Calculations Using Colligative Properties

Purified blood is pumped from the dialyzer back to the patient. 

Because it is not normally found in blood, fluoride ion, if present in the dialysate, will flow across the membrane into the blood. In fact, this is true of any sufficiently small solute that is not normally found in blood—necessitating requirements for the purity of water used to prepare dialysate solutions that far exceed those for drinking water. 

Think About It Check the result using the molecular formula of quinine C20H24N2O2 (324.4 g/mol). Multistep problems such as this one require careful B acking of units at each step. 

Quinine was the first drug widely u.sed to treat malaria, and it remains the treatment of choice for severe cases. A solution prepared by dissolving 10.0 g of quinine in 50.0 mL of ethanol has a freezing point 1.55°C below that of pure ethanol. Determine the molar mass of quinine. (The density of ethanol is 0.789 g/mL.) Assume that quinine is a nonelectrolyte. 

Strategy Use Equation 13.7 to determine the molal concentration of the solution. U.se the density of ethanol to determine the mass of solvent. The molal concentration of quinine multiplied by the mass of ethanol (in kg) gives moles of quinine. The mass of quinine (in grams) divided by moles of quinine gives the molar mass. 

The size of the membrane pores is such that only small waste products such as excess potassium ion, creatinine, urea, and extra fluid can pass through. Larger components in blood, such as blood cells and proteins, are too large to pass through the membrane. A solute will pass through the membrane from the side where its concentration is higher to the side where its concentration is lower. The composition of the dialysate ensures that the necessary solutes in the blood (e.g., sodium and calcium ions) are not removed. 

Practice Problem A Calculate the molar mass of naphthalene, the organic compound in mothballs, if a solution prepared by dissolving 5.00 g of naphthalene in exactly 100 g of benzene has a freezing point 2.00°C below that of pure benzene. 

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The following equations are used in calculations involving colligative properties and molality ... 

When the solution contains two or more solutes, the molality to be used in calculating the colligative properties is the total molality of all solutes ... 

Use the van t Hoff factors in Table 12.9 to calculate each colligative property ... 

The osmotic pressure is a colligative property and mathematically can be represented as 71 = (nRTIV) i, where It is the osmotic pressure in atmospheres n is the number of moles of solute R is the ideal gas constant 0.0821 L atm/Kmol T is the Kelvin temperature Vis the volume of the solution and i is the van t Hoff factor. Measurements of the osmotic pressure can be used to calculate the molar mass of a solute. This is especially useful in determining the molar mass of large molecules such as proteins. 

Know how to use the appropriate colligative properties equation to calculate the amount of vapor-pressure lowering, freezing-point lowering, van t Hoff factor, etc. 

As we saw in Section 17.5, the activity coefficient of a nonelectrolyte solute can be calculated from the activity coefficient of the solvent, which, in turn, can be obtained from the measurement of colligative properties such as vapor pressure lowering, freezing point depression, or osmotic pressure. We used the Gibbs-Duhem equation in the form [Equation (17.33)]... 

When the activity of the solvent is determined from a colligative property, then g can be calculated with Equation (19.44). If we use osmotic pressure as an example, we can combine Equation (15.33) and Equation (16.1) to obtain the expression... 

The analysis described above is useful for modelling colligative properties but does not address polyelectrolyte conformations. Polyelectrolyte conformations in dilute solution have been calculated using the worm-like chain model [103,104], Here, the polymer conformation is characterized by a persistence length (a measure of the local chain stiffness) [96]. One consequence of the... 

Another important equation, the Gibbs-Helmholtz equation, is derived from the Maxwell relations. A chemist may use this equation to determine the enthalpy change in a reaction, and a pharmaceutical scientist may use it to calculate colligative properties (i.e., freezing point depression and boiling point elevation). The expression for free energy with respect to temperature at constant pressure is given by Equation (1.105) ... 

Values of the mean ion activity coefficient may be determined experimentally using several methods, including electromotive force measurement, solubility determinations and colligative properties. It is possible, however, to calculate y+ in very dilute solution... 

Since osmotic pressure is not a readily measurable quantity, it is usual to make use of the relationship between the colligative properties and to calculate the osmotic pressure from a more easily measured property such as the freezing point depression. In so doing, however, it is important to realise that the red blood cell membrane is not a perfect semi-permeable membrane and allows through small molecules such as urea and ammonium chloride. Therefore, although the quantity of each substance required for an isotonic... 

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. 

Distinguish between a strong electrolyte, a weak electrolyte, and a nonelectrolyte. How can colligative properties be used to distinguish between them What is the van t Hoff factor Why is the observed freezing-point depression for electrolyte solutions sometimes less than the calculated value Is the discrepancy greater for concentrated or dilute solutions ... 

Osmotic pressure is a colligative property. A colligative property solely depends on the concentration of the dissolved molecules or ions and is independent of the nature of the solute. Freezing point depression is also a colligative property and can be indirectly used to determine osmotic pressure. In practice, it is much more difficult to determine the osmotic pressure of a solution than to measure its freezing point depression. The freezing point of a solution can be measured and the osmotic pressure can be calculated from it. 

One measure of the extent to which electrol5rtes dissociate is the van t Hoff factor, i. This factor is the ratio of the actual value of a colligative property to the value calculated assuming the substance to be a nonelectrolyte. Using the freezing-point depression, for example, we have... 

In this equation, m is the solution concentration expressed as a molality, a unit we have not discussed. For very dilute solutions, the molality m and molarity M are essentially equal, and M can be used in Equation 7.12 instead of m. This approximation will be used for calculating colligative properties of solutions in this book. The symbol AT is the boiling point or freezing point difference between pure solvent and solution. The specific equations used to calculate AT for boiling and freezing points are... 

Although these expressions provide no information about the activity coefficient of a solute, they are useful for estimating the solute molar mass. For example, from a measurement of any of the colligative properties of a dilute solution and the appropriate theoretical relation, we can obtain an approximate value of the solute molality niB- (It is only approximate because, for a measurement of reasonable precision, the solution cannot be extremely dilute.) If we prepare the solution with a known amount a of solvent and a known mass of solute, we can calculate the amount of solute from b = nAMpjnB, then the solute molar mass is the solute mass divided by ns-... 

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