Colligative properties of solutions

  Topic; Colligative properties of solutions

Supervised by;

                                   Dr. Khezar Hayat

Prepared by:

                 Dr. Ali Mansoor
                 Dr.Abdullah Yaqoob

Content;

1)                 Defination

2)                 Colligative properties

·      Osmotic-pressure Elevation

·      Vapor-pressure Lowering

·      Boiling-point Elevation

·      Freezing-point Depression

3)                 Ideal behavior & deviations

4)                 Colligative properties of electrolytes

5)                 Practical applications

6)                 References

Colligative Properties of Solution    

 Defination;

                            The colligative properties are those which depend upon the number of solute particles in solution, irrespective of whether these are molecule or ions, large or small.

Ideally, the effect of solute particle of one species is considered to be the same as that of an entirely different kind of particle, at least in dilute solution. Practically, there may be differences that may become substantial as the concentration of the solution is increased.

Types Of Colligative Properties;

1.       Osmotic pressure Elevation

2.       Vapor-pressure Lowering

3.       Boiling-point Elevation

4.       Freezing-point Depression

Of these four, all of which are related, osmotic-pressure has the greatest direct importance in the pharmaceutical sciences. It is the property that largely determines the physiological acceptability of a variety of solutions used for therapeutic purposes.

Ø Osmotic pressure Elevation;

·      OSMOSIS;

The phenomenon of osmosis is based on the fact that substances tend to move or diffuse from regions of higher concentration to regions of lower

 concentration. When a solution is separated from the solvent by means of a membrane that is permeable to the solvent but not to the solute (such a membrane is referred to as a semi-permeable membrane), it is possible to demonstrate visibly the diffusion of solvent into the concentrated solution, as volume changes will occur. In a similar manner if two solutions of different concentrations are separated by a membrane, the solvent will move from the solution of lower solute concentration to the solution of higher solute concentration. This diffusion of solvent through a membrane is called OSMOSIS.

There is a difference between the activity or escaping tendency of the water molecules found in solvent and salt solution separated by the semi-permeable membrane. Because activity, which is related to water concentration, is higher on the pure solvent side, water moves from solvent to solution, which might be visualized as follows.

A semi-permeable membrane is placed over the end of a tube, and a small amount of salt solution placed over the membrane in the tube. The tube is then immersed in a though of pure water so that the upper level of salt solution is initially at the same level as the water in the through. With time the solvent molecules will move from solvent into the tube. The height of solution will rise until the hydrostatic pressure exerted by the column of solution is equal to the osmotic pressure.

·      Osmotic pressure of Nonelectrolytes;

Quantitative studies of solutions containing varying concentrations of solute that does not ionize have demonstrated that osmotic pressure is proportional to concentration of solute; that is, twice concentration of given nonelectrolyte will produce twice the osmotic pressure in a given solvent. (This is not strictly true in solutions of fairly high solute concentration but does hold for dilute solutions)

Furthermore, the osmotic-pressure of solutions of different nonelectrolytes are proportional to the number of molecules in each solution. Stated in another manner, the osmotic pressures of two nonelectrolytes solutions of the same molal concentrations are identical. Thus a solution containing 34.2g of sucrose(mol. Wt 342) in 1000g of water has the same osmotic pressure as that of a solution containing 18.0g of anhydrous dextrose(mol. Wt 180) in 1000g of water. These solutions are said to be isoosmotic with each other because they have identical osmotic pressures.

·         Osmotic pressure of electrolytes;

In discussing the generalizations concerning the osmotic pressure of solutions of nonelectrolytes, it was stated that the osmotic pressure of two solutions of the same molal concentration are identical. This generalization, however , can’t be made for solution of electrolytes-acids, alkalies and salts.

For example NaCl is assumed to ionize as

                                                                           NaCl → Na(+) + Cl(-)

As sodium chloride ionizes to give one mole of each sodium and chloride ions so it is assumed that the solution after ionization will have twice osmotic pressure of the solution containing same molal concentration of nonionizing substances.

As  one mole of potassium sulphate ionizes to give three moles of ions of potassium and sulphate and the solution will have thrice of osmotic pressure  as compared to that of a solution containing nonionizing substances. The reaction is given as follows;

                                                                       K2SO4 →2K(+) + SO4(-2)

Similarly, the osmotic pressure will be four times for the ionized solution of FeCl3 as it produces four ions upon its ionization.         

                                                         FeCl3 → 3Fe(+) + Cl3(-)

Accordingly, the equation PV=nRT , which may be employed to calculate the osmotic pressure of a dilute solution of a nonelectrolyte, also may be applied to dilute solutions of electrolytes if it is changed to PV=inRT, where the value of i approaches the number of ions produced by the ionization of  the stronger electrolytes cited in the preceding examples. For weak electrolytes i represents the total number of particles, ions & molecules together in the solution, divided by the number of molecules that would be present if the solute didn’t ionize. The experimental evidence indicates that, at least in dilute solutions, the osmotic pressures approach the predicted values. It should be emphasized, however, that in more concentrated solutions of electrolytes, the deviation from this simple theory are considerable, due to interionic attraction, salvation, and other factors.

