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Freezing-point depression
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===For dilute solution=== [[File:Tfreeze vs SA.png|thumb|237x237px|Freezing temperature of seawater at different pressures and some substances as a function of salinity. See image description for source.]] If the solution is treated as an [[ideal solution]], the extent of freezing-point depression depends only on the solute concentration that can be estimated by a simple linear relationship with the cryoscopic constant ("[[Charles Blagden|Blagden]]'s Law"). :<math> \Delta T_f \propto \frac{\text{Moles of dissolved species}}{\text{Mass of solvent}}</math> :<math> \Delta T_f = K_fbi</math> where: * <math>\Delta T_f</math> is the decrease in freezing point, defined as the freezing point <math> T_f^0</math> of the pure solvent minus the freezing point <math> T_f</math> of the solution, as the formula above results in a positive value given that all factors are positive. From the <math> \Delta T_f</math> calculated using the formula above, the freezing point of the solution can then be calculated as <math> T_f = T_f^0 - \Delta T_f</math>. * <math>K_f</math>, the [[cryoscopic constant]], which is dependent on the properties of the solvent, not the solute. (Note: When conducting experiments, a higher ''k'' value makes it easier to observe larger drops in the freezing point.) * <math>b</math> is the [[molality]] (moles of solute per kilogram of solvent) * <math>i</math> is the [[van 't Hoff factor]] (number of ion particles per formula unit of solute, e.g. i = 2 for NaCl, 3 for BaCl<sub>2</sub>). Some values of the cryoscopic constant ''K''<sub>f</sub> for selected solvents:<ref>{{cite book|first = P. W.|last = Atkins|title = Physical Chemistry|edition = 4th |page = C17 (Table 7.2)|isbn = 978-0716720737|publisher = Freeman|date = 1990}}</ref> {| class="wikitable sortable" ! Compound !! Freezing point (Β°C) !! ''K''<sub>f</sub> in [[kelvin|K]]β kg/[[mole (unit)|mol]] |- | [[Acetic acid]] || 16.6 || 3.90 |- | [[Benzene]] || 5.5 || 5.12 |- | [[Camphor]] || 179.8|| 39.7 |- | [[Carbon disulfide]] || β112 || 3.8 |- | [[Carbon tetrachloride]] || β23 || 30 |- | [[Chloroform]] || β63.5 || 4.68 |- | [[Cyclohexane]] || 6.4 || 20.2 |- | [[Ethanol]] || β114.6 || 1.99 |- | [[Ethyl ether]] || β116.2 || 1.79 |- | [[Naphthalene]] || 80.2 || 6.9 |- | [[Phenol]] || 41 || 7.27 |- | [[Water]] || 0 || 1.86<ref>{{Citation | last1 = Aylward | first1 = Gordon | author-link = Gordon Aylward | last2 = Findlay | first2 = Tristan | author2-link = Tristan Findlay | title = SI Chemical Data 5th ed. | place = Sweden | publisher = John Wiley & Sons | year = 2002 | edition = 5 | pages = 202 | isbn = 0-470-80044-5}}</ref> |}
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