Properties, colligative

Colligative properties are properties of solutions that depend on the nature of the solvent and the concentrations of the solute particles, but not on the nature of those particles. There are four such properties, and they utilize three different concentration units (Chapter 6) be sure to use the correct unit with each one. With concentrations and colligative property data, it is possible to calculate the number of moles of substance present, and once the number of moles is established, all the calculations using moles (Chapter 4) are possible. 

The presence of a solute causes vapor-pressure lowering of a solvent. If the solute is nonvolatile (nonevaporating), the solution has a lower vapor pressure than the pure solvent does. (Review vapor pressure in Chapter 7.) From a molecular view, the solute particles at the surface of the liquid inhibit the movement of solvent molecules from going into the vapor phase, but do not inhibit solvent molecules in the vapor phase from returning to the liquid phase, so the rate of evaporation is lower than the rate of condensation until there are fewer solvent molecules in the vapor phase. For solving problems, the vapor pressure of any component (call it A) in the solution. Pa, is related to the vapor pressure of the pure substance, P, by Raoult s law  

EXAMPLE I (a) Calculate the vapor pressure of benzene in a solution of naphthalene (a nonvolatile solute) in benzene at 21.3°C in which the mole fraction of benzene is 0.900. The vapor pressure of pure benzene at that temperature is 10.7 kPa. (b) Calculate the vapor-pressure lowering, (c) What is the vapor pressure of the solution  

We can also use another form of Raoult s law for a solution of two components  

Colligative properties are properties that depend on the concentration of a solute but not on its identity. The name comes from a Latin word meaning tied together and is used because of the common dependence that these properties have on solute concentfation. The four principal colligative properties are freezing point depression, boiling point elevation, vapor pressure lowering, and osmotic pressure. 

Consider a solid solute that is soluble in a liquid solvent but insoluble in the solid solvent. Assume that the pure solid solvent (component number 1) is at equilibrium with a liquid solution containing the dilute solute. From the fundamental fact of phase equilibrium. 

We assume that the solution is sufficiently dilute that the solvent obeys the ideal solution equation  

Our strategy is to differentiate Eq. (6.7-2), then to apply thermodynamic relations to it and then to integrate. We divide by T and then differentiate with respect to T at constant P  

The equilibrium temperature will be lower than the freezing temperature of the pure solvent. We multiply Eq. (6.7-5) by dT and integrate both sides of Eq. (6.7-5) from the normal melting temperature of the pure solvent T, i to some lower temperature T.  

Some physical properties of solutions differ in important ways from those of the pure solvent. For example, pure water freezes at 0 °C, but aqueous solutions freeze at lower temperatures. We utilize this behavior when we add ethylene glycol antifreeze to a car s radiator to lower the freezing point of the solution. The added solute also raises the boiling point of the solution above that of pure water, making it possible to operate the engine at a higher temperature. 

The word colligative means bound togetheT (Latin colligare, to bind together) and serves as a class name for several properties of solutions, namely  

The essential feature of these four properties is that they depend only on the number of solute molecules present- -not on the chemical and physical characteristics. Consequently, there is an exact relationship between each of the colligative properties and any other one if one property is measured, the others can be calculated. From the measurement of a colligative property we can calculate the number of moles of solute present if we also know the mass of the substance. 

It is assumed that the reader has already been introduced to colligative properties here we will simply state the basic relationships, which will be derived in Chapter 5 from thermodynamics. 

Raoult s law is concerned with the partial vapor pressure p exerted by a solvent of mole fraction x. The equation is 

The depression of the freezing point is given by a similar equation  

Some properties in chemistry depend solely on the number of particles, irrespective of the type of particle. Such properties are called colligative. There are four colligative properties of solutions vapor pressure, boiling point, freezing point, and osmotic pressure. 

