Colligative properties, of solutions

VLB forms the basis of distillation, one of the most important chemical engineering processes. It is also important for drying, humidification, and some chemical reactions. 

Experimental measurement of VLB at modest temperatures and pressures is fairly easy. Several thousand binary mixtures have been tested, and the results catalogued. High pressure, high temperature, or mixtures with more than two species make the measurements more expensive and difficult. There are many fewer measurements of this type in the literature than measurements of binary systems at modest temperatures and pressures. 

In most low-pressure VLB the vapor phase is assumed to be a mixture of ideal gases. For higher pressures its nonideal behavior must be taken into account. High-pressure VLB is discussed in Chapter 10. 

If the Uquid forms an ideal solution (or close to it), then Raoult s law (and/or Henry s law) is used to estimate VLB behavior. 

With correlations of liquid-phase activity coefficients (Chapter 9) we can make very accurate estimates of the low-pressure VLB of many systems. These estimates normally require an equation for the sum of the mol fractions in each phase and a statement of equality of the fugacities for each species present The latter may involve subsequent equations for pure species vapor pressures, liquid-phase activity coefficients, and vapor-phase fugacity coefficients. For hand calcula- 

Physical properties of a solution that are affected by the number of solute particles but not by the identity of those particles are called 

The effects of solutes on colligative properties depend upon the actual concentration of solute particles. For nonelectrolytes, the solute particle concentration is the same as the solute concentration. This is because nonelectrolytes, such as sucrose, do not ionize in solution. Electrolytes are substances that ionize or that dissociate into ions. Thus, electrolytes produce particle concentrations higher than those of the original substance. For example, sodium chloride, NaCl, dissociates almost completely into separate sodium ions and chloride ions, so a Im NaCl solution is actually nearly 2m in particles. 

The temperature difference between the freezing point of a solution and the freezing point of its pure solvent is called freezing point depression. The freezing point of a solution is always lower 

What are the boiling point and freezing point of a 0.750m aqueous solution of the electrolyte potassium bromide (KBr)  

Find the effective solute particle concentration. Each formula unit of KBr dissociates into two ions, so the given molality must be doubled. 

I Determine the boiling point elevation and freezing point depression of a solution. 

COOKES Colligative properties depend on the number of solute particles in a solution. 

Real-World Reading Link If you live in an area that experiences cold winters, you have probably noticed people spreading salt to melt icy sidewalks and roads. How does salt help make a winter s drive safer  

Solutes affect some of the physical properties of their solvents. Early researchers were puzzled to discover that the effects of a solute on a solvent depended only on how many solute particles were in the solution, not on the specific solute dissolved. Physical properties of solutions that are affected by the number of particles but not by the identity of dissolved solute particles are called colligative properties. The word colligative means depending on the collection. Colligative properties include vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure. 

Dissolving 1 mol of NaCl in 1 kg of water would not yield aim solution of ions. Rather, there would be 2 mol of solute particles in solution—1 mol each of Na and Cl ions. 

Because chemical methods are rather limited, the most widely used techniques for measuring the molar mass of a polymer are physical. Methods that depend on the colligative properties of dilute solutions can be used to determine the molar mass of a substance. These include  

A colligative property is defined as one that is a function of the number of solute molecules present per unit volume of solution and is unaffected by the chemical nature of the solute. Thus, if Y represents any of the aforementioned colligative properties, then 

any colligative method should yield the number average molar mass M of a polydisperse polymer. Polymer solutions do not behave in an ideal manner, and nonideal behavior can be eliminated by extrapolating the experimental (F/c) data to c = 0. For example, in the case of boiling point elevation measurements (ebullio-scopy) Equation 9.2 takes the form 

Measurements of colligative properties such as boiling point elevation and freezing point depression are limited by the sensitivity of the thermometer used to obtain Ar and, for a precision of 1 X 10 K, the limit of accurate measurements of M is in the region 25,000 to 30,000 g mol.  

In Chapter 4, we classified solutes by their ability to conduct an electric current, which requires moving ions to be present. Recall that an electrolyte is a substance that dissociates into ions in aqueous solution strong electrolytes dissociate completely, and weak electrolytes dissociate very little. Nonelectrolytes do not dissociate into ions at all. To predict the magnitude of a colligative property, we refer to the solute formula to find the number of particles in solution. Each mole of nonelectrolyte yields 1 mol of particles in the solution. For example, 0.35 M glucose contains 0.35 mol of solute particles per liter. In principle, each mole of strong electrolyte dissociates into the number of moles of ions in the formula unit 0.4 M Na2S04 contains 0.8 mol of Na ions and 0.4 mol of S04 ions, or 1.2 mol of particles, per liter (see Sample Problem 4.1). 

