Molar mass defined

Equation (7) also holds for a polydisperse sample of PVOH, but the molar mass in this case is, the viscosity-average molar mass defined below. 

It has been tried to put the result of Kennedy et al (//) in a la-Mw graph (Fig. 7). Two samples families are distinguished quenched samples and slowly crystallized samples. In both families, the ductile-brittle transition occurs at lac = 6 nm. The corresponding critical molar mass defined in scheme A is higher for slowly crystallized samples (M c 100 kg.mof ) than for quenched ones (M c 60 kg.mof ). This result can be considered as a proof that scheme B is more pertinent than scheme A. 

We have seen that 1 mole of carbon-12 atoms has a mass of exactly 12 grams and contains 6.022 X 10 atoms. This mass of carbon-12 is its molar mass, defined as the mass (in grams or kilograms) of 1 mole of units (such as atoms or molecules) of a substance. Note that the molar mass of carbon-12 (in grams) is numerically equal to its atomic mass in amu. Likewise, the atomic mass of sodium (Na) is 22.99 amu and its molar mass is 22.99 grams the atomic mass of phosphorus is 30.97 amu and its molar mass is 30.97 grams and so on. If we know the atomic mass of an element, we also know its molar mass. 

In the case of a homopolymer the most important characteristic is its size of molar mass. The molar mass (defined by various averages and especially the molar mass distribution) determines a large range of properties of the polymer material. Naturally this qqrlies to copolymers as well, but in this case the di nical composition also plays an important role. 

Molal boiling point constant, 269,270t Molal freezing point constant, 269,270t Molality (m) A concentration unit defined as the number of moles of solute per kilogram of solvent, 259,261-262 Molar mass The mass of one mole of a substance, 55,68-68q alcohol, 591 alkane, 591... 

E.29 The king of Zirconia is naturally fond of the element zirconium and has established an independent definition of the mole based on zirconium. The mass of one zirconium-90 atom is 1.4929 X 10 22 g. If zirconium were the standard used for molar mass (instead of carbon-12), 1 mol would be defined as the amount of substance that contains the same number of entities as there are atoms in exactly 90 g of zirconium-90. In that case, what would be (a) the molar mass of carbon-12 (b) the (average) molar mass of gold ... 

Because molarity is defined in terms of the volume of the solution, not the volume of solvent used to prepare the solution, the volume must be measured after the solutes have been added. The usual way to prepare an aqueous solution of a solid substance of given molarity is to transfer a known mass of the solid into a volumetric flask, dissolve it in a little water, fill the flask up to the mark with water, and then mix the solution thoroughly by tipping the flask end over end (Fig. G.8I. 

The conversion is more involved because the molality is defined in terms of the mass of solvent but the molarity is defined in terms of the volume of solution. To carry out the conversion we need to know the density of the solution. 

The fundamental equation of sedimentation equihbrium can be manipulated to define a new function with dimensions of molar mass (g/mol) called M r). M (r) at a radial position r is defined by... 

The size of a polymer molecule may be defined either by its mass (see Chapter 6) or by the number of repeat units in the molecule. This latter indicator of size is called the degree of polymerisation, DP. The relative molar mass of the polymer is thus the product of the relative molar mass of the repeat unit and the DP. 

The methods by which polymers are prepared result in a mixture of molecular sizes whose properties depend on the average size of the molecules present. In principle there are a number of ways in which such an average can be calculated. The most straightforward is the simple arithmetic mean, usually called the number average molar mass, M. This is defined by the expression... 

Alternatively we can define the weight-average molar mass where we take terms inM , i.e. 

A further but less widely used average is the z-average molar mass, M, defined as ... 

Hence, the value of I/Iq is dependent on relative molar mass of the molecules involved in the light scattering. The Rayleigh ratio, Rg, may be defined as ... 

C03-0041. Write a paragraph that defines molar mass, mole, and molarity and explains the differences among them. 

Basic definitions Let X be some property of a polymer chain such as the degree of polymerization, molar mass, radius of gyration, or comonomer content of a copolymer, etc. In general, the polymer is heterogeneous with respect to X, which can assume discrete values X,. We now define for molecules with X = X,-. 

Figure 8 illustrates(29) the close relationship between the chain defining the molar mass between junction points of the perfect network (M ) and the chain of v bonds of the preceding sections. The illustrations in (b) and (c) are for the RA2 +... 

Figure 8. Part of a tetrafunctional network formed from an RA t and RBi polymerization corresponding to Mc°, the molar mass between junction points of the perfect network (a). Detail of the chain structure defining Mc° for HDl reacting with an OPPE, n is the number-average degree of polymerization of each arm with respect to oxypropylene units, (b). Part of the chain structure defining v, the number of bonds in the chain forming the smallest ring structure (C), for the reaction system in (b) (29). Reproduced, with permission, from Ref. 21. Copyright 1980, Stein-...

Turbidimetry is ideally suited to detect the temperature at which a transparent polymer solution turns opaque. The temperature corresponding to the onset of the increase of the scattered light intensity is usually taken as the cloud-point temperature, TcP, although some authors define the cloud point as the temperature for which the transmittance is 80% (or 90%) of the initial value. This technique is commonly known as the cloud-point method [199]. Turbidimetry was employed, for instance, to show that the cloud-point temperature of aqueous PNIPAM solutions does not depend significantly on the molar mass of the polymer [150]. 

The results of this consideration may be summarized as follows. The study of global properties of macromolecules in dilute solutions by means of static and dynamic LS and by viscometry allows the determination of the molar mass and four differently defined equivalent sphere radii, R, and (see... 

Table 2). All the radii have a certain molar mass dependence. The magnitudes of these radii, however, can deviate strongly from each other. These differences result from the fact that they are physically differently defined. The radius of gyration, R, is solely geometrically defined the thermodynamically equivalent sphere radius, R-p is defined by the domains of interaction between two macromolecules, or in other words, on the excluded volume. The two hydrodynamic radii R and R result from the interaction of the macromolecule with the solvent (where the latter differs from R by the fact that in viscometry the particle is exposed to a shear gradient field).

Generalized ratios of the four differently defined radii can be written. By this manipulation the molar mass dependence is widely eliminated, and the effects of branching becomes more evident. See Table 2. 

The leading parameter that characterizes the distributions of randomly branched samples is an exponent Tthat is defined in the next section. The average procedures for the z-average of the mean square radius of gyration and the weight average molar mass results in the relationship [7]... 

Fig. 31. Molar mass dependencies of four differently defined overlap concentrations c (ml/g) for amylopectin fractions in O.Smol/lNaOH [144]. Reprinted with permission from [144]. Copyright [1996] American Society...

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