In Chemistry Lecture 4, we saw that the addition of a nonvolatile solute will lower tire vapor pressure of the solution in direct proportion to the number of particles added, as per Raoult s law. The vapor pressure has an important relationship to the normal boiling point. When the vapor pressure of a solution reaches the local atmospheric pressure, boiling occurs. Thus, the boiling point of a substance is also dranged by the addition of a solute. The addition of a nonvolatile solute lowers the the vapor pressure and elevates the boiling point. The equation for the boiling point elevation of an ideally dilute solution due to the addition of a nonvolatile solute is  

You cannot apply the boiling point elevation equation to volatile solutes. As shown in Chemistry Lecture 4, a volatile solute can actually decrease the boiling point by increasing the vapor pressure. If you know the heat of solution, you can make qualitative predictions about the boiling point change when a volatile solute is added. For instance, since you know that an endothermic heat of solution indicates weaker bonds, which lead to higher vapor pressure, you can predict that the boiling point will go down. 

Melting point also changes when a solute is added, but it is not related to the vapor pressure. Instead, it is a factor of crystallization. Impurities (the solute) interrupt the crystal lattice and lower the freezing point. Freezing point depression for an ideally dilute solution is given by the equation  

the constant /q is specific for the substance being frozen. 

Some properties of a solution depend on the concentration of the solution but not on the particular identity of the solute. These are called colligative properties. Three colligative properties are discussed below vapor-pressure lowering, boiling-point elevation, and freezing-point depression. 

The effect of the concentration of a solution on the vapor pressure of the solvent is given approximately by Raoult s law, which states the vapor pressure (p ) of a solvent (A) above a solution is equal to the product of the vapor pressure of the pure solvent p% and the mole fraction of the solvent in the solution (iAa) That is. 

A solution that obeys Raoult s law exactly is called an ideal solution. Solutions that are associated with either exothermic or endothermic reactions are not ideal solutions. Raoult s law is most accurate when used to describe components of a solution that are present in high concentrations. At low concentrations there are often significant departures from Raoult s law. At very low concentrations the vapor pressure of a solute is given by Henry s law. 

A liquid boils when its saturated vapor pressure is the same as the atmospheric pressure. Since a nonvolatile solute will lower the vapor pressure of a solution, a higher temperature will be required to cause the solution to boil. The increase in the boiling point of a solution (ATb) above that of the pure solvent is approximately proportional to the molality (m) 

The freezing point of a substance is the temperature at which the saturated vapor pressures of the solid and liquid phases are the same. Since solutes are not normally soluble in the solid phase of the solvent, the vapor pressure of the solid is unaffected by the solute. On the other hand, if the solute is nonvolatile, the vapor pressure of the solution is reduced. Consequently, the temperature at which the solution and solid phase will have the same saturated vapor pressure (i.e., the freezing point) is reduced. The reduction in the freezing point of a solution (ATf) is given approximately by 

All the different methods to measure molecular properties yield average values for polydisperse samples. Colligative properties, being a property dependent on the number of solute molecules, result in the number average of M  

Some of the properties of solutions are dependent upon the chemical and physical nature of the individual solute. However, there are solution properties that depend only on the number of solute particles and not their identity. These properties are colligative properties and they include  

If a liquid is placed into a sealed container, molecules will evaporate from the surface of the liquid and will eventually establish a gas phase over the liquid that is in equilibrium with the liquid phase. This is the vapor pressure of the liquid. This vapor pressure is temperature dependent, the higher the temperature the higher the vapor pressure. If a solution is prepared, then the solvent contribution to the vapor pressure of the solution depends upon the vapor pressure of the pure solvent, P°soivenb and the mole fraction of the solvent. We can find the contribution of solvent to the vapor pressure of the solution by the following relationship  

There may be more than one solute present. If there is more than one solute, we find the contribution of each solute in the same way. If the solute is nonvolatile, P°solute = 0. 

The vapor pressure of a solution is the sum of the contributions of all solutes and the solvent. 

