Mass difference

Exact Mass Differences. If the exact mass of the parent or fragment ions are ascertained with a high-resolution mass spectrometer, this relationship is often useful for combinations of C, H, N, and O (Table 1.15b) ... 

Exact mass difference from nearest integral mass -I- 0.005 Iz — 0.003 ly 0.0078... 

When unusual mass differences occur between some fragments ions, the presence of F (mass difference 19), I (mass difference 127), or P (mass difference 31) should be suspected. 

The efficiency of separation of solvent from solute varies with their nature and the rate of flow of liquid from the HPLC into the interface. Volatile solvents like hexane can be evaporated quickly and tend not to form large clusters, and therefore rates of flow of about 1 ml/min can be accepted from the HPLC apparatus. For less-volatile solvents like water, evaporation is slower, clusters are less easily broken down, and maximum flow rates are about 0.1-0.5 ml/min. Because separation of solvent from solute depends on relative volatilities and rates of diffusion, the greater the molecular mass difference between them, the better is the efficiency of separation. Generally, HPLC is used for substances that are nonvolatile or are thermally labile, as they would otherwise be analyzed by the practically simpler GC method the nonvolatile substances usually have molecular masses considerably larger than those of commonly used HPLC solvents, so separation is good. 

In general terms, the main function of the magnetic/electric-sector section of the hybrid is to be able to resolve m/z values differing by only a few parts per million. Such accuracy allows highly accurate measurement of m/z values and therefore affords excellent elemental compositions of ions if these are molecular ions, the resulting compositions are in fact molecular formulae, which is the usual MS mode. Apart from accurate mass measurement, full mass spectra can also be obtained. The high-resolution separation of ions also allows ions having only small mass differences to be carefully selected for MS/MS studies. 

A constant-mass-difference scan. Source ions (m, f,. .., fj) are passed successively by Q1 into Q2, where collisionally induced dissociation occurs. Q3 is set to pass only those ions produced in Q2 that have a predetermined mass difference (Am) between the ions passed by Ql. In this example, they are m, - f, (= Am) and f, - fj (= Am), so, although all ions pass into Q2, only f, f, have a mass difference (Am) equal to that selected for Q3. 

In a (B/E)(l - E) -scanning mode, a mass difference is seiected. For exampie, in this case a precursor ion m, is chosen (it is shown as being made up of two parts of mass mj, n,). After fragmentation, the product ion is mj accompanied by a neutral particle of mass n,. The mass difference (n, = m, - mj) can be specified so only pairs of ions connected by this difference are found. 

An electron carries one unit of negative electrical charge (Figure 46.2). Its mass is about 1/2000 that of a proton or neutron. Therefore, very little of the mass of an atom is made from the masses of the electrons it contains, and generally the total mass of the electrons is ignored. For example, an atom of iron has a mass of 56 atomic units (au also called Daltons), of which only about 0.02% is due to the 26 electrons. Thus an iron atom (Fe ) is considered to have the same mass as a doubly charged cation of iron (Fe " ), even though there is a small mass difference. 

One of the most significant sources of change in isotope ratios is caused by the small mass differences between isotopes and their effects on the physical properties of elements and compounds. For example, ordinary water (mostly Ej O) has a lower density, lower boiling point, and higher vapor pressure than does heavy water (mostly H2 0). Other major changes can occur through exchange processes. Such physical and kinetic differences lead to natural local fractionation of isotopes. Artificial fractionation (enrichment or depletion) of uranium isotopes is the basis for construction of atomic bombs, nuclear power reactors, and depleted uranium weapons. 

Near a conduction band minimum the energy of electrons depends on the momentum ia the crystal. Thus, carriers behave like free electrons whose effective mass differs from the free electron mass. Their energy is given by equation 1, where E is the energy of the conduction band minimum, is the... 

The physical and thermodynamic properties of elemental hydrogen and deuterium and of their respective oxides illustrate the effect of isotopic mass differences. 

High mass resolution techniques are used to separate peaks at the same nominal mass by the very small mass differences between them. As an example, a combination of Si and H to form the molecular ion Si H , severely degrades the detection limit of phosphorous ( P) in a silicon sample. The exact mass of phosphorous ( P) is 31.9738 amu while the real masses of the interfering Si H and Si H2 molecules are 31.9816 amu and 31.9921 amu, respectively. Figure 8 shows a mass... 

Other technique—for example, dynamic secondary ion mass spectrometry or forward recoil spectrometry—that rely on mass differences can use the same type of substitution to provide contrast. However, for hydrocarbon materials these methods attain a depth resolution of approximately 13 nm and 80 nm, respectively. For many problems in complex fluids and in polymers this resolution is too poor to extract critical information. Consequently, neutron reflectivity substantially extends the depth resolution capabilities of these methods and has led, in recent years, to key information not accessible by the other techniques. 

