3.012 Fundamentals of Materials Science Fall 2005 Lecture 12: 10.19.05 Chemical reaction equilibria Today: LAST TIME .........................................................................................................................................................................................2 EQUATING CHEMICAL POTENTIALS DURING REACTIONS.................................................................................................................3 The extent of reaction ..................................................................................................................................................................3 The simplest case: reacting mixtures of gases1..........................................................................................................................4 REACTIONS OF GASES WITH CONDENSED PHASES2 ..........................................................................................................................7 An example: oxidation of a metal ...............................................................................................................................................7 Implications of the final result ......................................................................................................................................................................9 An example calculation .............................................................................................................................................................10 REFERENCES ...................................................................................................................................................................................11 Reading: Engel and Reid 6.7-6.9, 6.11, 6.12, 9.11-9.13 Supplementary Reading: Lecture 12 – Chemical reactions 1 of 11 11/2/053.012 Fundamentals of Materials Science Fall 2005 Last time • Last time we introduced models for the chemical potential of materials: Lecture 12 – Chemical reactions 2 of 11 11/2/053.012 Fundamentals of Materials Science Fall 2005 Equating chemical potentials during reactions • We already know the chemical potential dictates mass flow-driving molecules from one phase into another in closed systems, or driving the addition/subtraction of molecules in open systems. But what about the case where two components can chemically react and be consumed to create a 3rd, completely new component? The chemical potential again controls the outcome. The extent of reaction • When components of a closed system can react, they must still obey the Gibbs condition to reach equilibrium. Consider a generic simple reaction: ! "AA +"BB #"CC• The νi are the stoichiometric coefficients for the reactants and products. Equilibrium for this process (the reaction moving left to right as written) is achieved when the Gibbs free energy is minimized: ! dGrxn=µidnii=1C"= 0equilibrium condition at constant (T,P) for a closed system Lecture 12 – Chemical reactions 3 of 11 11/2/053.012 Fundamentals of Materials Science Fall 2005 • The value of the free energy per mole of reaction determines the direction of a reaction, just as free energy determines the direction of any other process: For example, for a simple generic reaction: ! "AA +"BB #"CC! "G rxn< 0! "G rxn= 0! "G rxn> 0The simplest case: reacting mixtures of gases1 • We can use the equilibrium condition to predict how far chemical reactions will proceed before coming to equilibrium. Let’s go through a simple example: the reaction of hydrogen and oxygen to form water vapor:1 ! H2(g )+12O2(g )" H2O(g )o The moles of each component present are: Moles: H2 O2 H2O Initially: During reaction: Lecture 12 – Chemical reactions 4 of 11 11/2/053.012 Fundamentals of Materials Science Fall 2005 o Plugging this information into the equilibrium condition: o The term on the left is the molar change in free energy for reaction of the components in their standard states if H2 and O2 react completely to become water: o A convention often used is that Pi/Pi,0 is implied if we write Pi-(confusing, but this is the historical convention). Note that our text is quite good about ‘keeping’ the reference pressure in the equations for ideal gas reactions. It’s a good habit for you as well. Thus the term on the right re-arranges to: Lecture 12 – Chemical reactions 5 of 11 11/2/053.012 Fundamentals of Materials Science Fall 2005 • In general for a reacting ideal gas mixture, we have: o Where ν is the stoichiometric coefficient for the reactant/product. ! "G rxnois also referred to as the molar free energy of formation for the products C and D. Lecture 12 – Chemical reactions 6 of 11 11/2/053.012 Fundamentals of Materials Science Fall 2005 Reactions of gases with condensed phases2 An example: oxidation of a metal • Suppose we wish to consider now a reaction between a gas and a solid or liquid. An example of great practical significance is the oxidation of a metal: 3and Bromberg(Figure modified from Dill ) • There are two key simplifying assumptions we will make to determine the equilibrium state of such reactions that are valid for most real materials: • i ill i is i l le i l (i l li i l l l i ). Approximation 1: The f rst we w make s that the oxygen nso ub n the meta .e. no mo ecu es of oxygen d ffuse nto the bu k of the meta att ce• The metal and metal oxide solids must be in equilibrium with their vapor phases: • Expanding these equations with the definitions of the chemical potentials for the gaseous and solid phases: Lecture 12 – Chemical reactions 7 of 11 11/2/053.012 Fundamentals of Materials Science Fall 2005 • li (PM in i l ial i ) ill l l - i i i ligibl is i i lli i ivi lid i ili i i i e i is l i! µMo,g+ RT ln PM=µMo,solid MµMOo,g+ RT ln PMO=µMOo,solid MOApproximation 2: The vapor pressure of most so ds the chem ca potent express on s so sma that the ast term on the eft hand s de of the equat on above s neg e. Th s typ ca y a very good approx mat on. In other words, the act ty of the so n equ br um w th ts vapor phase may btaken as un ty. Th eaves us w th: • Assume the reaction equilibrium is established in the gas phase: • Just as the case for the ideal gas reaction, we start with the Gibbs condition for equilibrium: ! "G rxn=µi#ii=1products$%µj#jj=1reac tan ts$= 0• ! "G rxnois the difference in free energy between 1 mole of gaseous MO
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