Q Sodium chloride is a strong electrolyte and conducts electricity well. Q Sucrose, while soluble in water, does not ionize and therefore does not conduct electricity. Which solute, sodium chloride or sucrose, produces more particles in solution per mole  

The vapor pressure of a pure solvent is greater than the vapor pressure of a solution containing a nonvolatile solute 

You can predict the relative effect of a solute on vapor pressure based on whether the solute is an electrolyte or a nonelectrolyte. For example, one mole each of the solvated nonelectrolytes glucose, sucrose, and ethanol molecules has the same relahve effect on the vapor pressure. However, one mole each of the solvated electrolytes sodium chloride, sodium sulfate, and aluminum chloride has an increasingly greater effect on vapor pressure because of the increasing number of ions each produces in solution. 

For nonelectrolytes, the value of the boiling point elevation, which is symbolized AT], is directly proportional to the solution s molality. 

The molal boiling point elevation constant, S), is the difference in boiling points between aim nonvolatile, nonelectrolyte solution and a pure solvent. It is expressed in units of °C/w and varies for different solvents. Values of A j, for several common solvents are found in Table 15-4. Note that water s A j, value is 0.512°C/w. This means that a m aqueous solution containing a nonvolatile, nonelectrolyte solute boils at 100.512°C, a temperature 0.512°C higher than pure water s boiling point of 100.0°C. 

Solution map moles BaCl2 moles AgCl grams AgCl ( LCUlATl (0.600 172 g AgCl 

How many grams of lead(II) iodide will be precipitated by adding sufficient Pb(N03)2 to react with 750 mL of 0.250 M KI solution  

Freezing Point Depression and Boiiing Point Eievation Constants of Seiected Soivents 

Solvent Freezing point of pure solvent (°C) Freezing point depression constant, Kf /°C kg solvent V mol solute J Boiling point of pure solvent CO Boiling point elevation constant, Kf, /°C kg solvent V mol solute / 

Vapor pressure curves of pure water and water solutions, showing 

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As noted earlier, colligative properties of solutions are directly proportional to the concentration of solute particles. On this basis, it is reasonable to suppose that, at a given concentration, an electrolyte should have a greater effect on these properties than does a nonelectrolyte. When one mole of a nonelectrolyte such as glucose dissolves in water, one mole of solute molecules is obtained. On the other hand, one mole of the electrolyte NaCl yields two moles of ions (1 mol of Na+, 1 mol of Cl-). With CaCl three moles of ions are produced per mole of solute (1 mol of Ca2+, 2 mol of Cl-). 

While Arrhenius was studying conductivity, others were characterizing colligative properties of solutions. The Dutch chemist J. T. van t Hoff studied osmotic pressure and derived the law of osmotic pressure,... 

Osmotic pressure is one of the colligative properties of solutions containing both low-Molecular weight compounds and high polymers. The major difficulty faced in the study of the behaviour of low Molecular weight compounds in solution by the Osmotic pressure measurement method is the selection of a suitable semi-permeable membrane. 

The second period, from 1890 to around 1920, was characterized by the idea of ionic dissociation and the equilibrium between neutral and ionic species. This model was used by Arrhenius to account for the concentration dependence of electrical conductivity and certain other properties of aqueous electrolytes. It was reinforced by the research of Van t Hoff on the colligative properties of solutions. However, the inability of ionic dissociation to explain quantitatively the properties of electrolyte solutions was soon recognized. 

The colligative properties of solutions are those properties that depend upon the number of dissolved molecules or ions, irrespective of their kind. They are the lowering of the vapor pressure, the depression of the freezing point, the elevation of the boiling point, and the osmotic pressure. These properties may be used in determining molecular weights of dissolved substances. 

Depression of Freezing Temperature. One of the colligative properties of solutions of nonvolatile solutes is that the freezing temperature is lower than that of the pure solvent. The depression of the freezing temperature is approximately proportional to the mass ratio of solute to solvent—that is,... 

We have seen in the preceding sections that the chemical potentials are extremely important functions for the determination of equilibrium relations. Indeed, all of the relations pertaining to the colligative properties of solutions are readily obtained from the conditions of equilibrium involving the chemical potentials. In many of the relations developed in the remainder of this chapter the chemical potentials appear as independent variables. It would therefore be extremely convenient if their values could be determined by direct experimental means. Unfortunately, this is not the case and we must consider them as functions of other variables. 

One-component, two-phase systems are discussed in the first part of this chapter. The major part of the chapter deals with two-component systems with emphasis on the colligative properties of solutions and on the determination of the excess chemical potentials of the components in the solution. In the last part of the chapter three-component systems are discussed briefly. 

