Physical chemistr Chapter 6 Chapter 6 Reaction Equilibrium in Ideal gas mixtures
Chapter 6 Reaction Equilibrium in Ideal Gas Mixtures Physical Chemistry Chapter 6
Physical Chemistry Chapter 6 Chemical potentials in an ideal gas mixture Chemical Potential of a pure Ideal gas dG=-SdT+vdP (436) dT+y dP G one-phase pure (4.86)2 substance TP H=1m=/ dp P isothermal, pure ideal gas , du=rt ddp u(T, P2)-u(T, P)=rt'hn u=u(T)+RTho p isothermal, pure ideal gas(6.1) pure ideal gas, Po=l bar(6.2)
Chemical Potentials in an Ideal Gas Mixture Chemical Potential of a Pure Ideal Gas dG = −SdT +VdP (4.36) dP P RT d Vm dP = = isothermal, pure ideal gas = 2 1 2 1 1 P P dP P d RT 1 2 2 1 ( , ) ( , ) ln P P T P − T P = RT isothermal, pure ideal gas (6.1) o o P P = (T) + RT ln pure ideal gas, P o1 bar (6.2) dGm = d = −Sm dT +Vm dP m i (4.86)* T P G n G , , i i = one-phase pure substance Physical Chemistry Chapter 6
Physical Chemistry Chapter 6 Chemical potentials in an ideal gas mixture For a pure ideal gas RT G=H-S Hm=f(T) - RTE P/P Sm=f(p) →>-0asP>0 2RTI Fig. 6. 1 T is fixed
Chemical Potentials in an Ideal Gas Mixture Fig. 6.1 T is fixed P/Po - o 0 1 2 3 RT -RT -2RT = Gm = Hm −TSm H f (T) m = S f (P) m = → − as P → 0 For a pure ideal gas Physical Chemistry Chapter 6
Physical Chemistry Chapter 6 Chemical potentials in an ideal gas mixture An ideal gas mixture (1)PV=n,orRT' Ideal gas mixture at 2)The mixture is separated by Tand p thermally conducting rigid membrane permeable to gas i only, and P=x, p P≡x.P membrane Pure gas po=1 bar mixture at and T (T,P2x12x2,…)=14(T,xP)=p1(T,P) Fig 6.2 ideal gas mixture (6.3)
Chemical Potentials in an Ideal Gas Mixture Fig. 6.2 ( , , , , ) ( , ) ( , ) * * i 1 2 i i P i T Pi T P x x = T x = An ideal gas mixture Ideal gas mixture at T and P Pi xi P * Pi Pure gas mixture at and T membrane (1) PV = ntotRT (2) The mixture is separated by thermally conducting rigid membrane permeable to gas i only, and Pi xi P P bar o 1 ideal gas mixture (6.3) Physical Chemistry Chapter 6
Physical Chemistry Chapter 6 Chemical potentials in an ideal gas mixture (T,P2x1,x2,…)=4(T,xP)=1(T,P) ideal gas mixture Ideal gas (6.3) mixture at Tand p No intermolecular interaction, no effect on u from other gases in the mixture P≡x.P membrane Pure gas mixture at A1=°(7)+RTh and T deal gas mixture P≡1br (64) Fig 6.2 The fundamental thermodynamic equation
Chemical Potentials in an Ideal Gas Mixture Fig. 6.2 ( , , , , ) ( , ) ( , ) * * i 1 2 i i P i T Pi T P x x = T x = Ideal gas mixture at T and P Pi xi P * Pi Pure gas mixture at and T membrane ideal gas mixture (6.3) o o i i i P P = (T) + RT ln ideal gas mixture P o 1 bar (6.4)* The fundamental thermodynamic equation No intermolecular interaction, no effect on from other gases in the mixture. i Physical Chemistry Chapter 6