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MKT04050701 Rev0.Qxd The Physical Chemistry, Theory and Technique of Freezing Point Determinations Table of Contents Chapter 1 — Physical Chemistry Review 1 1.1 Measuring the concentration of solutions 1 1.2 Comparison of concentrative indices 7 1.3 Osmotic concentration and fluid movement 8 Chapter 2 — Freezing Point Theory & Technique 11 2.1 Definitions 11 2.2 Theory 12 2.3 Thermodynamic Factors 16 2.4 Conclusion 17 1 Physical Chemistry Review 1.1 Measuring the concentration of solutions 1. Definition of a solution: A homogeneous single-phase mixture of solute and solvent, where: a. Solvent = the liquid component. b. Solute = the solid component, or liquid in lesser proportion. Suspensions or colloids are not solutions. The solvent must fully dissolve the solute. 2. Two common expressions of concentration: a. Molarity = grams of solute per liter of solution. b. Molality = grams of solute per kilogram of solvent. fluid volume liter mark displaced by solute molar molal Figure 1: A 1 molal solution is generally more dilute than a 1 molar solution. 1 The Physical Chemistry, Theory and Technique of Freezing Point Determinations 3. Methods of molality measurement... definition of osmolality a. Colligative properties: When one mole of non-ionic solute is added to one kilogram of water, the colligative properties are changed in the following manner and proportion: • freezing point goes down 1.86°C • osmotic pressure goes up 17000mmHg (17000mmHg = 22.4 atmospheres) • boiling point goes up 0.52°C • vapor pressure goes down 0.3mmHg (vapor pressure of pure water = 17mmHg) b. Osmolality: • One mole of non-ionic solute dissolved in a kilogram of water will yield Avogadro's number (6.02 × 1023) of molecules. • One mole of ionic solute (e.g., NaCl) dissolved in a kilogram of water will yield almost twice as many particles. The col- ligative properties are changed almost twice as much. • Osmolality = φ × n × molality φ = osmotic coefficient, or percent deviation from "ideal" behavior (complete dissociation, no water binding, etc.). n = number of particles into which the molecule can be broken (1 for sucrose, 2 for NaCl, 3 for K2SO4, etc.). • One osmol of any solute plus one kilogram of water will yield Avogadro's number of particles. • Avogadro's number of particles, regardless of their size or shape, will change the colligative properties the amount described in 3a. (when dissolved in a kilogram of water). 2 Physical Chemistry Review c. Converting other units to milliosmoles (mOsm/kg): mEq/l................................... divide by wc multiply by φ divide by v ppm...................................... divide by wc multiply by φ divide by v divide by atomic weight (aw) mg%..................................... divide by wc multiply by φ divide by mw multiply by n multiply by 10 millimolarity.........................divide by wc multiply by φ multiply by n millimolality......................... multiply by φ multiply by n millidegrees C.......................divide by 1.86 Explanation of symbols: wc = percent water content of solution, or, (wet weight - dried- weight) / wet weight φ = osmotic coefficient v = valence aw = atomic weight mw = molecular weight n = number of particles into which the molecule can be broken. 3 The Physical Chemistry, Theory and Technique of Freezing Point Determinations A few examples of converting some common concentrations into milliosmol values follow. Example 1: What is the osmolality of a 4% solution of formaldehyde? mw = 30.3 formula = CH2O n = 1 Assume φ =1 Assume wc error is negligible Therefore: 30 gms formaldehyde + 1000 gms H2O = 1000 mOsm A 4% solution = 40 gms formaldehyde + 1000 gms H2O Osmolality = (40/30) × 1000 = 1333 mOsm If you know: and you measure: the normal or original freezing point of a The freezing point of the solution solution and that contamination has taken place The weight of Solute A and the freezing The freezing point of A plus B point of Solvent B The specific gravity of a solution The freezing point of the solution The freezing point of a solution at time A The freezing point of solution at time B The type of dissolved molecule, the The freezing point of the solution weight of solute, and the weight of sol- vent The molecular weight of the dissolved The freezing point of the solution solute molecule, the weight of solute, and the weight of solvent 4 Physical Chemistry Review Example 2: What is the osmolality due to urea of a serum with a blood urea nitro- gen (BUN) level of 10 mg%? mw of urea = 60.06 mw of BUN = 28 Formula of urea = H2NCONH2 n = 1 Assume φ = 1 Assume wc error is negligible Therefore: 28 gms BUN + 1000 gms H2O = 1000 mOsm 10 mg% = 100 mg + 1000 gms H2O (100 mg/28 gms) x 1000 = 3.6 mOsm you can determine: the application is: The percentage dilution or change in Concentration of body fluids or quality concentration control of standards and solutions The volume of the container occupied Measuring volumes of containers, tanks, by B kettles, pipets, human