Ø Vapor-Pressure Lowering

When a nonvolatile solute is dissolved in a liquid solvent, the vapor pressure of the solvent is lowered. This easily can be described qualitatively by visualizing solvent molecules on the surface of the solvent, which normally could escape into the vapor, being replaced by solute molecules, which have little, if any, vapor pressure of their own. For ideal solutions of nonelectrolytes, the vapor pressure of solution follows Raoult’s Law .

                         PA =XA P⁰A

Where PA  is the vapor pressure of the solution, P⁰A is the vapor pressure of the pure solvent , and XA is the mole fraction of the solvent . This relationship states that the vapor pressure of the solution is proportional to the number of molecules of solvent in the solution , Rearranging        B

Where  is the mole fraction of the solute. This equation states that the lowering of the vapor pressure in the solution relative to the vapor pressure of pure solvent ( called simply the relative vapor pressure lowering ) is equal to the molar fraction of the solute. The absolute vapor pressure lowering of solution is defined by ;

                                                                                     =

Ø Boiling-point Elevation;

in consequence of the fact that the vapor pressure of any solution of a nonvolatile solute is less than that of the solvent, the boiling point of the solution-the temperature at which the vapor pressure is equal to the applied pressure (commonly 760 mmHg)- must be higher than that of the solvent. This is clearly evident from the figure.

Ø Freezing-Point Depression;

                                                The freezing point of the solvent is defined as the temperature at which the solid and liquid forms of the solvent coexist in equilibrium at a fixed external pressure, commonly 1atm (1 atm =760 mm [torr] of mercury). At this temperature the solid and liquid forms of the solvent must have the same vapor pressure,

For if this were not so, the form having the higher vapor pressure would change into that having the lower vapor pressure.

The freezing point of the solution is the temperature at which the solid form of the pure solvent coexists in equilibrium with the solution at a fixed external pressure, again commonly at 1 atm. Because the vapor pressure of the solution is lower than that of its solvent, it is obvious that solid solvent and solution can’t coexist at the same temperature as solid & liquid solvent; only at some lower temperature, where solid solvent and solution do have the same vapor pressure, is the equilibrium established. A schematic pressure-temperature diagram for water and an aqueous solution, not drawn to scale and exaggerated for the purpose of more effective illustration, shows the equilibrium conditions involved in both freezing-point depression & boiling-point elevation. (see above figure)

The freezing- point lowering of a solution may be quantitatively predicted for ideal solution. Or dilute solutions that obey Raoult’s Law, by mathematical operations similar to (though somewhat more complex than) those used in deriving the boiling point elevation constant. The equation for freezing point lowering ∆Tf is:

                                                        ∆Tf=  Kf m

The value of Kf  for water, which freezes at 273.1⁰K and has a heat of fusion of 79.7 cal/g, is:

                                               

                                                   

The molal freezing point depression constant is not intended to represent the freezing point depression for a 1-molal solution, which is too concentrated for the premise of ideal behavior to be applicable. In dilute solutions the freezing point depression, calculated to a 1-molal basis, approaches the theoretical value—the more dilute the solution, the better the agreement between experiment and theory.

To calculate the molecular weight of the solute, the freezing point of dilute of a nonelectrolyte solute may be used (as was the boiling point ). 

                                                

                                                           

The molecular weight of organic substances soluble in molten camphor may be determined by observing the freezing point of a mixture of the substance with camphor. This procedure, called the Rast Method, uses camphor because it has a very large molal freezing point depression constant, about 40. Because the constant may vary with different lots of camphor and with variations of technique, the method should be standardized using a solute of known molecular weight.

Freezing point determinations of molecular weights have the advantage over boiling point determinations of greater accuracy & precision by virtue of the larger magnitude or the freezing point depression compared to boiling point elevation. Thus, in the case of water the molal freezing point depression is approximately 3.5 times greater than the molal boiling point elevation.

