Absolute mass units

Here we encounter another term associated with a range whose definition has changed considerably with time. A trace was once understood to be a no longer determinable but nonetheless observable concentration of some undesired companion substance (impurity) within a matrix. In the meantime, trace analysis has become an important and very precise field of inquiry —. subject to certain restrictions with respect to the achievable reliability, but indispensable in a number of disciplines (- Trace Analysis). There is little point in attempting to express a trace in terms of absolute mass units data should instead be reported on the basis of content (concentration) in a form such as pg/kg (mass proportion) or pg/L (mass concentration). These units are to be used in preference to the very popular abbreviations ppm, ppb, and ppt , which need an additional indication to the respective unit (mass, volume, amount of substance). 

The order of magnitude of the mass of a single atom is 10 kg therefore, it is not practical to use absolute mass units in calculations. Instead, according to international conventions, the relative atomic mass Ar, defined in the following way is normally used ... 

Figure 8.30. Cumulative number distribution for the galaxies in the Universe. Mass is assumed proportional to absolute luminosity (units solar luminosity x 10 ). From Brown et al. (1983).

The Sauerbrey equation predicts a mass sensitivity per unit area of 0.226 Hz cm 2 ng . For a typical crystal the exposed area is c. 0.25 cm2 and the absolute mass sensitivity is 0.904 Hz ng 1. The resolution of modern frequency counters is easily +0,1 Hz in 10 MHz, giving a theoretical mass resolution of c. 9 x 10 10 g in practice this is usually found to be closer to 2 ng. 

The mass accuracy is defined as the difference between measured accurate mass and calculated exact mass. The mass accuracy can be stated as absolute units of u (or mmu) or as relative mass accuracy in ppm, i.e., absolute mass accuracy divided by the mass it is determined for. As mass spectrometers tend to have similar absolute mass accuracies over a comparatively wide range, absolute mass accuracy represents a more meaningful way of stating mass accuracies than the more trendy use of ppm. 

It is critical when performing quantitative GC/MS procedures that appropriate internal standards are employed to account for variations in extraction efficiency, derivatization, injection volume, and matrix effects. For isotope dilution (ID) GC/MS analyses, it is crucial to select an appropriate internal standard. Ideally, the internal standard should have the same physical and chemical properties as the analyte of interest, but will be separated by mass. The best internal standards are nonradioactive stable isotopic analogs of the compounds of interest, differing by at least 3, and preferably by 4 or 5, atomic mass units. The only property that distinguishes the analyte from the internal standard in ID is a very small difference in mass, which is readily discerned by the mass spectrometer. Isotopic dilution procedures are among the most accurate and precise quantitative methods available to analytical chemists. It cannot be emphasized too strongly that internal standards of the same basic structure compensate for matrix effects in MS. Therefore, in the ID method, there is an absolute reference (i.e., the response factors of the analyte and the internal standard are considered to be identical Pickup and McPherson, 1976). 

The dotted lines in Fig. 1 show the stopping powers for the different ions at a constant velocity in units of MeV/amu. This unit of energy is very often used in heavy ion radiolysis and it is based on the classical formula for kinetic energy, E = V2 MV, where M is the heavy ion mass. As seen in Eq. (1), the ion velocity is a dominant parameter in energy loss processes and the MeV/amu energy unit is more convenient to use than converting to absolute velocity units. Remember that MeV/amu is actually proportional to the square of the velocity. 

The mass number gives the total number of protons and neutrons in an atom of an element, but it does not convey the absolute mass of the atom. To work with the masses of elements, we use comparative masses. Initially, Dalton and the other pioneers of the atomic theory used the lightest element hydrogen and compared masses of other elements to hydrogen. The modern system uses C-12 as the standard and defines one atomic mass unit (amu) as 1/12 the mass of one C-12 atom. One amu is approximately 1.66 X 10 g. This standard means the masses of individual protons and neutrons are slightly more than 1 amu as shown in Table 4.6. 

Ever since instrumentation has been sophisticated enough to determine the masses of individual atoms in an indirect fashion, it has been possible to have a list ofabsolute values of the atomic masses. The mass of an atom is incredibly small expressed in grams, these values are cumbersome to use in day-to-day work and conversation. In recent years, this difficulty has been surmounted by using a special mass unit called a dalton (d) 1 d = 1.6604 x 10-J4g. 1S unit s chosen so that the mass of the most common isotope of the carbon atom equals 12.00000 d. Thus, the absolute atomic weight of H is 1.0079 d, and the absolute... 

G. Quincke gave T3 x 10 mass units V. I. Vaidyanathan gave 0 029 X 10 9 vol. units at ordinary temp, and at a low press. and for air at 182°, J. A. Fleming and J. Dewar gave 0-28Xl0 6 mass units E. Lehrer, 24T6X 10 8 absolute values and G. W. Hammar made observations on this subject. W. Schiitz, and K. S. Krishnan observed no orientation of the atoms in a magnetic field. 

The mass accuracy is usually described as either the absolute mass error in milli-daltons (or thousandths of a mass unit) or as a part-per-million error which is the ratio of the absolute error and the calculated mass multiplied by one million. For instance, if an ion has a calculated or theoretical mass of 400.000 and the measured mass is 400.002, then the error is 2 mDa. The ppm error is calculated by dividing the 2-mDa error by the calculated mass of 400.000 and multiplying by one million to give 5 ppm. Note that if the same absolute error of 2 mDa was found for a compound of theoretical mass of 800, the ppm error would be 2.5 ppm. For the same absolute error, the ppm error varies with mass. 

