Lecture_04 - CHAPTER 4 LECTURE NOTES Chemical Equilibrium...

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CHAPTER 4 LECTURE NOTES Chemical Equilibrium Involving Ideal Gases (Replaces Sections 4.1): Consider a reaction of the type n A A( g ) + n B B( g ) W n C C( g ) + n D D( g ), where A, B, C, and D all behave ideally. During the reaction, the partial pressure of each gas changes. The resulting free energy change for each gas can be expressed as , G A = n A RT ln æ è ç P A ,2 P A ,1 ö ø ÷ , , G B = n B RT ln æ è ç P B ,2 P B ,1 ö ø ÷ , and so on. If we assume that the reaction starts with each gas at the standard pressure, denoted as P °, we may write G A = G A ± + n A RT ln æ è P A P ± ö ø , G B = G B ± + n B RT ln æ è P B P ± ö ø , and so on. It is important to remember that the free energies in the expressions above are NOT molar quantities, i.e., we need to keep in mind that G A = n A G m , A , G ° A = n A G ° m , A , etc.. Now, the free energy change for the reaction may be written as , r G = , r G ± + RT ln é ë ê ( P C / P ± ) n C ( P D / P ± ) n D ( P A / P ± ) n A ( P B / P ± ) n B ù û ú , where r G = ( G C + G D ) ± ( G A + G B ) = ( n C G m , C + n D G m , D ) ± ( n A G m , A + n B G m , B ), and r G ° is similarly defined. 1
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Now, at equilibrium, r G = 0 and so, we get , r G ± = − RT ln é ë ê ( P C / P ± ) n C ( P D / P ± ) n D ( P A / P ± ) n A ( P B / P ± ) n B ù û ú eq . The partial pressures that enter into this expression are the values measured at equilibrium and, therefore, is a constant at a given temperature. Note that, because of the division of each pressure term by the standard pressure, the quantity within the square brackets is dimensionless . In other words, , r G ± = − RT ln K P ± , or K P ± = exp é ë , r G ± / ( RT ) ù û .
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