IDEAL BEHAVIOR AND DEVIATIONS;

In setting out to derive mathematical expressions for colligative properties, such phrases as for ideal solutions or for dilute solutions were used to indicate the limitations of the expressions. Sumuel Glasstone defines an ideal solution as ’’one which obeys Raoult’s law through the whole range of concentration and at all temperatures’’ & gives as specific characteristics of such solutions their formation only from constituents that mix in the liquid state without heat change & without volume change. These characteristics reflect the fact that addition of a solute to a solvent produces no change in the forces between molecules of the solvent. Thus, molecules have the same escaping tendency in the solution as in the pure solvent, & the vapor pressure above the solution is proportional to the ratio of the number of solvent molecules in the surface of the solution to the number of the molecules in the surface of the solvent which is the basis for Raoult’s law. Any change in inter molecular forces produced by mixing the components of a solution may result in deviation from ideality; such a deviation may expected particularly in solutions containing both a polar & non-polar substance. Solutions of electrolytes, except at high dilution, are especially prone to depart from ideal behavior, even though allowance is made for the additional particles that result from ionization. When solute and solvent combine to form solvates, the escaping tendency of the solvent may be reduced in consequence of the reduction in the number of free molecules of solvent; thus, a negative deviation from Raoult’s law is introduced. On the other hand, the escaping tendency of the solvent in a solution of non-volatile solute may be increased because the cohesive forces between molecules of solvent are reduced by the solute; this result in a positive deviation from Raoult’s law.

Although few solution exhibit ideal behavior over a wide range of concentration, most solutions behave ideally at least in high dilution, where deviations from Raoult’s law are negligible.

Ø  Colligative properties of electrolyte solution;

Since colligative properties depend on the number of particles dissolved, solutions of electrolytes (which dissociate in solution) should show greater changes than those of nonelectrolytes. However, a 1 M solution of NaCl does not show twice the change in freezing point that a 1 M solution of methanol does.

——————————————————————————————————————————

Ion Pairing and the van’tHoff Factor

One mole of NaCl in water does not really give rise to two moles of ions.

Some Na+ and Cl− reassociate for a short time, so the true concentration of particles is somewhat less than two times the concentration of NaCl.

• Reassociation is more likely at higher concentration.

• Therefore, the number of particles present is

concentration dependent.

[Ion pairing becomes more prevalent as the solution concentration increases]

So the deviation from ideality increases with the increase in concentration of electrolyte in the solution.

The van’t Hoff Factor calculation

This factor, is represented by i, can by calculated by taking the ratio of

Measurements for electrolytes To Measurements for nonelectrolytes

For example;            f  (For electrolyte)          (For nonelectrolyte)

                                           

                                               

For an ideal solution:

 The van’t Hoff factor equals the number of ions per formula unit.

For ideal solutions of NaCl and K2SO4 : i = 2 and i = 3, respectively.

In absence of information about the value of i for a solution, use

the ideal value in calculation.

                     

  Secondly there is another attraction present in the ions for the solvent molecules and it holds the solvent in the solution, it reduces the escaping-tendency , with consequent enhancement of the vapor-pressure lowering. Solvation also may reduce interionic attraction and thereby further lower the vapor-pressure.

These factors combine to effect a progressive reduction in the molal values of colligative properties as the concentration of electrolyte is increased from 0.5 to 1.0 molal, beyond which the molal quantities either increase (sometimes quite abruptly) or remain almost constant.

Ø Practical applications of colligative properties;

a)      One of the most important pharmaceutical applications of colligative properties is in the preparation of isotonic intravenous & isotonic lacrimal solutions.

b)      Applications of the colligative properties are found in experimental physiology.

One such application is in the immersion of tissues in salt solutions, which are isotonic with the fluids of the tissue, in order to prevent changes or injuries that may arise from osmosis.

c)       The colligative properties of solutions may also be used in determining the molecular weight of solutes, or in the case of electrolytes, the extent of ionization.

                                   I.            The method of determining the molecular weight depends on the fact that each of the colligative properties is altered by a constant value when a definite number of molecules of solute is added to a solvent . For example;

1)      In dilute solutions the freezing-point of water is lowered at the rate of 1.855 for each mole of a nonelectrolyte dissolved in 1000g of water.

2)      The boiling-point elevation may be used, similarly, for determining molecular weights. The boiling point of water is raised at the rate of 0.52⁰C for each mole of solute dissolved in 1000g of water; the corresponding values for Benzene, Carbon-tetrachloride & phenol are 2.57⁰C, 4.88⁰C, 3.60⁰C respectively.

                                 II.            To determine the extent to which an electrolyte is ionized, it is necessary to know its molecular weight, as determined by some other method and then to measure one of the four colligative properties.

The deviation of the results from similar values for nonelectrolytes then is used in calculating the extent of ionization.

References;

Ø Rimington the science & practice of pharmacy ( 22^ndedition, chapter #28 solutions and phase equilibria by Prdeep K.Gupta, Phd)

Ø campus.murraystate.edu/...sp.../Lecture_Chapter%2012_part6_wmf.pdf‎

Ø ADVANCED PHARMACEUTICS --Physico-chemical Principles by Cherng-ju Kim( chapter # 3, topics=3.4.1---3.4.2—3.4.3---3.4.4.1)