Average mass definition

The atomic mass of an element is the weighted average mass of the isotopes of that element. Based on this definition, which of these does NOT show the correct atomic mass for an element ... 

We may describe multicomponent diffusion by (1) the Maxwell-Stefan equation where flows and forces are mixed, (2) the Chapman-Cowling and Hirschfelder-Curtiss-Bird approaches where the diffusion of all the components are treated in a similar way, and (3) a reference to a particular component, for example, the solvent or mass average (baiycentric) definition. Frames of reference in multicomponent system must be clearly defined. Binary diffusion coefficients are often composition dependent in liquids, while they are assumed independent of composition for gases. 

The mass flux of a solute can be related to a mass transfer coefficient which gathers both mass transport properties and hydrodynamic conditions of the system (fluid flow and hydrodynamic characteristics of the membrane module). The total amount transferred of a given solute from the feed to the receiving phase can be assumed to be proportional to the concentration difference between both phases and to the interfacial area, defining the proportionality ratio by a mass transfer coefficient. Several types of mass transfer coefficients can be distinguished as a function of the definition of the concentration differences involved. When local concentration differences at a particular position of the membrane module are considered the local mass transfer coefficient is obtained, in contrast to the average mass transfer coefficient [37]. 

The mass mean diameter will not equal the diameter of average mass. Hinds definition (Hinds, 1982) is useful ... 

To generate a relationship between mass of carbon and number of carbon atoms, we need to know the weighted average mass of the carbon atoms found in nature. Experiments show that 98.90% of the carbon atoms in natural carbon are carbon-12, and 1.10% are carbon-13, with six protons, seven neutrons, and six electrons. Related experiments show that each carbon-13 atom has a mass of 13.003355 u. From the definition of atomic mass unit, we know that the mass of each carbon-12 atom is 12 u. The following setup shows how the weighted average mass of carbon atoms is calculated. 

Each nucleus is characterized by a definite atomic number Z and mass number A for clarity, we use the symbol M to denote the atomic mass in kinematic equations. The atomic number Z is the number of protons, and hence the number of electrons, in the neutral atom it reflects the atomic properties of the atom. The mass number gives the number of nucleons (protons and neutrons) isotopes are nuclei (often called nuclides) with the same Z and different A. The current practice is to represent each nucleus by the chemical name with the mass number as a superscript, e.g., 12C. The chemical atomic weight (or atomic mass) of elements as listed in the periodic table gives the average mass, i.e., the average of the stable isotopes weighted by their abundance. Carbon, for example, has an atomic weight of 12.011, which reflects the 1.1% abundance of 13C. 

Figure 33. Effect of resolution on peak shapes A) The protonated molecular cluster of human insulin (CisrHjgjNftjOyvSj,) recorded with FABMS B) Calculated at a resolution of 6000 (10% valley definition) with the monoisotopic mass at m/ = 5804.6455 C) The unresolved cluster with an average mass at rn/j = 5808.61 (Reproduced from [226], with permission)...

Measured accurate masses, when used to assign molecular formulas, should always be accompanied by their mass accuracies. [52], Ideally, this can be done by giving the mean mass value and the corresponding error in terms of standard deviation through several repeated measurements of the same ion. [40] This is definitely not identical to the error usually provided with a mass spectrometer s software, where the error is based on the difference of a single pair of calculated and measured values. The reduction of the average mass error goes with the square root of the number of determinations (Chap. 3.5.4) [39]. 

Table 23 Diffusion flux closures based on the mass average velocity definition ...

In this book, we always choose to use the local concentration difference at a particular position in the column. Such a choice implies a local mass transfer coefficient to distinguish it from an average mass transfer coefficient. Use of a local coefficient means that we often must make a few extra mathematical calculations. However, the local coefficient is more nearly constant, a smooth function of changes in other process variables. This definition was implicitly used in Examples 8.1-1, 8.1-3, and 8.1-4 in the previous section. It was used in parallel with a type of average coefficient in Example 8.1-2. 

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 ... 

Why do polymers not have definite molar masses How does the fact that polymers have average molar masses affect their melting points ... 

Polymers generally do not have definite molecular masses because there is no fixed point at which the chainlengthening process will cease. There is no fixed molar mass, only an average molar mass. Because there is no one unique compound, there is no one unique melting point, rather a range of melting points. 

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