CH131_14B_15A

CH131_14B_15A - Calculation of Gas Phase Equilibrium From K we can determine quantitatively the extent of reaction i.e concentration of products

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Calculation of Gas Phase Equilibrium From K we can determine quantitatively the extent of reaction, i.e. concentration of products and reactants at equilibrium At T = 250 o C (thermodynamic) K = 2.15 for PCl 5 (g) PCl 3 (g) + Cl 2 (g) If 0.1000 atm of PCl 5 is place in a closed container at 250 o C, a. What are the pressures of all gases at equilibrium? b. What is the extent of reaction? (what % PCl 5 unreacted.) All K problems solved by the same basic technique: 1. Tabulate initial concentrations/pressures 2. Use stoichiometric coefficients to indicate changes due to reaction 3. Use I C E table (initial, change, equilibrium)
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Make a table including all chemical species involved PCl 5 PCl 3 Cl 2 I nitial 0.1000 atm 0 0 C hange –x + x + x E quil. 0.1000 – x x x x = partial pressure (# mols) of PCl 5 that reacts Since P = nRT/V for T, V constant P n K = P PCl 3 P Cl 2 P PCl 5 = x 2 0.1- x = 2.15 PCl 5 (g) PCl 3 (g) + Cl 2 (g) x 2 + 2.15 x - 0.215 = 0 Solve by quadratic formula: ax 2 + bx + c = 0 x = - b b 2 - 4 ac 2 a Here: a = 1, b = 2.15, c = –0.215 Two roots for x: x = 0.0957 atm or x = –2.25 atm. Which correct? x = amt. of PCl 5 that reacts, must be between 0 and 0.100 X At equil., P PCl5 = 0.1000–.0957 = .0043 atm; P PCl3 = 0.0957 atm = P Cl2 % PCl 5 unreacted 0.0043 atm 0.1000 atm 100 = 4.3% Rxn nearly goes to completion
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Q : the reaction quotient and the direction of spontaneous change Remember for the gas phase reaction: aA(g) + bB(g) cC(g) + dD(g) G = D G o + RT ln P C / P ref ( ) c P D / P ref ( ) d P A / P ref ( ) a P B / P ref ( ) b At equilibrium, G = 0 & [ ] = K Away from equilibrium call [ ] = Q reaction quotient, and thus: G = D G o + RT ln Q G o = - RT ln K Substituting for G o , we have: G = - RT ln K + RT ln Q = RT ln Q K This expression will tell us about the direction of spontaneous change for any set of reactant & product concentrations (Remember: G < 0 for spontaneous direction)
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If Q < K , ln(Q/K) < 0 and G < 0; and reaction is spontaneous towards products as written. Numerator of Q must increase relative to denominator to approach K value. Reaction proceeds to right (products) . 2. If Q > K, Q/K > 0, ln(Q/K) > 0 and G > 0; and reaction is spontaneous towards reactants. Numerator of Q must decrease relative to denominator to approach K value. Reaction proceeds to left (reactants) . 3. If Q = K, ln(Q/K) = ln(1) = 0 and G = 0; system is already at equilibrium; no changes in concentrations observed. G
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This note was uploaded on 04/17/2008 for the course CAS CH131 taught by Professor Zigler during the Spring '08 term at BU.

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CH131_14B_15A - Calculation of Gas Phase Equilibrium From K we can determine quantitatively the extent of reaction i.e concentration of products

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