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Chapter 2

Chapter 2. Colligative Properties of Dilute Solution. Solubility. Vapor pressure and Vapor pressure lowering of solution. Boiling-point elevation and freezing-point depression. Osmosis. 2.1 Solubility. Solubility:

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Chapter 2

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  1. Chapter 2 Colligative Properties of Dilute Solution

  2. Solubility Vapor pressure and Vapor pressure lowering of solution Boiling-point elevation and freezing-point depression Osmosis

  3. 2.1 Solubility Solubility: The solubility is defined as the amount that dissolves in a given quantity of water at a given temperature to give a saturated solution. NaCl (s) + H2O Na+(aq) + Cl-(aq)

  4. 2.1.1 Saturated solution State: A solution is in dynamic equilibrium with respect dissolved substance. A dynamic equilibrium is reached in which the rate at which ions leave the crystals equals the rate at which ions return to the crystals.

  5. 2.1.2 Unsaturated solution A solution not in equilibrium with respect to a given dissolved substance and in which more of the substance can dissolve. 2.1.3 Supersaturated solution A solution that contains more dissolved substance than a saturated solution does.

  6. 2.2 Vapor Pressure Lowering of A Solution evaporation H2O (l) H2O (g) condensation l: liquid phase 2.2.1 Vapor-pressure g: gas phase Definition: When a dynamic equilibrium is reached in the liquid and gas phase at a given temperature, the saturated vapor pressure of this system is the vapor-pressure (symbolp ). The unit is Paor kPa

  7. pA0 Surface of water Gas phase Liquid phase

  8. P/kPa 101.3 Ether Ethanol Water Polyglycol 34.6 78.5 100 T/℃ The vapor pressure of Some liquid

  9. Essential • 2. prelated to the quality of solvent. Every kinds of liquid have different vapor-pressure. • 1. p: Its unit isPaor kPa. • 3. p related to the temperature of solvent. When the temperature is elevated, the pvaluewill increase. • 4. If the p value of a substance is larger, we’ll call it volatile. And less, nonvolatile. • 5. The p value of solid substance is very little. But it has the ability of sublimation.

  10. 2.2.2 Vapor-pressure lowering If the solute is nonvolatile, pA is the total vapor pressure of the solution. Because the mole fraction of solvent in a solution is always less than that for the pure solvent; the vapor pressure is lowered.

  11. pA Surface of water Gas phase Nonvolatile of solute Liquid phase

  12. manometer glucose solution Water constant temperature bath Vapor-Pressure Lowering of Solution

  13. Vapor-pressure lowering of a solvent is a colligative property equal to the vapor pressure of the pure solvent minus the vapor pressure of the solution. p = pA0- pA

  14. 2.2.3 Raoult’s law Consider a solution of volatile solvent, A, and nonelectrolyte solute, B, which may be volatile or nonvolatile. According to Raoult’s law, the partial pressure of solvent, pA, over a solution equals the vapor pressure of the pure solvent, PA0, times the mole fraction of solvent,xA, in the solution. So pA = pA0 ·xA p = pA0- pA pA0- pA0 · xA pA0(1- xA) = =

  15. But the sum of the mole fractions of the components of a solution must equal 1 ; that is (xA + xB = 1). So (xB = 1 – xA). Therefore, p = pA0 · xB From this equation,we can see that the vapor-pressure lowering is a colligative property—one that depends on the concentration, but not on the nature, of the solution.

  16. 2.3 Boiling-point Elevation and Freezing-point Depression 2.3.1 Boiling-point Elevation 2.3.1.1 Normal boiling point The normal boiling point of a liquid is the temperature at which its vapor pressure equals 101.3 kPa(1 atm).

  17. 2.3.1.2 Boiling-point Elevation The additionof a nonvolatile solute to a liquid reduces its vapor pressure, the temperature must be increased to a value greater than the normal boiling point to achieve a vapor pressure of 101.3 kPa The boiling-point elevation, ΔTb,is acolligative property of a solution equal to the boiling point of the solution minus the boiling point of the pure solvent.

  18. The boiling-point elevation, ΔTb, is found to be proportional to the molality, bB , of the solution (for dilute solution). ΔTb = Tb – Tb0= Kb•bB Kb : The constant of proportionality, (we called the boiling-point-elevation constant), it depends only on the solvent.

  19. Pure solvent Solid state of pure solvent Solution Phase diagram showing the effect of a nonvolatile solute on freezing point and boiling point

  20. Boiling-point-elevation constants( Kb )and Freezing-point-depression constants ( Kf )

  21. 2.3.1.3 Freezing point of pure solvent Time Cooling curve of pure water and solution

  22. a T/℃ b c Tf0 d Time Ideal cooling curve (1) of pure water

  23. a T/℃ b c Tf0 b` d Time Cooling curve of water (2) on condition of experiment

  24. 2.3.1.4 Freezing point of solution a T/℃ Tf0 b Tf c Time Ideal cooling curve (3) of solution

  25. a T/℃ Tf0 b Tf b` c Time Cooling curve of solution (4) on experiment condition

  26. Thefreezing-pointdepression, ΔTf , isa colligative property of a solution equal to the freezing point of the pure solvent minus the freezing point of the solution. ΔTf = Tf0 - Tf Freezing-point depression, ΔTf , like boiling-point elevation is proportional to the molality, bB(for dilute solution). ΔTf=Kf•bB Here Kf is the freezing-point-depression constant and depends only on the solvent.

  27. For example: A 0.638 g of urea was dissolved in 250 g of water. The value of freezing-point depression,by determined, was 0.079 K. What is the molecular weight of urea? Solution: The freezing-point-depression constant Kf is 1.86 K·kg·mol-1 in the table. mB ∵ ΔTf = Kf · bB = Kf mAMB Kf·mB ∴ MB = mA·ΔTf

  28. 1.86K·kg·mol-1×0.638g M(CON2H4) = 250g×0.079K = 0.060 kg·mol-1 = 60 g·mol-1 So, its molecular weight is 60.

