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Dean’s Analytical Chemistry Handbook 2nd Edition by Pradyot Patnaik 2

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(BQ) Part 2 book Analytical chemistry handbook has contents: Mass spectrometry, radiochemical methods, magnetic susceptibility, electroanalytical methods, thermal analysis, refractometry, elemental analysis of organic compounds,...and other contents.

Source: DEAN’S ANALYTICAL CHEMISTRY HANDBOOK SECTION 10 MASS SPECTROMETRY 10.1 INSTRUMENT DESIGN Figure 10.1 Components of a Mass Spectrometer 10.1.1 Inlet Sample Systems 10.2 IONIZATION METHODS IN MASS SPECTROMETRY 10.2.1 Electron Ionization 10.2.2 Chemical Ionization 10.2.3 Other Ionization Methods 10.3 MASS ANALYZERS 10.3.1 Magnetic-Deflection Mass Analyzer 10.3.2 Double-Focusing Sector Spectrometers 10.3.3 Quadrupole Mass Analyzer 10.3.4 Time-of-Flight Spectrometer Figure 10.2 Quardrupole Mass Analyzer 10.3.5 Ion-Trap Mass Spectrometer 10.3.6 Additional Mass Analyzers 10.3.7 Resolving Power 10.4 DETECTORS 10.4.1 Electron Multiplier 10.4.2 Faraday Cup Collector 10.5 CORRELATION OF MASS SPECTRA WITH MOLECULAR STRUCTURE 10.5.1 Molecular Identification 10.5.2 Natural Isotopic Abundances Table 10.1 Isotopic Abundances and Masses of Selected Elements 10.5.3 Exact Mass Differences 10.5.4 Number of Rings and Double Bonds 10.5.5 General Rules 10.5.6 Metastable Peaks 10.6 MASS SPECTRA AND STRUCTURE 10.6.1 Initial Steps in Elucidation of a Mass Spectrum 10.6.2 General Rules for Fragmentation Patterns 10.6.3 Characteristic Low-Mass Fragment Ions 10.6.4 Characteristic Low-Mass Neutral Fragments from the Molecular Ion Table 10.2 Mass Spectra of Some Selected Compounds 10.7 SECONDARY-ION MASS SPECTROMETRY 10.8 ISOTOPE-DILUTION MASS SPECTROMETERY (IDMS) 10.9 QUANTITATIVE ANALYSIS OF MIXTURES Table 10.3 Mass Spectral Data (Relative Intensities) for the C1 to C3 Alcohols 10.10 HYPHENATED GC-MS AND LC-MS TECHNIQUES 10.10.1 GC-MS 10.10.2 LC-MS Bibliography 10.2 10.2 10.2 10.3 10.3 10.3 10.4 10.4 10.5 10.5 10.5 10.5 10.6 10.6 10.7 10.7 10.7 10.7 10.8 10.8 10.8 10.8 10.8 10.9 10.10 10.10 10.10 10.11 10.11 10.11 10.12 10.12 10.13 10.23 10.24 10.24 10.25 10.26 10.26 10.27 10.28 10.1 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MASS SPECTROMETRY 10.2 SECTION TEN Mass spectrometry is the analytical technique that provides the most structural information for the least amount of analyte material It provides qualitative and quantitative information about the atomic and molecular composition of inorganic and organic materials and their chemical structures As an analytical technique it possesses distinct advantages: Increased sensitivity over most other analytical techniques because the analyzer, as a mass-charge filter, reduces background interference Excellent specificity from characteristic fragmentation patterns to identify unknowns or confirm the presence of suspected compounds Information about molecular weight Information about the isotopic abundance of elements Mass spectrometry often fails to distinguish between optical and geometrical isomers and the positions of substituent in o-, m- and p- positions in an aromatic ring Also, its scope is limited in identifying hydrocarbons that produce similar fragmented ions Sec 20 and in the environmental analysis of trace organic pollutants is highlighted in Sec 21 10.1 INSTRUMENT DESIGN Functionally, all mass spectrometers have these components (Fig 10.1): (1) inlet sample system, (2) ion source, (3) ion acceleration system, (4) mass (ion) analyzer, (5) ion-collection system, usually an electron multiplier detector, (6) data-handling system, and (7) vacuum system connected to components (1) through (5) To provide a collision-free path for ions once they are formed, the pressure in the spectrometer must be less than 10–6 torr 10.1.1 Inlet Sample Systems Gas samples are transferred from a vessel of known volume (3 mL), where the pressure is measured, into a reservoir (3 to L) Volatile liquids are drawn through a sintered disk into the low-pressure reservoir in which they are vaporized instantly Oftentimes a nonvolatile compound can be converted into a derivative that has sufficient vapor pressure The gaseous sample enters the source through a pinhole in a piece of gold foil For analytical work, molecular flow (where the mean free path of gas molecules is greater than the tube diameter) is usually preferred However, in isotope-ratio studies viscous flow (where the mean free path is FIGURE 10.1 Components of a mass spectrometer (From Shugar and Dean, The Chemist’s Ready Reference Handbook, McGraw-Hill, New York, 1990.) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MASS SPECTROMETRY MASS SPECTROMETRY 10.3 smaller than the tube diameter) is employed to avoid any tendency for various components to flow differently from the others 10.2 IONIZATION METHODS IN MASS SPECTROMETRY Ionization methods in mass spectrometry are divided into gas-phase ionization techniques and methods that form ions from the condensed phase inside the ion source All ion sources are required to produce ions without mass discrimination from the sample and to accelerate them into the mass analyzer The usual source design has an ion withdrawal and focusing system The ions formed are removed electrostatically from the chamber Located behind the ions is the repeller, which has the same charge as the ions to be withdrawn A strong electrostatic field between the first and second accelerating slits of 400 to 4000 V, which is opposite in charge to the ions, accelerates the ions to their final velocities 10.2.1 Electron Ionization The electron ionization source is a commonly used ionization method The ionizing electrons from the cathode of an electron gun located perpendicular to the incoming gas stream collide with the sample molecules to produce a molecular ion A source operating at 70 V, the conventional operating potential, also has sufficient energy to cause the characteristic fragmentation of sample molecules Some compounds not produce a molecular ion in an electron ionization source This is a disadvantage of this source A mass spectrometer is calibrated in the electron ionization mode Perfluoroalkanes are often used as markers because they provide a peak at intervals of masses corresponding to CF2 groups 10.2.2 Chemical Ionization1 Chemical ionization results from ion–molecule chemical interactions that involve a small amount of sample with an exceedingly large amount of a reagent gas The source must be tightly enclosed with an inside pressure of 0.5 to 4.0 torr The pressure outside the source is kept about orders of magnitude less than the inside by a differential pumping system Often the primary reason for using this technique is to determine the molecular weight of a compound For this purpose a low-energy reactant, such as tert-C4H9+ (from isobutane) is frequently used In the first step the reagent gas is ionized by electron ionization in the source Subsequent reactions between the primary ion and additional reagent gas produce a stabilized reagent gas plasma When a reagent ion encounters a sample molecule (MH), several products may be formed: MH2+ by proton transfer M+ by hydride abstraction MH+ by charge transfer Practically all the spectral information will be clustered around the molecular ion, or one mass unit larger or smaller, with little or no fragmentation This type of ionization is desirable when an analysis of a mixture of compounds is needed and the list of possible components is limited The general absence of carbon–carbon cleavage reactions for the chemical ionization spectra means that they provide little skeletal information B Munson, “Chemical Ionization Mass Spectrometry,” Anal Chem 49:772A (1977) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MASS SPECTROMETRY 10.4 SECTION TEN Negative chemical ionization2 can be conducted with hydroxide and halide ions For these studies the charges on the repeller and accelerating slits in the ion source are reversed with the repeller having a negative charge 10.2.3 Other Ionization Methods The less frequently used ionization methods receive only brief mention here For more details consult the references cited Field ionization3 and field desorption4 are techniques used for studying surface phenomena, such as adsorbed species and trapped samples, and the results of chemical reactions on surfaces; they are also suitable for handling large lipophilic polar molecules Fast atom bombardment5 and plasma (californium-252) desorption6 techniques deal rather effectively with polar substances (usually of higher molecular weight) and salts Samples may be bulk solids, liquid solutions, thin films, or monolayers In thermal ionization the sample is put on a filament substrate (a metal ribbon), which is heated in the mass spectrometer source until the sample evaporates (ca 2000°C) Filament-loading procedures tend to be element-specific Both positive and negative ions are produced, and thermal ionization usually results in the formation of long-lived, stable ion beams Thermal ionization is appropriate for inorganic compounds that have ionization potentials in the range from to eV On the other hand, the technique is inefficient for organic compounds because their ionization potentials usually range from to 16 eV Laser desorption methods7–9 produce a microplasma that consists of neutral fragments together with elementary molecular and fragment ions Suitable mass spectrometers are limited to time-offlight and Fourier-transform spectrometers The recent development of electrospray ionization10 has extended the range of masses amenable to study by mass spectrometery to above several hundred kilodaltons, and commercial instruments are available 10.3 MASS ANALYZERS The function of the mass analyzer is to separate the ions produced in the ion source according to their different mass–charge ratios The analyzer section is continuously pumped to a very low vacuum so that ions may be passed through it without colliding with the gas molecules The energies and velocities v of the ions moving into the mass analyzer are determined by the accelerating voltage V from the ion source slits and the charge z on the ions of mass m: 1 m1v12 = m2 v22 = m3 v32 = L = zV 2 2 (10.1) R C Dougherty, “Negative Chemical Ionization Mass Spectrometry,” Anal Chem 53:625A (1981) M Anbar and W H Aberth, “Field Ionization Mass Spectrometry,” Anal Chem 46:59A (1974) W D Reynold, “Field Desorption Mass Spectrometry,” Anal Chem 51:283A (1979) M Barber et al., “Fast Atom Bombardment Mass Spectrometry,” Anal Chem 54:645A (1982) R D MacFarlane, “Californium-252 Plasma Desorption Mass Spectrometry,” Anal Chem 55:1247A (1983) R J Cotter, “Lasers and Mass Spectrometry,” Anal Chem 56:485A (1984) E R Denoyer et al., “Laser Microprobe Mass Spectrometry: Basic Principles and Performance Characteristics,” Anal Chem 