Physical Chemistry Multicomponent Phase e Colligative Properties Freezing-point depression A △T (12.13) AT==k mB (12.15) A ideally dil soIn, pure A freezes out A() M,R(TS (12.16) a(sIn) T molar freezing -point-depression constant Freezing-point depression Fig. 12.2
6 Colligative Properties Freezing-point depression * Tf Tf −Tf (12.13) ideally dil. soln., pure A freezes out molar freezing-point-depression constant A T Fig. 12.2 Tf * Tf A(s) A(l) A(sln) Freezing-point depression f f mB T = −k (12.15)* fus m A A f f H M R T k , * 2 ( ) (12.16) Physical Chemistry Multicomponent Phase
Physical Chemistry Multicomponent Phase Colligative Properties Boiling-point elevation △T≡T-T △T=k,m (12.18) A ideally dil soln, nonvol. solute A(s) MRT (12.19) A(v) apm, A T molar boiling-point-elevation constant Boiling-point elevation
7 Colligative Properties Boiling-point elevation * Tb Tb −Tb ideally dil. soln., nonvol. solute molar boiling-point-elevation constant b b mB T = k (12.18)* vap m A A b b H M R T k , * 2 ( ) (12.19) A T Tb * Tb A(l) A(s) A(v) Boiling-point elevation Physical Chemistry Multicomponent Phase
Physical Chemistry Multicomponent Phase Colligative Properties The vapor pressure of a pure When solute is present, the liquid represents a balance disorder of the condensed phase between the increased disorder is relatively higher than that of arising from vaporization and the pure liquid, and there is a the decreased disorderof the decreased tendency to acquire the disorder characteristic o the vapor
8 Colligative Properties * PA PA The vapor pressure of a pure liquid represents a balance between the increased disorder arising from vaporization and the decreased disorder of the surroundings. When solute is present, the disorder of the condensed phase is relatively higher than that of the pure liquid, and there is a decreased tendency to acquire the disorder characteristic of the vapor. Physical Chemistry Multicomponent Phase
Physical Chemistr Multicomponent Phase s Colligative Properties HA(V)=HA(0+RT In x, Equilib. at T for vapor and liquid phases of the solvent rearranges to △G vap B (x4+xB=1) RT RT △G=△H-TAS vap vap B RT R(Assuming T independe lent When xr =0. the boiling point is t and △.H△.S RT R
9 Colligative Properties A (v) (l) RT ln x * A * A = + RT G RT v l x vap B = − − = ( ) ( ) ln(1 ) * A * A ( + =1) A B x x vapG = vapH −TvapS R S RT H x vap vap B − ln(1− ) = R S RT vapH vap − = * ln 1 Equilib. at T for vapor and liquid phases of the solvent rearranges to (Assuming T independent) When xB=0, the boiling point is and * T Physical Chemistry Multicomponent Phase