Surface composition analysis by LEIS is based on the use of noble gas ions as projectiles, making use of the superb surface sensitivity of LEIS under these conditions. A consequence of this surface sensitivity is that the LEIS energy spectrum consists of lines, one per element, if the masses differ sufficiently. The lines are narrow, because inelastic energy losses play a minor role here. Thus, the information on the atomic species present is deduced from the energy of the back-scattered ions, which can be converted to the mass of the scattering center. (Eig. 3.55 [3.141]). In Eig. 3.55 it is shown that the mass range, where LEIS is sensitive, depends on the projectile mass. 

A special type of substituent effect which has proved veiy valuable in the study of reaction mechanisms is the replacement of an atom by one of its isotopes. Isotopic substitution most often involves replacing protium by deuterium (or tritium) but is applicable to nuclei other than hydrogen. The quantitative differences are largest, however, for hydrogen, because its isotopes have the largest relative mass differences. Isotopic substitution usually has no effect on the qualitative chemical reactivity of the substrate, but often has an easily measured effect on the rate at which reaction occurs. Let us consider how this modification of the rate arises. Initially, the discussion will concern primary kinetic isotope effects, those in which a bond to the isotopically substituted atom is broken in the rate-determining step. We will use C—H bonds as the specific topic of discussion, but the same concepts apply for other elements. 

The resolution required in any analytical SEC procedure, e.g., to detect sample impurities, is primarily based on the nature of the sample components with respect to their shape, the relative size differences of species contained in the sample, and the minimal size difference to be resolved. These sample attributes, in addition to the range of sizes to be examined, determine the required selectivity. Earlier work has shown that the limit of resolvability in SEC of molecules [i.e., the ability to completely resolve solutes of different sizes as a function of (1) plate number, (2) different solute shapes, and (3) media pore volumes] ranges from close to 20% for the molecular mass difference required to resolve spherical solutes down to near a 10% difference in molecular mass required for the separation of rod-shaped molecules (Hagel, 1993). To approach these limits, a SEC medium and a system with appropriate selectivity and efficiency must be employed. 

Unfortunately, this value is sample and system dependent just by using polymer standards with different molar masses, different values of peak resolution can be generated. 

It would appear, therefore, that the oil of the mass differs in com. posilioD from the cil of the t aru id contaioiDga far lower proportion of aulphiic oompouiids. and is certainly less offersive in smell. 

The energy liberated in nuclear reactions is of such magnitude that mass differences are relatively easy to detect. The same mass-energy considerations pertain to chemical reactions. However, the energies involved are millions of times smaller, and mass differences are virtually impossible to detect. Discussions of energies involved in chemical reactions do not include mass energy. Nevertheless, there is eveiy reason to believe that mass energy is involved. 

At the same time it is recognized that the pairs of substances which, on mixing, are most likely to obey Raoult s law are those whose particles are most nearly alike and therefore interchangeable. Obviously no species of particles is likely to fulfill this condition better than the isotopes of an element. Among the isotopes of any element the only difference between the various particles is, of course, a nuclear difference among the isotopes of a heavy element the mass difference is trivial and the various species of particles are interchangeable. Whether the element is in its liquid or solid form, the isotopes of a heavy element form an ideal solution. Before discussing this problem we shall first consider the solution of a solid solute in a liquid solvent. 

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. 

Compare this mass difference of about 0.02 g/mole with one of about 5 X 10" g/mole for the combustion of carbon. 

To aid in determining the number of carboxyl groups, prepare a derivative using trideuterated Methyl-8 (Pierce cat. no. 49200), using the same procedure previously given. Inject 1-2 pd of the trideuterated methyl ester separately or mix equal portions of the nondeuterated methyl ester with the trideuterated methyl ester, and inject 2 pd immediately into the GC/MS system. From the mass difference, it is easy to determine the number of carboxyl groups present. 

B. Method for determining the number of —COOH groups in a molecule The TMS derivative of an acid can be converted to the methyl ester using anhydrous methanolic HQ. 1 2 3 Obtain a mass spectrum of the TMS derivative of the acid, and then evaporate the TMS reaction mixture with clean, dry nitrogen. Add 250 pd of anhydrous methanolic HC1 (Pierce cat. no. 33050) and heat at 60° for 20 min. Many TMS derivatives of acids are converted to methyl esters at room temperature after 20 min. If the sample is rerun as the methyl ester, the number of carboxyl groups can be determined by the mass differences before and after making the methyl ester from the TMS derivative. 

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