11 Properties of solutions oncentration Molarity (M; 體積莫耳濃度 ) mol/l (mol of solute/volume of solution) Mole fraction ( 莫耳分率 ) mole fraction of = n /n T = X (n :mole of ; n T :mole of total) Molality (m; 重量莫耳濃度 ) mol/kg (mole of solute/weight of solvent) Mass percent or weight percent ( 重量百分濃度 ) mass percent of = (W /W T ) 100% (W :weight of ; W T :total weight) The energies of solution formation Solute 溶質溶質溶質溶質 + 溶質溶質溶質 Solution 溶質溶劑溶質溶劑 溶質溶質溶劑溶劑溶質 Solvent 溶劑 溶劑溶劑溶劑 溶劑溶劑 溶劑 溶劑 溶質 溶劑 sloute-solute solvent-solvent solute-solvent Solvation E involved ( 溶劑合 ) 1
Ex. Nal (s) + 2 O (l) o soln = 3 kj/mol Na (aq) + l (aq) Na (g) + l (g) o = 786 kj/mol lattice E ( 晶格能 ) + 2 O o hydration + 2 O o hydration 783 kj/mol Free energy determines the direction: G o soln = o soln - TSo soln usually positive onclusion solubility is difficult to predict General rule like dissolves like polar compound dissolves in polar compound nonpolar compound dissolves in nonpolar compound 2
Factors affecting solubility Structure effects Pressure effects Little effects on s and l For gas: Governed by enry s law = kp constant oncentration in M Obeyed most accurately under dilute condition solute does not dissociate solute does not react with solvent Partial pressure Temperature effects Difficult to predict Usually decreases for gas (negative, negative S) Ex. O 3 2 (aq) + O 2 (aq) + 2 O(l) 2O 3 (aq) In hard water: a(o 3 ) 2 soluble ao 3 insoluble T [O 2 (aq)] equlibrium O 3 2 (aq) ao 3 (s) 3
The vapor pressures of solutions Raoult s law ( 拉午耳定律 ) For a nonvolatile solute P soln = X solv P o solv Psoln : vapor pressure of the soln model: X solv : P o solv : the mole fraction of solv vapor pressure of the pure solv When solute is also volatile For ideal solution: follows Raoult s law P = X P o P = X P o P o P o X = 1 X = 0 X X = 0 X = 1 4
Nonideal solutions With positive deviation weak solute-solvent interactions P o P o Ex. X = 1 X = 0 ethanol O X X = 0 X = 1 hexane Negative deviation strong solute-solvent interactions P o P o Ex. X = 1 X = 0 3 3 O X O X = 0 X = 1 acetone 5
oiling-point elevation and freezing-point depression oiling-point elevation Ex. queous solution of a nonvolatile solute P vap pure water aqueous solution 1 atm a b T b = T b ' T b T b = K b m solute molal boiling-point elevation constant T b T b ' T Freezing-point depression P ice pure water aqueous solution 1 atm a b T f T b T T m = K f m solute T f ' 6
Distillation of a mixture T bp of pure n gas y p m liquid o l mole fraction x bp of pure bp range with a composition l 下方為液態上方為氣態兩個弧線中間是氣態與液態平衡共存的區域 l 點的液體加熱在 m 點開始沸騰一直到 p 點才完全氣化 m 點的液體與 n 點的氣體平衡共存 n 點的氣體含有較多低沸點的 m 點到 p 點都是氣態與液態平衡的狀態隨著溫度的不同氣態與液態的成分會有所不同 一個純的物質具有單一的沸點 ; 一個混合物具有一個沸點的範圍 Fractional distillation Distilled through a fractionating column gas and liquid in equilibrium vapors out T gas T 1 T 2T3 q T r 4 t s p n liquid o m one theoretical plate T 4 T 3 T 2 T 1 valve gas liquid in equilibrium l mole fraction vapors in temperature:t 1 >T 2 >T 3 >T 4 7
zeotropes ( 共沸物 ) minimum or maximum in the boiling point-composition diagram an not be separated by ordinary distillation process Solid mixtures T a mp of pure S() + L L(+) c b d S() + L f e S(+) X mp of pure 純物質具有單一的熔點混合物具有一個熔點的範圍 沿紅線由上而下到達 c 點時固體 開始產生 溫度繼續下降時更多的 結晶出來留在液體的部分含 的量就增加因此隨著溫度的下降液體的成分沿著 c-d-e 的弧線下降 待溫度降至 f 點時 固體也開始結晶出來, 在 f-e 的水平線下是固體 c-f 之間是固體與液體共存的平衡區 ( 此混合物的熔點範圍 ) e 點的組成具有單一的熔點, 稱為共熔點 (eutectic point) 8
Osmotic pressure pure solvent semipermeable membrane solution Isotonic solutions ( 等滲壓溶液 ): having identical = MRT (M: molarity; T in K) good way to determine MW Ex. 1.00 10-3 g of a protein in 1.00 ml water = 1.12 torr, at 25.0 o ns 1.12 torr 760 torr/atm 3 1.47 10 atm M(0.08206)(25.0 273) The colligative properties ( 依數性 ) P vap T b T b Depend on concentration only: colligative property Electrolyte solution may not dissociate completely forms ion pair van' t off moles of particles in soln factor i moles of solute dissolved Ex. 0.10 m Nal(aq) i = 1.87 (from experiment) T = imk = imrt 9
olloids ( 膠體 ) suspension of tiny particles in a medium (1-1000 nm) Tyndall effect light scattering by these particles + heating + Major stabilizing factor: electrostatic repulsion To destroy: heating add electrolytes (neutralize the charge) discharge through electrodes Examples of colloids Type Fog liq in gas aerosol ( 氣溶膠 ; 霧劑 ) Smoke s in gas aerosol Whipped cream g in liq foam Milk liq in liq emulsion Paint, gel s in liq sol Polystyrene foam g in solid foam heese liq in solid emulsion Ruby glass s in solid sol 10