Precise atomic masses

Element Precise Atomic Mass Acceptable Rounded-Off Value... 

Problem 437. Calculate the formula masses of the following compounds, using precise atomic masses (a) BaC03 (6) KjCrjO, (c) C,oH,2 (d) (NH4)2C204 (e) Zn2P202. 

Precise Atomic Masses for Fundamental Physics Determined at SMILETRAP... 

Che Cheng, M., Brown, J.M., Rosmus, P., Linguerri, R., Komiha, N., Myers, E.G. Dipole moments and orientation polarizabilities of diatomic molecular ions for precision atomic mass measurement, Phys. Rev. A 75 (2007) 012502, p. 1-13. 

The molecular formula of a substance can be determined through the use of precise atomic masses. High-resolution mass spectrometers are required for this method. Atoms are normally thought of as having integral atomic masses for example, H =1, C =12, and O =16. If you can determine atomic masses with sufficient precision, however, you find that the masses do not have values that are exactly integral. The mass of each atom actually differs from a whole mass number by a small fraction of a mass unit. The actual masses of some atoms are given in Table 28.1. 

The primary nuclear properties of the known isotopes of einsteinium are listed in Table 12.1 (see also refs 2 and 3). From detailed studies of their nuclear decay, the nuclear levels of their daughters have been obtained and the precise atomic mass... 

The previous discussion has centered on how to obtain as much molecular mass and chemical structure information as possible from a given sample. However, there are many uses of mass spectrometry where precise isotope ratios are needed and total molecular mass information is unimportant. For accurate measurement of isotope ratio, the sample can be vaporized and then directed into a plasma torch. The sample can be a gas or a solution that is vaporized to form an aerosol, or it can be a solid that is vaporized to an aerosol by laser ablation. Whatever method is used to vaporize the sample, it is then swept into the flame of a plasma torch. Operating at temperatures of about 5000 K and containing large numbers of gas ions and electrons, the plasma completely fragments all substances into ionized atoms within a few milliseconds. The ionized atoms are then passed into a mass analyzer for measurement of their atomic mass and abundance of isotopes. Even intractable substances such as glass, ceramics, rock, and bone can be examined directly by this technique. 

The abundance of a trace element is often too small to be accurately quantihed using conventional analytical methods such as ion chromatography or mass spectrometry. It is possible, however, to precisely determine very low concentrations of a constituent by measuring its radioactive decay properties. In order to understand how U-Th series radionuclides can provide such low-level tracer information, a brief review of the basic principles of radioactive decay and the application of these radionuclides as geochronological tools is useful. " The U-Th decay series together consist of 36 radionuclides that are isotopes (same atomic number, Z, different atomic mass, M) of 10 distinct elements (Figure 1). Some of these are very short-lived (tj j 1 -nd are thus not directly useful as marine tracers. It is the other radioisotopes with half-lives greater than 1 day that are most useful and are the focus of this chapter. 

Accurate atomic weight values do not automatically follow from precise measurements of relative atomic masses, however, since the relative abundance of the various isotopes must also be determined. That this can be a limiting factor is readily seen from Table 1.3 the value for praseodymium (which has only 1 stable naturally occurring isotope) has two more significant figures than the value for the neighbouring element cerium which has 4 such isotopes. In the twelve years since the first edition of this book was published the atomic weight values of no fewer than 55 elements have been improved, sometimes spectacularly, e.g. Ni from 58.69( 1) to 58.6934(2). 

Elements with 1 predominant isotope can also, potentially, permit very precise atomic weight determinations since variations in isotopic composition or errors in its determination have a correspondingly small effect on the mass-spectrometrically determined value of the atomic weight. Nine elements have 1 isotope that is more than 99% abundant (H, He, N, O, Ar, V, La, Ta... 

In the periodic table, atomic masses are listed directly below the symbol of the element. In the table on the inside front cover of this text, atomic masses are cited to four significant figures. That ordinarily will be sufficient for our purposes, although more precise values are available (see the alphabetical list of elements on the inside back cover). 

Atomic masses calculated in this manner, using data obtained with a mass spectrometer can in principle be precise to seven or eight significant figures. The accuracy of tabulated atomic masses is limited mostly by variations in natural abundances. Sulfur is an interesting case in point. It consists largely of two isotopes, fiS and fgS. The abundance of sulfur-34 varies from about 4.18% in sulfur deposits in Texas and Louisiana to 4.34% in volcanic sulfur from Italy. This leads to an uncertainty of 0.006 amu in the atomic mass of sulfur. 

