版权所有：华东理工大学物理化学教研室 11 2) Partial molar Gibbs energies 7.1 Partial molar quantities For a pure substance Tp n G μ G , m ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ == For a substance in a mixture J ', J nTp n G μ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ =
版权所有：华东理工大学物理化学教研室 11 2) Partial molar Gibbs energies 7.1 Partial molar quantities For a pure substance Tp n G μ G , m ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ == For a substance in a mixture J ', J nTp n G μ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ =
版权所有：华东理工大学物理化学教研室 12 2) Partial molar Gibbs energies 7.1 Partial molar quantities The chemical potential of a substance is the slope of the total Gibbs energy of a mixture with respect to the amount of substance of interest. In general, the che m ic al po tentia l varies with composition. J ', J nTp n G μ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = = nG μ + n μBBAA The total Gibbs energy of binary mixture is
版权所有：华东理工大学物理化学教研室 12 2) Partial molar Gibbs energies 7.1 Partial molar quantities The chemical potential of a substance is the slope of the total Gibbs energy of a mixture with respect to the amount of substance of interest. In general, the che m ic al po tentia l varies with composition. J ', J nTp n G μ ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ = = nG μ + n μBBAA The total Gibbs energy of binary mixture is
版权所有：华东理工大学物理化学教研室 13 2) Partial molar Gibbs energies 7.1 Partial molar quantities In an open system of constant composition, the Gibbs energy depends on the ni, p, and T. Thus, G may change when p, T, and the ni. And dG=Vdp-SdT becomes: = − + + + ⋅⋅⋅ TSpVG μ n μ ddddd nBBAA At constant p and T: = + + ⋅ ⋅ ⋅ G μ n μ ddd nBBAA
版权所有：华东理工大学物理化学教研室 13 2) Partial molar Gibbs energies 7.1 Partial molar quantities In an open system of constant composition, the Gibbs energy depends on the ni, p, and T. Thus, G may change when p, T, and the ni. And dG=Vdp-SdT becomes: = − + + + ⋅⋅⋅ TSpVG μ n μ ddddd nBBAA At constant p and T: = + + ⋅ ⋅ ⋅ G μ n μ ddd nBBAA
版权所有：华东理工大学物理化学教研室 14 2) Partial molar Gibbs energies 7.1 Partial molar quantities Non-expansion work can arise from the changing composition of a system. = = + + ⋅ ⋅ ⋅ maxe, Gw μ n μ dddd nBBAA
版权所有：华东理工大学物理化学教研室 14 2) Partial molar Gibbs energies 7.1 Partial molar quantities Non-expansion work can arise from the changing composition of a system. = = + + ⋅ ⋅ ⋅ maxe, Gw μ n μ dddd nBBAA
版权所有：华东理工大学物理化学教研室 15 3) The wider significance of the chemical potential 7.1 Partial molar quantities The generalization equation (that dU = TdS –pdV) to systems in which the composition may change: Since G=U +pV-TS, = − − + + +dddddd GSTTSpVVpU = − − + + + − TSpVSTTSpVVp + μ n + μ nBBAA + ⋅⋅⋅)dddd(dddd −= + + + + ⋅ ⋅ ⋅ STVpU μ n μ ddddd nBBAA
版权所有：华东理工大学物理化学教研室 15 3) The wider significance of the chemical potential 7.1 Partial molar quantities The generalization equation (that dU = TdS –pdV) to systems in which the composition may change: Since G=U +pV-TS, = − − + + +dddddd GSTTSpVVpU = − − + + + − TSpVSTTSpVVp + μ n + μ nBBAA + ⋅⋅⋅)dddd(dddd −= + + + + ⋅ ⋅ ⋅ STVpU μ n μ ddddd nBBAA