True mass

If the mass of a substance in air is its density the density of weights used in making the weighing p, and the density of air p, the true mass of the substance in vacuo, is... 

One way to characterize the data in Table 4.1 is to assume that the masses of individual pennies are scattered around a central value that provides the best estimate of a penny s true mass. Two common ways to report this estimate of central tendency are the mean and the median. 

If the mean or median provides an estimate of a penny s true mass, then the spread of the individual measurements must provide an estimate of the variability in the masses of individual pennies. Although spread is often defined relative to a specific measure of central tendency, its magnitude is independent of the central value. Changing all... 

Mass Sample (g) True Mass of Analyte (g) Proportional Error (%) Mass of Analyte Determined (g) Percent Analyte Reported (%w/w)... 

Consider, for example, the data in Table 4.1 for the mass of a penny. Reporting only the mean is insufficient because it fails to indicate the uncertainty in measuring a penny s mass. Including the standard deviation, or other measure of spread, provides the necessary information about the uncertainty in measuring mass. Nevertheless, the central tendency and spread together do not provide a definitive statement about a penny s true mass. If you are not convinced that this is true, ask yourself how obtaining the mass of an additional penny will change the mean and standard deviation. 

Typical Cl processes in which neutral sample molecules (M) react with NH to give either (a) a protonated ion [M + HJ or (b) an adduct ion [M + NHJ+ the quasi-molecular ions are respectively 1 and 18 mass units greater than the true mass (M). In process (c), reagent ions (CjHf) abstract hydrogen, giving a quasi-molecular ion that is 1 mass unit less than M. 

Positive-ion electrospray mass spectrum of human hemoglobin (a) as initially obtained with all the measured masses, and (b) after calculation of true mass, as in Figure 8.3. The spectrum transforms into two main peaks representing the main alpha and beta chains of hemoglobin with accurate masses as given. This transformation is fnlly automated. The letters A, B, C refer to the three chains of hemoglobin. Thus, A13 means the alpha chain with 13 protons added. 

The ions so produced are separated by their mass-to-charge (m/z) ratios. For peptides and proteins, the intact molecules become protonated with a number (n) of protons (H+). Thus, instead of the true molecular mass (M), molecular ions have a mass of [M + uH]. More importantly, the ion has n positive charges resulting from addition of the n protons [M + uH]". Since the mass spectrometer does not measure mass directly but, rather, mass-to-charge (m/z) ratio, the measured m/z value is [M + uH]/u. This last value is less than the true molecular mass, depending on the value of n. If the ion of true mass 20,000 Da carries 10 protons, for example, then the m/z value measured would be (20,000 + 10)/10 = 2001. 

This last m/z value is easy to measure accurately, and, if its relationship to the true mass is known (n = 10), then the true mass can be measured very accurately. The multicharged ions have typical m/z values of <3000 Da, which means that conventional quadrupole or magnetic-sector analyzers can be used for mass measurement. Actually, the spectrum consists of a series of multicharged protonated molecular ions [M + nWY for each component present in the sample. Each ion in the series differs by plus and minus one charge from adjacent ions ([M + uH] + n -an integer series for example, 1, 2, 3,. .., etc.). Mathematical transformation of the spectrum produces a true molecular mass profile of the sample (Figure 40.5). 

When multicharged ions are formed, the simple rule of thumb used widely in mass spectrometry that m/z = m because, usually, z = 1 no longer applies for z > 1 then m/z < m, and the apparent mass of an ion is much smaller than its true mass. Accurate mass measurement is much easier at low mass than at high, and the small m/z values, corresponding to high mass with multiple charges, yield accurate values for the high mass. 

General Principles There are two main types of mass flowmeters (1) the so-called true mass flowmeter, which responds directly to mass flow rate, and (2) the inferential mass flowmeter, which commonly measures volume flow rate aud flmd density separately. A variety of types of true mass flowmeters have been developed, including the following (a) the Maguus-effect mass flowmeter, (b) the axial-flow, transverse-momentum mass flowmeter, (c) the radial-flow, transverse-momentum mass flowmeter, (d) the gyroscopic transverse-momentum mass flowmeter, aud (e) the thermal mass flowmeter. Type b is the basis for several commercial mass flowmeters, one version of which is briefly described here. 

Between absorption edges, the photoelectric (true) mass absorption coefficient r can be expressed as the following approximate empirical function of Z and X ... 

The tedium of carrying out a number of these calculations each time an electrospray spectrum is acquired has been removed by the provision of transformation software with the mass spectrometer data system. This software not only carries out the calculations automatically, but also plots the mass spectrum on a true mass scale. 

Transformation The mathematical process of changing a raw electrospray spectrum containing a number of multiply charged ions into a mass spectrum plotted on a true mass scale. 