The nuclear charge and the electrons it attracts primarily determine the ways in which atoms behave toward other atoms. Mass differences cause only minor chemical effects. Since the isotopes of an element have the same nuclear charge and the same number of electrons per neutral atom, they react in the same ways. Thus we can speak of the chemistry of oxygen without specifying which one of the three stable isotopes is reacting. Only the most precise measurements will indicate the very slight chemical differences among them. 

The relative error is the absolute error divided by the true value it is usually expressed in terms of percentage or in parts per thousand. The true or absolute value of a quantity cannot be established experimentally, so that the observed result must be compared with the most probable value. With pure substances the quantity will ultimately depend upon the relative atomic mass of the constituent elements. Determinations of the relative atomic mass have been made with the utmost care, and the accuracy obtained usually far exceeds that attained in ordinary quantitative analysis the analyst must accordingly accept their reliability. With natural or industrial products, we must accept provisionally the results obtained by analysts of repute using carefully tested methods. If several analysts determine the same constituent in the same sample by different methods, the most probable value, which is usually the average, can be deduced from their results. In both cases, the establishment of the most probable value involves the application of statistical methods and the concept of precision. 

Different isotopes differ in their atomic masses. The intensities of the signals from different isotopic ions allow isotopic abundances to be determined with high accuracy. Mass spectrometry reveals that the isotopic abundances in elemental samples from different sources have slightly different values. Isotopic ratios vary because isotopes with different masses have slightly different properties for example, they move at slightly different speeds. These differences have tiny effects at the level of parts per ten thousand (0.0001). The effects are too small to appear as variations In the elemental molar masses. Nevertheless, high-precision mass spectrometry can measure relative abundances of isotopes to around 1 part in 100,000. 

Despite his numerous achievements, Mendeleyev is remembered mainly for the periodic table. Central to his concept was the conviction that the properties of the elements are a periodic function of their atomic masses. Today, chemists believe that the periodicity of the elements is more apparent when the elements are ordered by atomic number, not atomic mass. However, this change affected Mendeleyevs periodic table only slightly because atomic mass and atomic number are closely correlated. The periodic table does not produce a rigid rule like Paulis exclusion principle. The information one can extract from a periodic table is less precise. This is because its groupings contain elements with similar, but not identical, physical and chemical properties. 

ICP-MS presents various shortcomings as compared to the requirements of an ideal PS-MS technique (Tables 8.62 and 8.56). Simultaneous detectors, as in ToF-MS or array-detector atomic mass spectra (ADAMS), offer several advantages in terms of sensitivity, precision, LOD (50ppq), resolving power and sample throughput. PS-ToFMS and ICP-ADAMS are still in their infancy. 

In the graphic form the abscissa represents the mass of ions (to be more precise, the mass-to-charge ratio, m/z), while the ordinate represents the relative intensity of these ions peaks. Atomic mass units (unified atomic mass unit) or daltons are used as units to measure masses of ions, while intensity is represented in percent relative to the base peak in the spectmm or to the total abundance of all the ions in the spectra. The atomic mass unit (dalton) is equal to the mass of one-twelvth of the mass of a 12C atom (1,661 x 10-27 g) (see Chapter 1). 

Named by a French chemist, Lavoisier, hydrogen (H) is the first chemical element of the periodic table of elements with an atomic number of one. At standard temperature and pressure, hydrogen is a colourless, tasteless, odourless and easily flammable gas. With its atomic mass of 1.00797 g/mol, hydrogen is the lightest element. The British scientist, Henry Cavendish, was the first to identify H as a distinct element in 1766, publishing precise values for its specific weight and density (NHA, 2007). 

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 total atomic mass (weight) of an atom consists almost entirely of the total mass of both the protons and the neutrons. The negatively charged electron has a mass of less than 1/2000 that of the proton. (The precise figure is 1/1837.) Therefore, the electrons mass is negligible when considering the total atomic mass of an atom. 

Instead of using the integers 37 and 35 as atomic masses, take the more precise atomic weights of the isotopes from Table 3-3 ... 

Precise measurements of the amounts of different isotopes can be important. You need to know the exact measurements if you re asked to figure out an element s atomic mass. To calculate an atomic mass, you need to know the masses of the isotopes and the percentage of the element that occurs as each isotope (this is called the relative abundance ). To calculate an average atomic mass, make a list of each isotope along with its mass and its percent relative abundance. Multiply the mass of each isotope by its relative abundance. Add the products. The resulting sum is the atomic mass. 

---