NPL has a well-established facility for the production of primary gas concentration standards by absolute gravimetric techniques. Standards of a range of different gases with widely differing concentrations are prepared in carefully selected passivated containers by the accurate consecutive weighings of the constituent gases. The concentrations of the gas standards prepared in this manner, which are expressed in absolute molar units, are traceable to the primary standard of mass. 

Generally in mass spectrometry, the charge is indicated in multiples of the elementary charge or charge of one electron in absolute value (1 e = 1.602 111 x 10-19 C) and the mass is indicated in atomic mass units (1 u = 1.660 540 x 10-27 kg). As already mentioned, the physical property that is measured in mass spectrometry is the mass-to-charge ratio. When the mass is expressed in atomic mass units (u) and the charge in elementary charge units... 

Fig. 2. Mass spectrum of the products formed by heating antimony with a mixture of 1,2-I2C6H4 and 1,2-I2C6F4. Note the absolute lack of Sb2(C6H4)3 at 472 mass units even though the mixed H/F species Sb2(C6F4)2C6H4 and Sb2(C6F4)(C6H4)2 are well in evidence.

The system of units is based upon the general dimensions of space, mass, and time. Space may be in terms of displacement or volume and mass may be in terms of absolute mass or relative mass. An example of absolute mass is the gram, and an example of relative mass is the mole. The mole is a relative mass, because it expresses the ratio of the absolute mass to the molecular mass of the substance. When the word mass is used without qualification, absolute mass is intended. 

Molecular weight is an incorrect scientific term The numerical value being referenced is a relative molecular mass. It is a mass, measuring a quantity of matter, not the influence on that matter by an external gravitational field. It is a relative mass, not an absolute mass measured in grams, because it is expressed in relation to the standard atomic mass of 12.000000 units... 

Since the concentration of SM-C/IGF-I has traditionally been expressed in U/ml, with I U/ml arbitrarily defined as the activity in a pool of normal adult plasma, it has been difficult to compare in absolute terms the values obtained in different laboratories. As purified peptides have become available, it is now possible to express both SM-C/IGF-I and IGF-II in mass units, generally ng/ml. In a number of laboratories which report in mass units or provide conversion foctors between U/ml and ng/ml, the level of SM-C/IGF-I in apparently healthy adults is generally about 200-300 ng/ml, although some laboratories have reported different mean values in different studies. Some typical mean values and ranges (either presented as published or calculated from data provided) are shown in Table 2. In recent years reference ranges for IGF-II have also become established. As seen in Table 2, mean values are 2 to 3 times higher than for SM-C/IGF-I. 

This expression indicates that the volume of a given mass of gas varies directly with the absolute temperature and inversely with the pressure. Notice that, while T and Tj must be in kelvins, any convenient absolute pressure unit may be used for Pi and P2, and any convenient volume unit may be used for Vi and V2. 

The mass of an atom is measured relative to the mass of an atomic standard. The modern atomic mass standard is the carbon-12 atom. Its mass is defined as exactly 12 atomic mass units. Thus, the atomic mass unit (amu) is -j the mass of a carbon-12 atom. Based on this standard, the H atom has a mass of 1.008 amu in other words, a C atom has almost 12 times the mass of an H atom. We will continue to use the term atomic mass unit in the text, although the name of the unit has been changed to the dalton (Da) thus, one C atom has a mass of 12 daltons (12 Da, or 12 amu). The atomic mass unit, which is a unit of relative mass, has an absolute mass of 1.66054 X10 " g. 

The MALDI-TOF-MS analysis of the polyMMA, obtained in linear mode shows only one series of peaks, whose interval was regular, ca. 100, the molar mass of MMA unit. It indicates the absence of irreversible chain termination processes via recombination or disproportionation. According the proposed mechanism of polymerization the absolute masses of the peaks should be equal... 

The universal mass unit, abbreviated u (sometimes amu for atomic mass imit), is defined as one-twelfth of the mass of the atom which has been defined to be exactly 12 u. The absolute mass of a atom is obtained by dividing the value 12 by the Avogadro number (N = 6.022 137 X 10 ). The value for the mass of a atom, i.e. the nucleus plus the 6 extranuclear electrons, is thus 1.992 648 X 10 g. Atomic masses are expressed in umts of u relative to the standard. This text uses M to indicate masses in imits of u, and m in units of kilograms m = MUC N. ... 

DENSITY, ABSOLUTE - Mass per unit volume of a solid material, expressed usually in kg/m. ... 

Molecular mass is the average mass of a compound obtained when an accounting is made for all isotopes of the elements present based on their relative abundances, e.g., C = 12.0108 Da, O = 15.9994 Da. If the instrument used cannot resolve the individual isotopes, the observed peaks include all isotopes present. Molecular mass is sometimes referred to as average mass. For cholesterol the molecular (average) mass is 386.6616 Da. (Note the difference between this number and the mono-isotopic exact mass value, 386.3549 Da, as described above.) Molecular mass does have a dimension as it is an absolute value unit, based on 1/12 of the mass of the isotope (in lUPAC units), i.e., 1.6605 x 10- kg. If, however, the mass of an analyte is considered as a ratio with respect to the mass of C, then the dimensions cancel out and the resulting dimensionless number is the relative molecular mass. These two terms are equivalent in everyday usage. 

Intensive quantities related to the activity. In most samples, the radionuclides are not carrier free but inactive isotopes carry them and/or an inactive substance called matrix contains them. (The term no-carrier-added or n.c.a. only means that the production process of a radionuclide sample does not involve adding carrier to it. However, it may not be carrier free.) The specific activity of a radioactive sample is defined as the (absolute) activity of the radioactive sample divided by its mass (unit Bq/kg). Similar quantities are the molar activity (unit Bq/mol) and the activity concentration (unit Bq/dm ), defined as the activity of the sample divided by its molar amount and volume, respectively. 

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