Measuring Mass

Measurements are made using appropriate equipment or instruments. The array of equipment and instrumentation used in analytical chemistry is impressive, ranging from the simple and inexpensive, to the complex and costly. With two exceptions, we will postpone the discussion of equipment and instrumentation to those chapters where they are used. The instrumentation used to measure mass and much of the equipment used to measure volume are important to all analytical techniques and are therefore discussed in this section. 

To evaluate the effect of indeterminate error on the data in Table 4.1, ten replicate determinations of the mass of a single penny were made, with results shown in Table 4.7. The standard deviation for the data in Table 4.1 is 0.051, and it is 0.0024 for the data in Table 4.7. The significantly better precision when determining the mass of a single penny suggests that the precision of this analysis is not limited by the balance used to measure mass, but is due to a significant variability in the masses of individual pennies. 

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. 

Isotope Dilution Another important quantitative radiochemical method is isotope dilution. In this method of analysis a sample of analyte, called a tracer, is prepared in a radioactive form with a known activity. Ax, for its radioactive decay. A measured mass of the tracer, Wf, is added to a sample containing an unknown mass, w, of a nonradioactive analyte, and the material is homogenized. The sample is then processed to isolate wa grams of purified analyte, containing both radioactive and nonradioactive materials. The activity of the isolated sample, A, is measured. If all the analyte, both radioactive and nonradioactive, is recovered, then A and Ax will be equal. Normally, some of the analyte is lost during isolation and purification. In this case A is less than Ax, and... 

Quasi-molecular ions, [M + nH], from a protein (myoglobin) of molecnlar mass 16,951.5 Da. In this case, n ranges from 21 (giving a measured mass of 808.221) to 12 (corresponding to a measured mass of 1413.631). The peaks with measured masses in between these correspond to the other values of n between 12 and 21. By taking snccessive pairs of measnred masses, the relative molecular mass of the myoglobin can be calculated very accurately, as shown in Figure 8.4. 

For two successive measured mass-to-charge ratios m and m two equations can be written,... 

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 Q in Q/TOF stands for quadrupole (see Chapter 25, Quadrupole Ion Optics ). A Q/TOF instrument — normally used with an electrospray ion inlet — measures mass spectra directly to obtain molecular or quasi-molecular mass information, or it can be switched rapidly to MS/MS mode to examine structural features of ions. The analyzer layout is presented in Figure 20.2. 

Simple fragmentation of the molecular ion of iodobenzene gives a fragment ion, CjH,. The difference in measured masses between the molecular and fragment ions gives the mass of the ejected neutral iodine atom. 

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. 

A mass spectrometer measures mass-to-charge ratio (m/z) and, often, the charge on the ion is unity, so that m/z = m/1 = m. Thus, a mass spectrometer can be used to measure mass. 

In theory, this process can be reversed in that any measured mass leads to an elemental composition. For example, a measured value of 17 would imply the composition, NH3. 

For larger masses, the possibilities increase enormously. At mass 100, there would be literally thousands of possible elemental compositions so that, although integer mass can be measured mass spectromet-rically, attempts to obtain elemental compositions will not lead to a definite answer. 

A mass spectrometer that can measure mass accurately to several decimal places (rather than just to the nearest integer) can be used to measure such differences. 

In the example given above, a measured mass of 17.0265 would indicate the definite composition NHj and eliminate the other possibility of OH. 

In molecular weight determinations it is conventional to dissolve a measured mass of polymer m2 into a volumetric flask and dilute to the mark with an appropriate solvent. We shall use the symbol Cj to designate concentrations in mass per volume units. In practice, 100-ml volumetric flasks are often used, in which case C2 is expressed in grams per 100 ml or grams per deciliter. Even though these are not SI units, they are encountered often enough in the literature to be regarded as conventional solution units in polymer chemistry. 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

Bulk-wave piezoelectric quartz crystal sensors indirecdy measure mass changes of the coating on the surface of the sensing device. This change in mass causes changes in the resonant frequency of the device, and measurements ate based on frequency differences. 

For theJth. component, my = m iDy is the component mass flow rate in stream i is the mass fraction of component j in stream i and q is the net reaction rate (mass generation minus consumption) per unit volume V that contains mass M. If it is inconvenient to measure mass flow rates, the product of density and volumetric flow rate is used instead. 

Typical mass resolution values measured on the LIMA 2A range from 250 to 750 at a mass-to-charge ratio M/ Z= 100. The parameter that appears to have the most influence on the measured mass resolving power is the duration of the ionization event, which may be longer than the duration of the laser pulse (5—10 ns), along with probable time broadening effects associated with the l6-ns time resolution of the transient recorder. ... 

The measured mass susceptibility values for bucky-bundle (both xb aid xu). Qo. the gray-shell material, the polycrystalline graphite anode, and the... 

The simplest calibration procedure for a gas flow-measuring device is to connect it in series with a reference meter and allow the same flow to pass th tough both instruments. This requires a reference instrument of better metrological quality than the calibrated instrument. One fact to consider when applying this method is that the mass flow rate in the system containing both instruments is constant (assuming no leakage), but the volume flow rate is not. The volume flow rate depends on the fluid density and the density depends on the pressure and the temperature. The correct way to calibrate is to compare either the measured mass... 

To measure product characteristics, such as devices which measure mass, length, or time, or derivatives of these parameters... 

In the old pharmaceutical system of measurements, masses were expressed in grains. There are 5.760 X 103 grains in 1 lb. An old bottle of aspirin lists 5 grains of active ingredient per tablet How many milligrams of active ingredient are there in the same tablet ... 

Allhough (he mass numbers of the proton and neutron are both one, the masses of these fundamental particles are not identical. The mass of one mole of protons is 1.00762 grams and (hai of one mole of neutrons is 1.00893 grams. Furiher invesiigation would show that the experimentally measured mass of the nucleus of any given isotope is not the exact sum of the masses of protons and neutrons confined in ihe nucleus according to our model. For example, the mass of ihe nucleus of the uranium isotope of mass number 233 is less than the exact sum of the masses of 92 protons and 143 neutrons. 

Fig. 3-3. Attenuation and filtering of polychromatic x-rays by aluminum. Variation of effective wavelength with thickness. The effective wavelengths shown in tin figure correspond to the measured mass absorption coefficients. The change ir effective wavelength accounts for the deviations from the (dashed) straight lines The x-ray intensities used gave 210 /xamp through 0.0127-cm aluminum (curve A) 3200 /xamp through 0.381-cm aluminum (curve B). (Liebhafsky, Smith, Tanis, anc Winslow, Anal. Chem., 19, 861.)...

Spectrometric measurements, mass, with irridium effusion cells, heats... 

The results from EQCM studies on conducting polymer films can be ambiguous because the measured mass change results from a combination of independent ion transport, coupled ion transport (i.e., salt transport), and solvent transport. In addition, changes in the viscoelasticity of the films can cause apparent mass changes. The latter problem can be minimized by checking the frequency response of the EQCM,174 while the various mass transport components can be separated by careful data analysis.175,176... 

Figure 2.2. Thermal desorption spectra of carbon monoxide, measured mass spectrometically at mass 28 (atomic units, a.u.), on a platinum (100) surface upon which potassium has been pre-adsorbed to a surface coverage of 0K.7 Reprinted with permission from Elsevier Science.

The measured masses are obtained from the LC-ESMS analysis. 

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