Not all solutions obey Raoult s law. Any solution that follows Raoult s law is an ideal solution. However, many solutions are not ideal solutions. A solution may have a vapor pressure higher than predicted by Raoult s law. A solution may have a vapor pressure lower than predicted by Raoult s law. Solutions with a 

There are some properties of solutions which are common to all solutions with non-volatile solutes, and which vary only with the concentration of particles added to the solution and do not depend on the identity of the particles. These properties are called colligative properties. The most important of these properties are  

These properties can only be accurately predicted for dilute solutions. 

In a pure liquid, there is a tendency for some of the molecules of solvent to escape from the liquid and pass into the vapour phase. That is, the molecules form an atmosphere of gas above the liquid. Eventually equilibrium will be reached, with molecules evaporating from the surface at a rate equal to the rate at which they are condensing back into the liquid. This equilibrium pressure of the vapour above the liquid (partial pressure, see Section 4.5.7) is called the vapour pressure. Each solvent will have its own vapour pressure, which will increase with temperature. If the liquid is a mixture, both components contribute to the vapour pressure depending on their relative concentrations, and the total vapour pressure will be the sum of the two. 

The total vapour pressure above the mass of water will he WX 100%. 

the total vapour pressure will only be due to the liquid. 

In this section, we examine some effects on the properties of a pure liquid when a small amount of solute is added. When the mixture forms an ideal solution, the change in these properties depends only on the amount of solute present, not on the chemical nature of the solute. Such properties, termed colligative properties, include boiling-point elevation, freezing-point depression, and osmotic pressure. 

Boiling Point Elevation and Freezing Point Depression 

We first qualitatively examine these phenomena in terms of ideal solution behavior then we will apply the principles of phase equilibrium to quantify these phenomena for both nonideal and ideal solutions. To understand why the boiling point elevates, we can apply the principles of phase equilibrium that we have just developed. We compare 

In system I, the system pressure is, by definition, the saturation pressure, that is. 

we examine the equilibrium criteria for species a in system II. If we are at low pressure and the solute is dilute enough, Raoult s law applies  

Equation (13.8) relates the chemical potential of the solute to the mole fraction of the solute in the solute. This expression is analogous to Eq. (13.5), and the symbols have corresponding significances. Since the p for the solute has the same form as the p for the solvent, the solute behaves ideally. This implies that in the vapor over the solution the partial pressure of the solute is given by Raoult s law  

If the solute is involatile, pi is immeasurably small and Eq. (13.9) cannot be proved experimentally thus it has academic interest only. 

The p versus T diagram displays the freezing-point depression and the boiling-point elevation clearly. In Fig. 13.4(a) the solid lines refer to the pure solvent. Since the solute is 

From the equilibrium conditions, we get for a system that is embedded in a thermostat (dr = 0) and connected to a manostat (dp = 0) the free enthalpy being constant dG(7 , p.) = 0 for the process under consideration. Here we are dealing with a process running at constant temperature and at constant pressure. 

Question 6.5. How can we come to the ebullioscopic equation, in which we have a variation of the temperature itself The same open question holds for the other common equations, like osmosis, etc. 

If a solute is nonvolatile (that is, it does not have a measurable vapor pressure), the vapor pressme of its solution is always less than that of the ptrre solvent. Thus, the relationship between solution vapor pressttre and solvent vapor presstrre depends on the concentration of the solute in the solution. This relatiortship is given by RaouU s 

To review the concept of equilibrium vapor pressure as it applies to pure liquids, see Section 12.6. 

In a solution containing only one solute, Xi = 1 - X2, in which X2 is the mole fraction of the solute (see Section 5.5). Equation (13.6) can therefore be rewritten as 

We see that the decrease in vapor pressure, AP, is directly proportional to the concentration (measured in mole fraction) of the solute present. 

Calculate the vapor pressure of a solution made by dissolving 218 g of glucose (molar mass = 180.2 g/mol) in 460 mL of water at SOT. What is the vapor-pressure lowering The vapor pressure of pure water at 30°C is given in Table 5.2. Assume the density of the solution is 1.00 g/mL. 

