Multicomponent Phase Chapter 12 Multicomponent phase Equilibrium
1 Chapter 12 Multicomponent Phase Equilibrium Physical Chemistry Multicomponent Phase
Physical Chemistry A Student's Question Question and Answering P我昨天晚上看了第9章的38题,想到了 个问题,在2种组分的理想混合溶液中, 种组分所占整个体系的摩尔分数与它的 2蒸汽所占整个体系气体的摩尔分数和它的 液态部分所占整个体系液态部分的摩尔分 数之间有什么关系?也就是与和者 有什么关系?是不是x=2但好细想 又不对
2 Question and Answering Physical Chemistry A Student’s Question 我昨天晚上看了第9章的38题，想到了一 个问题，在2种组分的理想混合溶液中， 一种组分所占整个体系的摩尔分数与它的 蒸汽所占整个体系气体的摩尔分数和它的 液态部分所占整个体系液态部分的摩尔分 数之间有什么关系？也就是 与 和 三者 有什么关系？是不是 ？但仔细想 又不对！ v i l i x = x + x i i x v i x l i x Question:
Physical Chemistry A Student's Question Question and Answering 5m2 Raoult's law: P=PA+PB=PAxA+PBxB Dalton,'s Law: PA=PxA Case(3) PD= P B B x;=x+x Case(1) Case(2) P B A B x B
3 Question and Answering Physical Chemistry A Student’s Question Raoult’s Law: v i l i x = x + x i l B o B l A o A A P = P + P = P x + P x B v PB = PxB v PA = PxA Answers. Dalton’s Law: A B B → x o PB o PA Case (1) Case (2) Case (3)
Physical Chemistr Multicomponent Phase Colligative Properties Colligative propertiesstem from the reduction of the chemical potential of the liquid solvent as a result of the presence of solute (1) The solute is not volatile (2)The solute does not dissolve in the solid solvent Vapor-pressure lowering Colligative Freezing-point depression Properties Boiling-point elevation Osmotic pressure
4 Colligative Properties Colligative propertiesstem from the reduction of the chemical potential of the liquid solvent as a result of the presence of solute. Colligative Properties Vapor-pressure lowering Freezing-point depression Boiling-point elevation Osmotic pressure (1) The solute is not volatile (2) The solute does not dissolve in the solid solvent Physical Chemistry Multicomponent Phase
Physical Chemistr Multicomponent Phase Colligative Properties Vapor-pressure lowering AP/torr 0 y nonvolatile solute (12.1) △P=P nonvolatile solute (12.2) (No contribution to the vapor) e If the solution is very dilute, LAI 0 x(sucrose)0.1 Fig.12.1 △P=P-P ideally dilute solution, nonvolatile solute (12.3)5
5 Colligative Properties Vapor-pressure lowering * A A PA P P xA = = * A A * A P = P − P = ( A x −1)P PA /torr x (sucrose) 0 -4 0 0.1 Fig. 12.1 nonvolatile solute (12.1) nonvolatile solute (12.2) (No contribution to the vapor) If the solution is very dilute, A 1 * A A * A P = P − P = (x −1)P ideally dilute solution, nonvolatile solute (12.3) Physical Chemistry Multicomponent Phase
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
Physical Chemistry Multicomponent Phase s Colligative Properties h△,H△ 0 RT R △H△S vap RT R △H B RT T Suppose that the amount of solute present is so small that xB<<1 then In(1-xB)a-xB △nH(11 B R T 10
10 Colligative Properties ln 1 0 * = − = R S RT vapH vap R S RT vapH vap = * − − = * 1 1 ln(1 ) R T T H x vap B Suppose that the amount of solute present is so small that xB 1 B B then ln(1− x ) −x − = R T T H x vap B 1 1 * Physical Chemistry Multicomponent Phase