Chapter 6 Reaction Equilibrium in Ideal Gas Mixtures Physical Chemistry Chapter 6

Chemical Potentials in an Ideal Gas Mixture Chemical Potential of a Pure Ideal Gas (4.36) isothermal, pure ideal gas (6.1) pure ideal gas, P o 1 bar (6.2) (4.86)* one-phase pure substance Physical Chemistry Chapter 6

Chemical Potentials in an Ideal Gas Mixture Fig. 6.1 T is fixed P/P o - o RT -RT -2RT For a pure ideal gas Physical Chemistry Chapter 6

Chemical Potentials in an Ideal Gas Mixture Fig. 6.2 An ideal gas mixture Ideal gas mixture at T and P Pure gas mixture at and T membrane (1) (2) The mixture is separated by thermally conducting rigid membrane permeable to gas i only, and ideal gas mixture (6.3) Physical Chemistry Chapter 6

Chemical Potentials in an Ideal Gas Mixture Fig. 6.2 Ideal gas mixture at T and P Pure gas mixture at and T membrane ideal gas mixture (6.3) ideal gas mixture(6.4)* The fundamental thermodynamic equation No intermolecular interaction, no effect on from other gases in the mixture. Physical Chemistry Chapter 6

Chemical Potentials in an Ideal Gas Mixture Fig. 6.1 (modified) P i /P o i - i o RT -RT -2RT For an ideal gas mixture Physical Chemistry Chapter 6

Ideal Gas Reaction Equilibrium For the ideal-gas reaction (4.36) the equilibrium condition (6.4)* Physical Chemistry Chapter 6

Ideal Gas Reaction Equilibrium (6.5) Physical Chemistry Chapter 6 the equilibrium condition

Ideal Gas Reaction Equilibrium (6.6) (6.7) Physical Chemistry Chapter 6

Ideal Gas Reaction Equilibrium (6.7) (6.8) Physical Chemistry Chapter 6 the equilibrium condition

Ideal Gas Reaction Equilibrium (6.9) (6.10) Physical Chemistry Chapter 6 (6.11)*

Ideal Gas Reaction Equilibrium (6.12) (6.11)* (6.13)* (6.14)* (6.15) Physical Chemistry Chapter 6 (6.10)

Ideal Gas Reaction Equilibrium (6.15) (6.9) Since depends only on T, for a given ideal-gas reaction is a function of T only. At a given temperature, is constant for a given reaction. the standard equilibrium constant the standard pressure equilibrium constant Physical Chemistry Chapter 6

Ideal Gas Reaction Equilibrium (6.19) Since is dimensionless, the standard equilibrium constant is dimensionless. has dimensions of pressure raised to the change in mole numbers for the reaction as written. the equilibrium constant the pressure equilibrium constant (6.13)* Physical Chemistry Chapter 6

Ideal Gas Reaction Equilibrium (6.23) (6.13)* the molar concentration(6.21)* ideal gas mixture(6.22) Physical Chemistry Chapter 6

Ideal Gas Reaction Equilibrium (6.23) n/mol same dimension as P o (6.24)(6.13)* Physical Chemistry Chapter 6

Ideal Gas Reaction Equilibrium (6.24)(6.13)* the standard equilibrium constant the concentration equilibrium constant the standard equilibrium constant the standard pressure equilibrium constant Physical Chemistry Chapter 6

Ideal Gas Reaction Equilibrium (6.23) (6.25) (6.26) (6.27) Physical Chemistry Chapter 6

vant Hoff Equation From (6.14) (6.31) (6.9) (6.32) Physical Chemistry Chapter 6

vant Hoff Equation From (6.31) (6.33) (6.34) (6.32) Physical Chemistry Chapter 6

vant Hoff Equation (6.36)*(6.34) (6.32) Physical Chemistry Chapter 6

Gibbs-Helmholtz Equation Physical Chemistry Chapter 6

Gibbs-Helmholtz Equation When it is applied to changes Physical Chemistry Chapter 6

Differentiation of lnK P o with respect to temperature gives vant Hoff Equation From (6.14) (6.36)* The differentials are complete because K and G depend only on temperature, not on pressure. Using Gibbs-Helmholtz equation Physical Chemistry Chapter 6

vant Hoff Equation (6.36)* (6.37) (6.38) (6.39) Physical Chemistry Chapter 6

vant Hoff Equation (6.36)* (6.40) The vant Hoff equation is an expression for the slope of a graph of the equilibrium constant (specially, lnK) plotted against the temperature. It may be expressed in either of two ways: Physical Chemistry Chapter 6

Ideal Gas Reaction Equilibrium The equilibrium extent of reaction the reaction quotient(6.41) The reaction goes to right The reaction reaches equilibrium The reaction goes to left (6.19) the equilibrium constant The extent of reaction Physical Chemistry Chapter 6

Simultaneous Equilibria A system with several simultaneous reactions that have species in common. (6.47) (6.48) Physical Chemistry Chapter 6

Simultaneous Equilibria At 600 K, CH 3 Cl(g) and H 2 O(g) react to form CH 3 OH, and then form (CH 3 ) 2 O with a simultaneous equilibrium shown: (1) Starting with equal amount of CH 3 Cl and H 2 O, find the equilibrium amounts of all species. (2) Physical Chemistry Chapter 6

Simultaneous Equilibria Suppose that a system initially contains 1 mole of CH 3 Cl(g) and H 2 O(g), x moles of HCl and y moles of (CH 3 ) 2 O are formed at equilibrium. (1) (2) 1-x1-x+yx-2yx y1-x+y Physical Chemistry Chapter 6

Simultaneous Equilibria Suppose that a system initially contains 1 mole of CH 3 Cl(g) and H 2 O(g), x moles of HCl and y moles of (CH 3 ) 2 O are formed at equilibrium. Physical Chemistry Chapter 6

Simultaneous Equilibria The equilibrium amounts of all species are (1) (2) Physical Chemistry Chapter 6