Cryoscopic Constants for Calculation

Cryoscopic Constants, A0, B° Cryoscopic constants for calculating mole °U purity. See /. Research Natl. Bur. Standards, 35 (1945) RP 1676. 

CRYOSCOPIC CONSTANTS FOR CALCULATION OF FREEZING POINT DEPRESSION... 

Cryoscopic Constants for Calculation of Ereezing Point Depression.15-28... 

Calculate the cryoscopic constant for cyclohexane, CgHi2, given that its enthalpy of fusion is 2630 J/mol and its melting point is 6.6°C. What are the units for the constant ... 

One-fifth mole of a weak monobasic acid is dissolved in 1000 cc of water (cryoscopic constant 1.86 degrees). The freezing point of the resulting solution is —0.396 degrees. Calculate for the acid. 

The kinetics of butadiene polymerized by bis(7T-allyl nickel trifluoro-acetate) has been studied by Teyssie et al. [173]. Equilibrium constants for the formation of the complex (with aromatic compounds which give the equibinary polymer), calculated from cryoscopic measurements or polymer micro-structure, are 6—7 and 26—35 respectively for benzene and nitrobenzene. The higher concentration of active centres compared with... 

Applications of Solid-solution Theory. If a melting curve shows evidence of appreciable solid-solution formation, it may require application of a solid-solution treatment 14,15) to give an accurate impurity value, although Smit (1) has critized one of the treatments 14> Unfortunately, the method often has failed to give an adequate representation of observed melting curves. In some instances, the solid-solution treatment has given an excellent representation of experimental data, but the high sensitivity of the method to small thermometric errors makes the calculated impurity values unreliable. For example, the difference in temperatures observed with 70 and 90% of a sample melted may easily be in error by +0.0005°C. For the solid-solution treatment, such an error would correspond to an uncertainty of 500% in the impurity value for very pure compounds with normal cryoscopic constants, whereas the same 0.0005°C error corresponds to 150% uncertainty if solid insolubility is assumed. 

This paper reports cryoscopic measurements for NiS04 aqueous solutions (0.00 > t /°C > - 0.21), and demonstrates the dependence of the calculated value of K on the assumptions in the complexation model. Based on the arguments of Brown and Prue, it is clear that use of the SIT as is done in the TDB project imposes constraints on the data analysis, and that these constraints should lead to a specific value for K. However, recalculations show that the association constant is also strongly dependent on the concentration at which the data set is truncated. For the purposes of the present review, recalculations were done using the SIT, but only results for molalities < 0.03 were used in the selection of the value of log . When data for higher concentrations were included, the calculated value for the association constant increased, and log,Q = 300 was obtained if the entire data set was used. 

The i.r. and Raman data suggest a strongly hydrogen-bonded complex, with the association at the carbonyl oxygen of the phenazone and not at the nitrogen. Infrared studies of the complex in carbon tetrachloride solution have been used to calculate a stability constant for the complex (1 1), and cryoscopic measurements on dilute aqueous solutions show the molecular com-... 

Anhydrous acetic acid melts at 16.635°C and has a cryoscopic constant, Ac = 3.59 Kkgmol . ° Raoult used this solvent for molecular weight determinations and it has been used by several workers " for the investigation of hydrocarbon solutes. The dielectric constant is 6.194 at 18°C. Few investigations of electrolyte solutions have been reported and association is pronounced. Lithium salts in particular, appear to polymerise in acetic acid solution. Turner and Bissett found that lithium iodide, and to a lesser extent lithium nitrate, appear to polymerise, though sodium iodide did not exhibit similar behaviour. Kenttamaa calculated equilibrium constants for the reaction... 

Freezirig prant curves were computed for pora- and o/rfio-xylene using Eq. (11.2-6) (the van t Hoff equation) and Eq. (11.2-7) which ured cryoscopic constants. Data from Table 11.2-1 were used in the equations and calculated equilibriom compositions are shown as a Ainction of temperature in Table 11.2-2. The computed liquid compositions are nearly identical in the high concentration range and diverge... 

Calculate the cryoscopic and ebullioscopic constants for liquid bromine, Br2. You will need the following data ... 

The accirrate determination of freezing points by time-temperature analysis was extensively used by the American Petroleirm Institute Research Project 6 for the determination of the pirrities of hydrocarbon samples. Also, the method has been developed for determining the cryoscopic constant, from which the molar enthalpy of fusion can be calculated. Accirracy of freezing points determined by this method is estimated to be 0.01 K. However, inaccirracy of enthalpy of fusion estimated from the method is more than +10 percent, or even 50 percent in some cases. Especially, the method can not separate the enthalpy of a solid transition from the enthalpy of fusion if the temperatures of these phase transition are within a few Kelvin. 

In addition to solubility and cryoscopic studies, the association of solute molecules may be investigated by the variation of the dielectric constant with concentration. If the solution is non-polar, the value of the dipole moment calculated from the value of the dielectric constant at infinite dilution, obtained by extrapolation, may be close to the value obtained in the gaseous phase. If this be so, there are no anomalous solvent effects, but cases exist where this is not so and such behaviour may be explained by two theories. The first assumes that association of solute molecules persists at low concentrations and may be illustrated with reference to the curious variation of polarization of ethyl alcohol in hexane solution. As the concentration is increased, the polarization falls, passes through a minimum, rises to a maximutn value and then falls to the value for the polarization of pure ethyl alcohol. In dilute solution the molecules are evidently associated in such a way that the dipole moment is decreased, this may occur through the formation of quadrupoles by means of hydrogen bonds, viz... 

---