body, etc The approximate size and number of Measuring the dialyzability of solute. dissolved molecules The change in number of molecules due Measurement of enzyme activity to diastasis or other factors. If the freez- ing point is measured over a number known time intervals, then the rate of reaction can be measured The molecular weight of the solute Molecular weight determinations The osmotic coefficient of the solute in Determination of water binding, activity, the solvent etc. 5 The Physical Chemistry, Theory and Technique of Freezing Point Determinations Example 3: What is the osmolality of a 0.15% ethanol solution? mw = 46 formula= C2H5OH n = 1 Assume φ = 1 Therefore: 46 gms ethanol + 1000 gms H2O = 1000 mOsm 1% = 10 gms ethanol + 1000 gms H2O = (10/46) x 1000 = 218 mOsm 0.15% = 1.5 gms + 1000 gms H2O = (1.5/46) x 1000 = 32 mOsm d. Comparison of techniques. Any of the colligative properties may be used to indicate osmolality. There are advantages and disadvantages to each one. 1. Vapor pressure. This technique allows the measurement to be made at the temperature desired. It is more complicated, however, not as reproducible in the biological range, and the instrumenta- tion is more expensive. Some vapor pressure osmometers will not detect volatile solutes, which compromises their application in the clinical laboratory. 2. Osmotic pressure. Although this method is the most desirable from several points of view, it is difficult to obtain "ideal" mem- branes, especially for biological solutions. The primary use of "membrane" osmometers is in determining the molecular weights of large molecules. These instruments are very expensive. 3. Boiling point. Ebulliometry has been used extensively for the measurement of molecular weights. It is a relatively simple and inexpensive technique. The major limitation, especially with bio- logical fluids is the destruction of the solute molecules at the boil- ing temperature. 6 Physical Chemistry Review 4. Freezing point. With the available commercial instruments, freez- ing point is the most sensitive of the colligative techniques for the biological range of concentrations. In addition, it is the only tech- nique in which the sample may be recovered. The table on the preceding pages represents the range of application for freezing point osmometers. 1.2 Comparison of concentrative indices 1. General. There are many other methods of measuring the concentra- tion of solids in liquids. Many of these, however, include the effect of non-solutes (undissolved particles) as well as solutes. 2. Six non-specific concentrative indices and their dependence upon certain physical parameters of the solids: Physical parameters of solutes and solids Commonly used non-specific concentrative indices opacity size of particlesshape of particlescharge undissolved particles, number of particles number size, shape Specific Gravity (density) 1 1 1 2 1 Refractive Index 1 1 1 2 Conductivity 1,2 2 2 1 1,2 Viscosity 1 1 1 2 1 Turbidity 1 1 1 1 1 Freezing Point 1 “1” indicates primary dependence. “2” indicates secondary dependence. Freezing point (osmotic concentration) depends only on the number dissolved particles, not on their size or shape. Refractive index, which does depend on the size and shape of the dis- solve molecules, is most closely related to the total dissolved solids. 7 The Physical Chemistry, Theory and Technique of Freezing Point Determinations 3. Freezing point and specific gravity comparison: mOsm solute specific gravity 500 NaCl 1.006 500 Sucrose 1.029 The freezing point combined with specific gravity or refractive index can be used to indicate the approximate size of the dissolved solute (for instance in urine). It can be a very accurate indicator of molecular weight, as well as a means for monitoring changes in molecular weight as in hydrolysis or other chemical and enzymatic reactions. 1.3 Osmotic concentration and fluid movement. 1. Osmotic concentration (osmolality) is the concentration of osmoti- cally active particles. 2. Total osmotic pressure. Osmotic pressure is the tendency for solvent to pass through a membrane from a solution of lower concentration to a solution of higher concentration. Total osmotic pressure is an "ideal" concept. To define it, it is neces- sary to construct a model with an "ideal" semipermeable membrane as well as "ideal" solute and solvent. In this "ideal" system, the sol- vent will pass freely through the membrane, while the solute will not pass. In Figure 2, the total osmotic pressure is the force necessary to prevent water transfer from B to A. Semipermeable membrane A B X X X Figure 2 X X X If A and B differ in concentration by one milliosmol, the osmotic pressure will be 17mmHg. 8 Physical Chemistry Review 3. Effective osmotic pressure or tonicity. Most membranes will allow some solutes to pass through as well as solvent. The effective osmotic pressure, or tonicity, is the force exerted as a result of the solute(s) that does not pass through.
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