When the component is the minor component, it obeys Henry s law when it is the major component, it obeys Raoult s law. p and P2 are the vapor pressures of the pure substances p and P2 are the partial pressures of the two components in the mixture and p is the total vapor pressure. The deviation from the partial pressure predicted by Henry s law or Raoult s law can be used to obtain the activity coefficients 

The deviation from Raoult s law or Henry s law is a measure of y. For nonideal solutions, as an alternative to the activity coefficient, an osmotic coeflBcient is defined through 

As we will see in the following section, the significance of the osmotic coefficient lies in the fact that it is the ratio of the osmotic pressure to the osmotic pressure of an ideal solution. From (8.1.13) and (8.1.14) it is easy to see that 

Using the chemical potential of ideal solutions, we can derive several properties of ideal solutions that depend on the total number of solute particles and not on 

Equation (8.1.11) could be used to obtain an expression for the increase in the boiling point and the decrease in the freezing point of solutions (Fig. 8.4). As we noted in Chapter 7, a liquid boils when its vapor pressure p = pext. the atmospheric or applied external pressure. Let T be the boiling temperature of the pure solvent and T the boiling temperature of the solution. We assume the mole fraction of the solvent is X2 and the rnole fraction of the solute is xy. We assume the solute is nonvolatile, so the gas phase of the solution is pure solvent. At equilibrium, the chemical potentials of the liquid and gas phases of the solvent must be equal  

Strategy Use Equation 13.3 and the given Henry s law constant to solve for the molar concentration (moLU) of CO2 at 25°C and the two CO2 pressures given. 

Think About It With a pressure approximately 15,000 times smaller in part (b) than in part (a), we expect the concentration of CO2 to be approximately 15,000 times smaller—and it is. 

FIGURE 7.26 In zone refining of silicon, a heating coil melts a small part of the boule at a time. As the liquid slowly solidifies, impurities remain concentrated in the liquid phase. As the molten zone passes along the boule, eventually the impurities are collected at one end, which can then be removed from the pure material. 

We have already addressed vapor pressure depression, in the form of Raoult s law. The vapor pressure of a pure liquid is lowered when a solute is added, and the vapor pressure is proportional to the mole fraction of the solvent  

FIGURE 7.27 Rate of evaporation from solution. When a solution forms, the presence of the solute particles reduces the rate of evaporation of the solvent, thm decreasing the equilibrium vapor pressure. 

Unless otherwise noted, all art on this page is Cengage Learning 2014. 

Before considering the next colligative properties, we recall the concentration unit molality. The molality of a solution is similar to molarity except that it is defined in terms of the number of kilograms of solvent, not liters of solution  

If the mixture of A and B is sufficiently dilute, it will behave as an ideal solution, for which the following holds [8]  

If at the same pressure P, pure A boils at temperature Tj, then it is obvious that 

Integrating Eq. (8.3.6) from temperature I), to temperature T at constant pressure and noting that T and, therefore, PI), P,  

Applying Eq. (8.3.7) to pure A in the vapor phase and then to pure A in the liquid phase and introducing the results in Eq. (8.3.5) gives 

Because Injc equals ln(l — Xg), which for small Xg is the same as —Xg, we see the following  

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Completely ah initio predictions can be more accurate than any experimental result currently available. This is only true of properties that depend on the behavior of isolated molecules. Colligative properties, which are due to the interaction between molecules, can be computed more reliably with methods based on thermodynamics, statistical mechanics, structure-activity relationships, or completely empirical group additivity methods. 

Osmotic pressure is one of four closely related properties of solutions that are collectively known as colligative properties. In all four, a difference in the behavior of the solution and the pure solvent is related to the thermodynamic activity of the solvent in the solution. In ideal solutions the activity equals the mole fraction, and the mole fractions of the solvent (subscript 1) and the solute (subscript 2) add up to unity in two-component systems. Therefore the colligative properties can easily be related to the mole fraction of the solute in an ideal solution. The following review of the other three colligative properties indicates the similarity which underlies the analysis of all the colligative properties ... 

