126 dt b m or dt b k b m b d vap h m b where kb is

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Unformatted text preview: his gives D H æ DT ö x B = fus m ç 2f ÷ , R è Tf ø which can be further simplified to yield (see the text above Eq. 5.119) RT 2 M A f m or DT f = K f m B , DT f = (5.119, 5.120) D fus H m B where Kf is called the cryoscopic constant of the solvent. Boiling Point Elevation: By considering the liquid-vapor equilibrium in which the vapor contains only the component A, we can derive an expression analogous to that obtained above: RT 2 M A b (5.126) DT b = m or DT b = K b m B , D vap H m B where Kb is called the ebullioscopic constant of the solvent. The elevation of boiling point is a rather weak effect compared to the depression of freezing point. Therefore, the latter property is overwhelmingly used for the practical applications of colligative properties. Practical Applications: Ÿ Problems 5.37, 5.38, 5.44 Ÿ These equations are useful to determine the freezing points or boiling points of various solutions of nonvolatile solutes. Problem 5.54 Ÿ A somewhat “liberal” interpretation of Eq. (5.115) or (5.116) can be used to calculate the solubility of various solutes at temperature T in a solvent whose enthalpy of fusion and freezing point are known. Problem 5.46 Ÿ The “simplified” forms are also useful to determine the molar masses of unknown solutes using Eq. (5.122). Problems 5.50, 5.53 Colligative properties depend on number of “particles” in solution rather than actual “concentration.” For instance, a 1 m solution of NaCl leads to a 2 m solution of ions (Na+ and Cl–). Such a solution, therefore, will yield twice the expected ∆Tf. This effect must be taken into account when dealing with ionic substances (See problem 5.24)....
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