Determination of Molar Mass

By the second law of thermodynamics, when a solution is in equilibrium with solid solvent, the solvent vapor pressures of the two must be equal. Therefore, for a solution 

The equation of the sublimation curve is conveniently obtained from the integrated Clausius-Clapeyron equation, 

It is worth noting here that Eq. (5) may be derived more elegantly on a somewhat different set of assumptions, in which those pertaining to properties of the solvent vapor do 

We wish to derive expressions for calculating the molality m of the solution (or the molar mass Mof the solute) from a measured freezing-point depression AT. The molality of the solution is given by 

The expressions commonly used for determination of molalities or molar mass from freezing-point depressions are derived with the following approximations  

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Determination of Molar Masses from Colligative Properties... 

In addition to the determination of molar mass distributions and various molar mass averages there are many experiments, requiring sometimes sophisticated data evaluation, that can be carried out with an analytical ultracentrifuge. Examples are the analysis of association, the analysis of heterogeneity, the observation of chemical reactions, and protein characterization, to mention only a few. A detailed discussion is beyond the scope of this article, but there is excellent literature available [77-79,81,87-89]... 

Many polymer properties can be expressed as power laws of the molar mass. Some examples for such scaling laws that have already been discussed are the scaling law of the diffusion coefficient (Equation (57)) and the Mark-Houwink-Sakurada equation for the intrinsic viscosity (Equation (36)). Under certain circumstances scaling laws can be employed advantageously for the determination of molar mass distributions, as shown by the following two examples. 

Microgels are distinguished from linear and branched macromolecules by their fixed shape which limits the number of conformations of their network chains like in crosslinked polymers of macroscopic dimensions. The feature of microgels common with linear and branched macromolecules is their ability to form colloidal solutions. This property opens up a number of methods to analyze microgels such as viscometry and determination of molar mass which are not applicable to the characterization of other crosslinked polymers. 

Determination of molar mass by freezing-point depression... 

Experiment 3 Determination of Molar Mass by Vapor Density... 

Note 2 Any molar-mass average can be defined in terms of mass fractions or mole fractions. In this document only a few of the important molar-mass averages are given in terms of the mass fractions, Wi, of the species with molar mass M. These definitions are most closely related to the experimental determination of molar-mass averages. 

Fig. 3.4. Determination of Vo and Vt by gel permeation chromatography. Dashed line dextran blue (defines void volume Vo) dotted line DNP-alanine (defines total volume Vt). Inset plot of a calibration curve for determination of molar mass...

Write down all of the calculations required to determine the identity of the metal chloride in the Determination of Molar Mass activity (eChapter 11.9). Use similar calculations to identify the alkaline earth metal chloride that gives a solution with osmotic pressure of 1.32 atm upon addition of 100.0 mg to water under the same conditions of volume and temperature. 

Determination of molar mass by vapor density barometer, beaker, Erlenmeyer flask, graduated cylinder, clamp, analytical balance, support stand... 

Determination of molar mass by freezing-point depression test tube, thermometer, pipet, beaker, stirrer, stopwatch, ice... 

One of the laboratory procedures that you are expected to know involves the determination of molar mass from gas density. In the sample calculation that follows, you will solve for the density of a gas, but understand that a simple rearrangement of the equation allows you to solve for the molar mass. 

All of the physical methods presently used for the determination of molar mass of polymers require the molecules contribute individually, i.e., additively, to the property being measured, contribution due to interactions between pairs (or... 

Of all the methods used for the determination of molar masses of macromolecules, the viscosity method, introduced by H. Staudinger, is the one most commonly employed in research. Accurate measurement of absolute viscosity being difficult, it is convenient to measure relative viscosity, x e denned as... 

The good agreement between theory and experiment in S-FFF was confirmed by experiments with standard samples [81 ]. Good agreement was also found for the determination of molar masses of different biopolymers [171] and sizes of... 

Partial Molar Volume 1 0. Cryoscopic Determination of Molar Mass 1 1. Freezing-Point Depression of Strong and Weak Electrolytes 12. Chemical Equilibrium in Solution... 

Apparatus for cryoscopic determination of molar mass. The cryoscopic mercury thermometer can be replaced by a resistance thermometer or a calibrated thermistor. 

Number-Average and Viscosity-Average Molar Mass. For a polydisperse polymer, any determination of molar mass must yield an average of some sort. When a col-ligative property such as osmotic pressure is used, the average is a number average ... 

Figure 4-2S. SDS-PAGE determination of molar masses of proteins under denaturing conditions. The pattern of bands from a standard protein mix after SDS-PAGE is shown...

A HE CHARACTERIZATION OF MODERN HIGH-PERFORMANCE POLYMERS is still a challenge for polymer scientists. Copolymers and complex polymer blends play an important role in many applications (i). A fast, reliable, and comprehensive method is needed to succeed in this task. Size-exclusion chromatography (SEC) is a standard method for the determination of molar mass distributions (MMDs) and molecular weights, if... 

Gel permeation chromatography (GPC) is the established method for the determination of molar mass averages and the molar mass distributions of polymers. GPC retention is based on the separation of macromolecules in solution by molecular sizes and, therefore, requires a molar mass calibration to transform elution time or elution volume into molar mass information. This kind of calibration is typically performed with narrow molecular mass distribution polymer standards, universal, or broad calibration methods or molar-mass-sensitive detectors like light-scattering or viscosity detectors. 

Further data analysis allows the determination of molar mass, chemical composition, and relative concentration for each component. The 2D chromatography data can be displayed in various forms (cf. Fig. 2) ... 

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