for the general case): G = -RT ln K + RT ln Q = RT ln Q/K

15 G = RT ln Q/K Ths allows us to develop a set of crtera to determne n whch drecton a reacton wll proceed under non-standard condtons. Ths s because Q/K wll determne the sgn of G: 1. If Q/K < 1, then G s negatve, and the reacton s spontaneous as wrtten 2. If Q/K = 1, then G = 0 and the system s at equlbrum 3. If Q/K > 1, then G s postve, and the reacton s spontaneous n the opposte drecton as wrtten

16 Sample Calculaton #2 Agan consder the dssoluton of CaCO 3 (calcte): CaCO 3 Ca 2+ + CO 3 2- In the surface ocean, does the reacton proceed spontaneously as wrtten? Use G = -RT ln K From Sample Calculaton #1, we know: G = +12 kcal/mole Thus: kcal mol ( ) cal 1 kcal ( 298 K) lnk 12 = 1000 K mol cal (all unts cancel out) ln K = K = 1.58 x 10-9 ( equlbrum constant )

17 Surface seawater: {CaCO 3 } 1 [Ca 2+ ] = 0.01 mol/l; γ = 0.28; {Ca 2+ } = [CO 3 2- ] = 45 µmol/l; γ = 0.21; {CO 3 2- } = 9.45 x 10-6 Q Q K = { Ca }{ CO } 2+ 2 { CaCO } 2.65x10 = 1.58x = = ( 2.8x10 )( 9.45x10 ) 1 = 2.65x10 8 Therefore: The reacton goes n the opposte drecton as wrtten (Q/K > 1) CaCO 3 precptates n the surface ocean Surface seawater s supersaturated wth respect to calcte Note: No nformaton s gven on the knetcs of the reacton!

18 Temperature and Pressure Effects The amount of heat that s released or taken up by a reacton s called the enthalpy change ( H ). Smlarly to G, we can calculate H usng tabulated data: H r = υh f products υh f reactants where ν s the stochometrc coeffcent (a,b,c,d), and H f s the enthalpy of formaton of speces (kcal/mol or kj/mol) at standard state. The van t Hoff equaton gves the temperature dependence of K: lnk T For a small change n T, H does not change much, so we can ntegrate drectly: K T* Hr 1 1 ln = K298 R 298 T * where T* s the temperature of nterest. P H = RT r 2

19 The change n the partal molar volume ( V ) durng a reacton at standard state s also calculated usng tabulated data: V r = υv f products υv f reactants where ν s the stochometrc coeffcent (a,b,c,d), and V f s the partal molar volume of formaton of speces (cm 3 /mol) at standard state. The pressure dependence of K s also known: ln K P T Vr = RT Agan ntegratng drectly: ln K K 1atm V RT ( P* 1atm) P* r = where P* s the pressure of nterest (n atm).

20 See the followng example n the handout for an example of temperature-correctng the equlbrum constant:

21 Homework Due Tues 1/22/13 Problems 4, 5, 9 and 11 on pages of the handout (Chapter 3 of Snoeynk and Jenkns, 1980). Reference Snoeynk, V.L., and D. Jenkns (1980) Water Chemstry. John Wley & Sons, New York.

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