One way to describe this situation is to say that the colligative properties provide a method for counting the number of solute molecules in a solution. In these ideal solutions this is done without regard to the chemical identity of the species. Therefore if the solute consists of several different components which we index i, then nj = S nj j is the number of moles counted. Of course, the total mass of solute in this case is given by mj = Sjnj jMj j, so the molecular weight obtained for such a mixture is given by... 

As noted above, all of the colligative properties are very similar in their thermodynamics if not their experimental behavior. This similarity also extends to an application like molecular weight determination and the kind of average obtained for nonhomogeneous samples. All of these statements are also true of osmotic pressure. In the remainder of this section we describe osmotic pressure experiments in general and examine the thermodynamic origin of this behavior. 

Before doing this, however, it is informative to compare the sensitivity of the four colligative properties in the determination of molecular weight. In the following example this is done by making the appropriate numerical calculations. 

As Morawetz puts the matter, an acceptance of the validity of the laws governing colligative properties (i.e., properties such as osmotic pressure) for polymer solutions had no bearing on the question whether the osmotically active particle is a molecule or a molecular aggregate . The colloid chemists, as we have seen, in regard to polymer solutions came to favour the second alternative, and hence created the standoff with the proponents of macromolecular status outlined above. 

M depends not on the molecular sizes of the particles but on the number of particles. Measuring colligative properties such as boiling point elevation, freezing point depression, and vapor pressure lowering can determine the number of particles in a sample. 

The relationships among colligative properties and solute concentration are best regarded as limiting laws. They are approached more closely as the solution becomes more dilute. In practice, the relationships discussed in this section are valid, for nonelectrolytes, to within a few percent at concentrations as high as 1 Af. At higher concentrations, solute-solute interactions lead to larger deviations. 

Vapor pressure lowering is a true colligative property that is, it is independent of the nature of the solute but directly proportional to its concentration. For example, the vapor pressure of water above a 0.10 M solution of either glucose or sucrose at 0°C is the same, about 0.008 mm Hg less than that of pure water. In 0.30 M solution, the vapor pressure lowering is almost exactly three times as great, 0.025 mm Hg. 

Boiling point elevation and freezing point lowering, like vapor pressure lowerings are colligative properties. They are directly proportional to solute concentration, generally expressed as molality, m. The relevant equations are... 

Osmotic pressure, like vapor pressure lowering, is a colligative property. For any nonelectrolyte, ir is directly proportional to molarity, M. The equation relating these two quantities is very similar to the ideal gas law ... 

Determination of Molar Masses from Colligative Properties... 

Colligative properties, particularly freezing point depression, can be used to determine molar masses of a wide variety of nonelectrolytes. The approach used is illustrated in Example 10.9. 

A laboratory experiment on colligative properties directs students to determine the molar mass of an unknown solid. Each student receives 1.00 g of solute, 225 mL of solvent and information that may be pertinent to the unknown. 

Molar masses can also be determined using other colligative properties. Osmotic pressure measurements are often used, particularly for solutes of high molar mass, where the concentration is likely to be quite low. The advantage of using osmotic pressure is that the effect is relatively large. Consider, for example, a 0.0010 M aqueous solution, for which... 

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-). 

This behavior is generally typical of electrolytes. Their colligative properties deviate considerably from ideal values, even at concentrations below 1 m. There are at least a couple of reasons for this effect... 

Because of electrostatic attraction, an ion in solution tends to surround itself with more ions of opposite than of like charge (Figure 10.12). The existence of this ionic atmosphere, first proposed by Peter Debye (1884-1966), a Dutch physical chemist in 1923, prevents ions from acting as completely independent solute particles. The result is to make an ion somewhat less effective than a nonelectrolyte molecule in its influence on colligative properties. 

Freezing point lowering (or other colligative properties) can be used to determine the extent of dissociation of a weak electrolyte in water. The procedure followed is illustrated in Example 10.11. 

Use colligative properties to determine molar mass of a solute. 

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