The corresponding liquid-phase chemistry can be used to promote ion formation by appropriate choice of solvent and pH, salt addition to form M.Na+ or M.NH4+, and postcolumn addition of reagents. The primary applications of ESI-MS are in the biopolymer field. The phenomenon of routine multiple charging is exclusive to electrospray, which makes it a very valuable technique in the fine chemical and biochemical field, because mass spectrometers can analyse high-molecular-mass samples without any need to extend their mass range, and without any loss of sensitivity. However, with ESI, molecules are not always produced with a distribution of charge states [137], Nevertheless, this phenomenon somehow complicates the determination of the true mass of the unknown. With conventional low-resolution mass spectrometers, the true mass of the macromolecule is determined by an indirect and iterative computational method. 

You have purchased a 5 oz. bar of gold (100% pure), at a cost of 400/oz. Because the bar was weighed in air, you conclude that you got a bargain, because its true mass is greater than 5 oz due to the buoyancy of air. If the true density of the gold is 1.9000 g/cm3, what is the actual value of the bar based upon its true mass ... 

The standard uncertainty arising from random effects is typically measured from precision studies and is quantified in terms of the standard deviation of a set of measured values. For example, consider a set of replicate weighings performed in order to determine the random error associated with a weighing. If the true mass of the object being weighed is 10 g exactly, then the values obtained might be as follows ... 

Processes such as decarbonylation, decarboxylation, elimination of water, and several other reactions may also occur prior to ionization, i.e., as non-mass spectral reactions, typically as a result of thermal degradation upon heating of the sample to enforce evaporation. In such a case, the mass spectrum obtained is not that of the analyte itself, but of its decomposition product(s). Sometimes, those thermal reactions are difficult to recognize, because the same neutral loss may also occur by a true mass spectral fragmentation of the corresponding molecular ion. 

In addition to high-profile fuel cell applications such as automotive propulsion and distributed power generation, the use of fuel cells as auxiliary power units (APUs) for vehicles has received considerable attention (see Figure 1-9). APU applications may be an attractive market because it offers a true mass-market opportunity that does not require the challenging performance and low cost required for propulsion systems for vehicles. In this section, a discussion of the technical performance requirements for such fuel cell APUs, as well as the current status of the technology and the implications for fuel cell system configuration and cost is given. 

Before moving on to true mass transport issues it is worthwhile to point out that the quantity vep(Y - Yp) is in fact the water load per unit of time (whichever units of time v is expressed in.) Further that with an a-priori design process we may not know the required cross sectional area for flow and hence it may be more convenient to multiply the above relationship by and thus obtain the adsorbable contaminant input rate ... 

For oxide CMP at PMD and ILD levels, a pilot wafer must be run to estimate the optimal polish time, prior to processing a whole lot. This not only wastes precious production time but also adds a human factor into the process control, a major obstacle that hinders CMP from becoming a true mass-production tool in Si processing. In addition, due to the fact that the polish rate may vary from wafer to wafer in CMP, the final remaining PMD... 

While the experiments are thus conceptually straightforward, this is not always the case with respect to the interpretation and extraction of the true mass accommodation coefficient because of the simultaneous occurrence of all of the processes depicted in Fig. 5.12. The approach to extracting a from the measurements of the net gas uptake was treated above in Section E.l. 

Buoyancy correction Conventional masses are based on weighing at sea level with air density 1.2 kg m 3 and sample density 8000 kg m 3 Rarely needed. Usually ignore with error in true mass of less than 0.01 %... 

Peak maximum standard deviation or maximum difference between the predicted and actual mass. During calibration the difference between the measured mass in the acquired calibration file and the true mass in the reference file is taken for each pair of matched peaks. If this value exceeds the set value, the calibration will fail. Reducing the value of the standard deviation gives a more stringent limit, while increasing the standard deviation means that the requirement is easier to meet, but this may allow incorrect peak matching. 

The protonation reaction leading to MH + depends on the proton affinity of M. Because hydrocarbons of type RH have a low proton affinity, the R+ ion is often seen in the spectrum. Since proton transfer in chemical ionisation can lead to either M + H + or M — H 1, uncertainties can exist as to the true mass of the molecular ion. 

If mass m is read from a balance, the true mass m of the object weighed in vacuum is given by10... 

A pure compound called tris is used as a primary standard to measure concentrations of acids. The volume of acid required to react with a known mass of tris tells us the concentration of the acid. Find the true mass of tris (density = 1.33 g/mL) if the apparent mass weighed in air is 100.00 g. 

Solution Assuming that the balance weights have a density of 8.0 g/mL and the density of air is 0.001 2 g/mL, we find the true mass by using Equation 2-1 ... 

Figure 2-5 shows buoyancy corrections for several substances. When you weigh water with a density of 1.00 g/mL, the true mass is 1.001 I g when the balance reads 1.000 0 g. The... 

B. A sample of ferric oxide (Fc2(), density = 5.24 g/mL) obtained from ignition of a gravimetric precipitate weighed 0.296 1 g in the atmosphere. What is the true mass in vacuum ... 

Potassium hydrogen phthalate is a primary standard used to measure the concentration of NaOH solutions. Find the true mass of potassium hydrogen phthalate (density = 1.636 g/mL) if the... 

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