Lecture 12: Chemical reaction equilibria

Transcription

1 3.012 Fundamentals f Materials Science Fall 2005 Lecture 12: Chemical reactin equilibria Tday: LAST TIME...2 EQUATING CHEMICAL POTENTIALS DURING REACTIONS...3 The extent f reactin...3 The simplest case: reacting mixtures f gases REACTIONS OF GASES WITH CONDENSED PHASES An example: xidatin f a metal...7 Implicatins f the final result...9 An example calculatin...10 REFERENCES...11 Reading: Engel and Reid , 6.11, 6.12, Supplementary Reading: Lecture 12 Chemical reactins 1 f 11 11/2/05

2 3.012 Fundamentals f Materials Science Fall 2005 Last time Last time we intrduced mdels fr the chemical ptential f materials: Lecture 12 Chemical reactins 2 f 11 11/2/05

3 3.012 Fundamentals f Materials Science Fall 2005 Equating chemical ptentials during reactins We already knw the chemical ptential dictates mass flw- driving mlecules frm ne phase int anther in clsed systems, r driving the additin/subtractin f mlecules in pen systems. But what abut the case where tw cmpnents can chemically react and be cnsumed t create a 3 rd, cmpletely new cmpnent? The chemical ptential again cntrls the utcme. The extent f reactin When cmpnents f a clsed system can react, they must still bey the Gibbs cnditin t reach equilibrium. Cnsider a generic simple reactin: " A A + " B B #" C C The ν i are the stichimetric cefficients fr the reactants and prducts. Equilibrium fr this prcess (the reactin mving left t right as written) is achieved when the Gibbs free energy is minimized: C dg rxn = " µ i dn i = 0 i=1 equilibrium cnditin at cnstant (T,P) fr a clsed system Lecture 12 Chemical reactins 3 f 11 11/2/05

4 3.012 Fundamentals f Materials Science Fall 2005 The value f the free energy per mle f reactin determines the directin f a reactin, just as free energy determines the directin f any ther prcess: Fr example, fr a simple generic reactin: " A A + " B B #" C C "G rxn < 0 "G rxn = 0 "G rxn > 0 The simplest case: reacting mixtures f gases 1 We can use the equilibrium cnditin t predict hw far chemical reactins will prceed befre cming t equilibrium. Let s g thrugh a simple example: the reactin f hydrgen and xygen t frm water vapr: 1 H 2(g) O 2(g ) " H 2 O (g ) The mles f each cmpnent present are: Mles: H 2 O 2 H 2 O Initially: During reactin: Lecture 12 Chemical reactins 4 f 11 11/2/05

5 3.012 Fundamentals f Materials Science Fall 2005 Plugging this infrmatin int the equilibrium cnditin: The term n the left is the mlar change in free energy fr reactin f the cmpnents in their standard states if H 2 and O 2 react cmpletely t becme water: A cnventin ften used is that P i /P i,0 is implied if we write P i - (cnfusing, but this is the histrical cnventin). Nte that ur text is quite gd abut keeping the reference pressure in the equatins fr ideal gas reactins. It s a gd habit fr yu as well. Thus the term n the right re-arranges t: Lecture 12 Chemical reactins 5 f 11 11/2/05

6 3.012 Fundamentals f Materials Science Fall 2005 In general fr a reacting ideal gas mixture, we have: Where ν is the stichimetric cefficient fr the reactant/prduct. "G rxn mlar free energy f frmatin fr the prducts C and D. is als referred t as the Lecture 12 Chemical reactins 6 f 11 11/2/05

7 3.012 Fundamentals f Materials Science Fall 2005 Reactins f gases with cndensed phases 2 An example: xidatin f a metal Suppse we wish t cnsider nw a reactin between a gas and a slid r liquid. An example f great practical significance is the xidatin f a metal: 3 (Figure mdified frm Dill and Brmberg ) There are tw key simplifying assumptins we will make t determine the equilibrium state f such reactins that are valid fr mst real materials: Apprximatin 1: The first we will make is that the xygen is insluble in the meta l (i.e. n mlecules f xygen diffuse int the bulk f the metal latti ce). The metal and metal xide slids must be in equilibrium with their vapr phases: Expanding these equatins with the definitins f the chemical ptentials fr the gaseus and slid phases: Lecture 12 Chemical reactins 7 f 11 11/2/05

8 3.012 Fundamentals f Materials Science Fall 2005 Apprximatin 2: The vapr pressure f mst sli ds (P M in the chemical ptential expressi n) is s small that the last term n the left-hand side f the equatin abve is negligible. This is typically a very gd apprximatin. In ther wrds, the activity f the slid in equilibrium with its vapr phase may be taken as unity. This leaves us with: µ M,g + RT lnp M = µ M,slid M µ,g,slid MO MO + RT lnp MO = µ MO Assume the reactin equilibrium is established in the gas phase: Just as the case fr the ideal gas reactin, we start with the Gibbs cnditin fr equilibrium: prducts reac tan ts "G rxn = $ µ i # i % $ µ j # j = 0 i=1 j=1 "G rxn is the difference in free energy between 1 mle f gaseus MO at P = 1 atm and the sum f the free energies f 1/2 mle f O 2 (g) at P = 1 atm and 1 mle f gaseus M at P = 1 atm, all at temperature T. (Exactly analgus t the standard state free energy f reactin we derived fr the pure gas reactin). Lecture 12 Chemical reactins 8 f 11 11/2/05

9 3.012 Fundamentals f Materials Science Fall 2005 The expressin abve is the same result we btained fr simple reactins between gases. Hwever, we can utilize the slid-vapr equilibrium expressins t further simplify the result: Implicatins f the final result Our equilibrium expressin states that there is nly ne unique xygen partial pressure at a given temperature that will cause the reactin t be in equilibrium (i.e. reversible frmatin and disslutin f MO). When an xidatin/reductin reactin is carried ut in a pure xygen atmsphere (at P O2 = 1 atm pressure), "G rxn = "G rxn,. A plt f "G rxn vs. temperature, called an Ellingham diagram, can be used t predict the utcme f the reactin. Lecture 12 Chemical reactins 9 f 11 11/2/05

10 3.012 Fundamentals f Materials Science Fall 2005 An example calculatin Calcium carbnate is a majr cmpnent f many bilgical hard materials such as seashells, and is ften studied t learn hw rganisms build materials via bttm up mlecular assembly (a prcess called bimineralizatin). It underges thermal decmpsitin n heating accrding t the reactin: CaCO 3(s) " CaO (s) + CO 2(g ) Given the standard state free energies (free energies f frmatin) fr each cmpnent, calculate the pressure f CO 2 in equilibrium with ne mle f calcium carbnate at 2000 K: "G f,caco3( s ) "G f,co2( g) = µ CaCO3( s ) = µ CO2( g) = #1,084kJ /mle "G f,cao( s ) = #394.4kJ /mle = µ CaO( s ) = #603.3kJ /mle (Mdified frm Example 6.11 in Engel and Reid) Lecture 12 Chemical reactins 10 f 11 11/2/05

11 3.012 Fundamentals f Materials Science Fall 2005 References 1. Carter, W. C. (2002). 2. Gaskell, D. R. Intrductin t Metallurgical Thermdynamics (Hemisphere, New Yrk, 1981). 3. Dill, K. & Brmberg, S. Mlecular Driving Frces (New Yrk, 2003). Lecture 12 Chemical reactins 11 f 11 11/2/05