As solutes are added to a solution, the physical properties of the solution change. Some properties, such as electrical conductivity, depend, at least to some extent, on the identity of the solute. However, some properties do not depend on the identity of the solute, but only on the number of solute particle in the solution. The properties of a solution that depend only on the number of solute particles, and not the identity of the solute particles, are called the colligative properties of solutions. 

Effect of Pressure on Solubility 203 Effect of Temperature on Solubility 204 Colligative Properties of Solutions 205 Vapor Pressure 205 Boiling Point 207 Freezing Point 208 Osmotic Pressure 209 Colloids 212 Review Questions 213... 

Pharmaceutical products can be classified as liquid solutions, disperse systems (e.g., emulsions, suspensions), semisolids (e.g., ointments), and solid dosage forms. Liquid solutions are homogeneous mixtures of one or more substances in pharmaceutical liquids. The understanding of the physicochemical properties of liquid solutions and processes to prepare the liquid solutions is an important step in preparing final liquid solution dosage forms. In this chapter, the solutions of gases in liquids, liquids in liquids, and solids in liquids, as well as colligative properties of solutions and their application to pharmacy, are discussed. Disperse systems will be discussed in Chapter 4. 

D) The van t Hoff factor is in the calculations for colligative properties of solutions. Because the number of solute particles in solution affects these factors, an adjustment must be made for electrolytic solutes. This is due to the fact that electrolytes, when dissolved, yield as many particles as the number of ions in the... 

Colligative properties of solutions measure the sums of all the species in solution. 

As solutes are added to the liquid phase and the mole fraction of water is thereby lowered, water molecules have less tendency to leave the solution. Hence, the water vapor partial pressure in the gas phase at equilibrium becomes less —this is one of the colligative properties of solutions that we mentioned earlier. In fact, adjacent to dilute solutions P at equilibrium depends linearly on the mole fraction of water (Nw) in the liquid phase. This is Raoult s law (also mentioned in Appendix IV). For pure water, Nw equals 1 and Pwv has its maximum value, namely P w> the saturation vapor pressure. 

This chapter first considers the nature of the solution process (Section 15.1) and the quantity of solute that can dissolve in a given quantity of solvent (Section 15.2). Covered next are three temperature-independent measures of concentration— percent by mass (Section 15.3), molality (Section 15.4), and mole fraction (Section 15.5). Finally, colligative properties of solutions are considered in Section 15.6. 

As we have seen, the colligative properties of solutions depend on the total concentration of solute particles. For example, a 0.10 m glucose solution shows a freezing-point depression of 0.186°C ... 

When dealing with chemical reactions, the first questions usually have to do with the identity of the material. What s the reactant What s the product What s that smell WTien it comes to the colligative properties of solutions, however, the question is how much, not what kind, of solute is in the solution. In other words, it may matter to you whether you put sugar or brandy in your tea, but as long as it is the same number of molecules from sugar as from brandy, it would not matter a whit to the colligative properties of the tea. 

The colligative properties of solutions are physical properties, not chemical properties, because the chemical nature of the solute and the solvent remain unchanged. In truth, in solutions where there are significant intermolecular forces between particles, different solutes may... 

As osmosis proceeds, pressure builds up on the side of the membrane where volume has increased. Ultimately, the pressure prevents more water from entering, so osmosis stops. The osmotic pressure of a solution is the pressure needed to prevent osmosis into the solution. It is measured in comparison with pure solvent. The osmotic pressure is directly related to the different heights of the liquid on either side of the membrane when no more change in volume occurs. Osmotic pressure depends on the temperature and the original concentration of solute. Interestingly, it does not depend on what is dissolved. Two solutions of different solutes, for example alcohol and sugar, will each have the same osmotic pressure, provided they have the same concentration. Osmotic pressure is therefore a colligative property of solutions, one which depends only on the concentration of dissolved particles, not on their chemical identity. 

The four colligative properties that are of importance are 1) the vapor pressure lowering 2) the elevation of boiling point 3) the freezing-point depression and 4) the osmotic pressure. An attempt is made below to describe qualitatively and quantitatively each colligative property of solutions, with an emphasis on their interrelationship and their application later in measurement and adjustment of the tonicity of solutions, with particular reference to parenteral formulations. Although theoretical derivations based on thermodynamics can be used to show how each of the colligative properties of solution arises and relate to each other, textbooks on physical chemistry for theoretical derivations are recommended. 

The additional water molecules on the solution side of the membrane create pressure and push some water molecules back across the membrane. The amount of additional pressure caused by the water molecules that moved into the solution is called the osmotic pressure. Osmotic pressure depends upon the number of solute particles in a given volume of solution. Therefore, osmotic pressure is another colligative property of solutions. 

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