  29. 2.3 Osmosis What is osmosis Why does an osmosis occur What is osmotic pressure Colligative properties of ionic solutions Osmolarity The Significance of Osmotic Pressure in Medicine Reverse Osmosis

  30. 2.3.1 Osmosis and Osmotic Pressure 2.3.1.1 Osmosis Certain membranes allow solvent molecules to pass through them but not solute molecules, particularly not those of large molecular weight. Such a membrane is called semipermeable and might be an animal bladder, a vegetable tissue, or a piece of cellophane. Osmosis is the phenomenon of solvent flow through a semipermeable membrane to equalize the solute concentrations on both sides of the membrane.

  31. Membrane Glucose molecule Water molecule

  32. An experiment in osmosis Water passes through the membrane into the glucose solution in the inverted funnel, the liquid level rises in the stem of the funnel until the downward pressure exerted by the solution above the membrane eventually stops the upward flow of water. Funnel Glucose solution Π Water Membrane

  33. 2.3.1.2 Osmotic pressure Osmotic pressure is defined as the pressure that must be applied to a solution to prevent any net transfer of pure solvent into it through a semipermeable membrane. net transform of solvent osmotic pressureΠ pure solvent solution The osmotic pressure Πof a solution is related to the molarity of solution, c,(van’t Hoff law) : ΠV = nRT or Π = bRT Here R is the gas constant and T is the absolute temperature. There is similarity between this equation for osmotic pressure and the equation for an ideal gas.

  34. For the dilute solution, the molarity is close to molality, cB bB. So, the low of van’t Hoff can write like as following. Π  RTbB Example: A 2.00g of sucrose (C12H22O11) was dissolved in 50.0ml of water. What is the osmotic pressure at 37℃ ?

  35. Solution: The molar mass of sucrose is 342 g·mol-1. n 2.00 g b(C12H22O11) = = 342 g·mol-10.0500L V = 0.117 mol·L-1 Π = bBRT = 0.117 mol·L-1  8.314 J·K-1·mol-1 × 310K = 302 kPa

  36. Example : Calculate the molecular weight of hemachrome at 20℃ of an aqueous solution containing 1.00g heme in 100ml of solution. The osmotic pressure of this solution is 0.366kPa. Solution: According to the van’t Hoff equation: mB ΠV = nRT = RT MB mBRT MB = ΠV

  37. Here MB is the molecular weight of heme(g·mol-1), mB is the mass of heme (g) and V is volume of solution(L). 1.00g×8.314J·K-1·mol-1×293K MB = 0.366kPa×0.100L = 6.66×104g·mol-1 In most osmotic-pressure experiments, much more dilute solutions are employed. Often osmosis is used to determine the molecular weight of macromolecular or polymeric substances. The freezing-point depression is usually too small to measure, though the osmotic pressure may be appreciable.

  38. 2.3.2 The signification of Osmotic Pressure in Medicine 2.3.2.1 The colligative property of Ionic solutions Osmotic pressure is a colligative property of a solution. Other colligative properties of a solution are vapor pressure lowering, boiling point elevation and freezing point depression. To explain the colligative properties of ionic solutions, we must realize that it is the total concentration of ions, rather than the ionic substance, that is important. For instance, NaCl Na+ + Cl- Total of concentration = c(Na+) + c(Cl-)

  39. So, the van’t Hoff equation changes like as: Π= [c(Na+)+c(Cl-)]RT= icBRT  ibBRT Other colligative properties of solution like as van’t Hoff equation: ΔTb = iKbbB ΔTf = iKfbB Π  ibBRT

  40. 2.3.2.2 Osmolarity The osmotic pressure of solutions in living systems (such as plasma, intracellular fluid, etc.), depends on the amount of solute dissolved in plasma or body fluid. In body fluids, there are ions, small molecules, large molecules, and compounds formed by joining ions with large molecules. All these substances have an osmotic effect. They are called osmotically active substances. The osmolarity (cos) is a term to express the total osmotic pressure of plasma or body fluid. The unit of osmolarity is mol·L-1 or mmol·L-1, and refers to the total number of osmotically active substances per unit volume in body fluids.

  41. Osmolarity of osmotically active substances in body ofhealth human

  42. 2.3.2.3 Osmolarity in biological processes The osmotic pressure of the hypertonicsolution is greater than that of the cell; the red blood cell has collapsed. The osmotic pressure of the isotonicsolution is equal to that of the cell; the cell has it normal round shape with depressed center. The osmolarity of a isotonic solution is about 280~320 mmol·L-1. The osmotic pressure of the hypotonicsolution is less than that of the cell; the cell has a bloated shape. This phenomena was called hemolysis in medicine.

  43. 2.3.2.4 Crystalloid and colloid Osmotic pressure The body fluids were formed by electrolytes(NaCl, KCl, NaHCO3, etc.), small molecules( glucose, amino acid, urea, etc. ), macromolecules ( protein, glucide, lipide, etc.) dissolved in water. In medicine, electrolytes and small molecules are called crystalloid substances and macromolecules are called colloid substances. Crystalloid osmotic pressure is produced by crystalloid substances. Colloid osmotic pressure is produced by colloid substances.

  44. Brief Summary of Chapter 2 1. Solubility 2. Vapor pressure lowing 3. Raoult’s law and colligative property 4. Boiling point elevation 5. Freezing point depression 6. Osmotic pressure 7. Osmotic pressure of electrolyte 8. Osmotic pressure in Medicine

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