Mass resolution equation

Three important parameters for mass spectrometers are mass resolution, mass range, and sensitivity. The resolution, R, required to separate two ions of mass m and (m + Am) is given by equation 1. 

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. 

Mass resolution describes the capability of an MS to distinguish ions with different m/z values. It is defined by the M/AM equation in which M is the m/z ratio of a mass peak and AM is the full width of a peak at half its maximum height. The mass resolution of an instrument often correlates with its accuracy. Mass range indicates the m/z range at which the mass analyzer best functions. For example, quadrupole mass analyzers exhibit a mass range of up to 4000 m/z, while the mass ranges of TOF extend up to 100,000. The operating principles of common MS instruments are discussed below. 

The size, shape and charge of the solute, the size and shape of the organism, the position of the organism with respect to other cells (plankton, floes, biofilms), and the nature of the flow regime, are all important factors when describing solute fluxes in the presence of fluid motion. Unfortunately, the resolution of most hydrodynamics problems is extremely involved, and typically bioavailability problems under environmental conditions are in the range of problems for which analytical solutions are not available. For this reason, the mass transfer equation in the presence of fluid motion (equation (17), cf. equation (14)) is often simplified as [48] ... 

In addition to high mass resolution, another important feature of FTMS is its wide mass range (7,8). From examination of the cyclotron equation (Eq. 1), the mass range of FTMS appears to have no upper limit. However, an instrumental upper limit in excess of 100,000 has been suggested (16), based on a detailed study of ion motion (30). From a practical standpoint, the cyclotron... 

The effectiveness factor is obtained by the resolution of the mass transfer equations [12] in a spherical pellet with simple assumptions ... 

The resolution achievable by a quadrupole filter depends on the selection of the U/ Vo ratio and can thus be adjusted throughout the mass range. For this reason the resolution varies throughout a scan of the mass range, with AM in the resolution equation remaining constant. 

As described, PBPK models are systems of mass balance equations describing the mass or concentration of chemicals at various loci within the tissues. Most often the loci have been at the level of the whole organ. However, the mass can be described at as fine a resolution as is necessary and as knowledge allows. For example, a PBPK model can describe the concentration at the cellular or subcellular level (Blancato and Bischoff 1993). Ultimately, the chemical input into pharmacodynamic and systems level models could easily be the output of PBPK models at whatever the necessary resolution. For example, if a perturbation in a specific cell is directly related to a concentration or mass of chemical at that cell, the PBPK model would be expanded to describe that mass or concentration. This though raises... 

In equation (3.1), m is the mass at which two adjacent peaks are resolved by one mass unit (Am = l). Resolved is normally taken to mean overlap at 10% of the height of the peaks. Thus, an analyser with a resolution of 500 can provide unit mass resolution at mass 500 Da. That is, molecules separated by one mass unit can be distinguished. However, that analyser can only distinguish molecules that differ by two mass units at 1000 Da. This illustrates the need for high-resolution analysers to characterize large molecules such as organic phosphates. Furthermore, unit mass resolution is not always sufficient when complex mixtures such as... 

Finally, once the mean volumetric growth rate is known, the resolution of the mass balance equation for biomass can serve to calculate biomass concentration and productivity as a function of operating parameter (lighting conditions and dilution rate D—or residence time Tp = 1 /D—resulting from the liquid flow rate of the feed) ... 

The constraint variable suggested in our previous study of fault-effect tree model (Lee et al., 1999) are used to increase the resolution. It represents the quantitative governing equation such as the balance equation and valve relation as variables. The previous study used a mass balance and two control valve equations for CSTR. As the control valve equations are expressed by DELS model, this study uses only mass balance equation. Reactor leaking (RX-LK) is a root cause of the positive deviation of the constraint variable, DF that is defined as Fq - Fp... 

The practical mass resolution of this configuration is called the resolving power and calculated as shown in the following equation ... 

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