54:26A (1982) D M Hercules et al., “Laser Microprobe Mass Spectrometry: Applications to Structural Analysis,” Anal Chem 54:280A (1980) 10 C M Whitehouse et al., Anal Chem 57:675 (1985) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MASS SPECTROMETRY MASS SPECTROMETRY 10.5 10.3.1 Magnetic-Deflection Mass Analyzer In a single-focusing magnetic-sector mass analyzer, the ion source, the collector slit, and the apex of the sector shape (usually 60°) are colinear Upon entering the magnetic field, the ions are classified and segregated into beams, each with a different m/z ratio m H 2r2 = 2V z (10.2) where H is the strength of the magnetic field and r is the radius of the circular path followed by the ions Since the radius and the magnetic field strength are fixed for the particular sector instrument, only ions with the proper m/z ratio will pass through the analyzer tube without striking the walls, where they are neutralized and pumped out of the system as neutral gas molecules Focusing is accomplished by changing either the electrostatic accelerating voltage or the magnetic field strength; often the former is allowed to diminish while the spectrum is scanned Each m/z ion from light to heavy is successively swept past the detector slit at a known rate The detector current is amplified and displayed on a strip-chart recorder Since the ion paths are separated from one another, the recorder signal will fall to the baseline and then rise as each mass strikes the detector The height of the peaks on the chart will be proportional to the number of ions of the corresponding mass– charge ratio A magnetic-sector mass analyzer has a mass range of 2500 Da at 4-kV ion accelerating voltage Mass resolution is continuously variable up to 25 000 (10% valley definition) Metastable peaks that aid in structural elucidation are also recorded 10.3.2 Double-Focusing Sector Spectrometers Because single-focusing mass analyzers are not velocity focusing for ions of a given mass, their resolving power is limited In double-focusing mass spectrometers an electrostatic deflection field is incorporated between the ion source and the magnetic analyzer Resolving power lies in the range of 100 000 Additional focusing is achieved with quadrupole lenses placed before the electrostatic field and between the electrostatic and magnetic fields 10.3.3 Quadrupole Mass Analyzer In the quadrupole mass analyzer, ions from the ion source are injected into the quadrupole array, shown in Fig 10.2 Opposite pairs of electrodes are electrically connected; one pair at +Udc volts and the other pair at −Udc volts An rf oscillator supplies a signal to each pair of rods, but the signal to the second pair is retarded by 180° When the ratio Udc/Vrf is controlled, the quadrupole field can be set to pass ions of only one m/z ratio down the entire length of the quadrupole array When the dc and rf amplitudes are changed simultaneously, ions of various mass–charge ratios will pass successively through the array to the detector and an entire mass spectrum can be produced Registration of negative ions, as from a chemical ionization source, is possible with two electron multipliers, one for positive and one for negative ions Scan rates can reach 780 Da ⋅ s–1 before resolution is significantly affected The quadrupole mass analyzer is ideal for coupling with a gas chromatograph Practical m/z limits are 4000 Da 10.3.4 Time-of-Flight Spectrometer In the time-of-flight (TOF) mass spectrometer, the ions leave the source as discrete ion packets by pulsing the voltage on the accelerating slits at the exit of the ion source Upon leaving the accelerating slits, the ions enter into the field-free region (drift path) of the flight tube, 30 to 100 cm long, Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MASS SPECTROMETRY 10.6 SECTION TEN FIGURE 10.2 Quadrupole mass analyzer (From Shugar and Dean, 1990.) with whatever velocity they have acquired [Eq (15.1)] Because their velocities are inversely proportional to the square roots of their masses, the lighter ions travel down the flight tube faster than the heavier ions The original ion packet becomes separated into “wafers” of ions according to their mass–charge ratio The wafers are collected sequentially at the detector A spectrum can be recorded every 10 s This makes the TOF mass spectrometer suitable for kinetic studies and for coupling with a gas chromatograph to examine effluent peaks 10.3.5 Ion-Trap Mass Spectrometer A quadrupole ion-trap consists of three electrodes; two end-cap electrodes normally are held at ground potential and between them a ring electrode to which an rf potential, often in the megahertz range, is applied to generate a quadrupole electric field These components can be held in the palm of the hand Ionization in ion traps is commonly achieved by electron ionization, which occurs within the trap Chemical ionization uses the variable time scale of the ion trap first to generate reagent ions via electron impact and then allows these reagent ions to react with the vaporized analyte molecules Both ionization methods are limited to gaseous samples Desorption ionization methods enable mass spectrometry application to fragile nonvolatile compounds, which can be implemented by forming ions in an external source by fast ion bombardment or secondary ion mass spectrometry, and then injecting them into the trap Although trapped ions can be mass-analyzed by several methods, a mass-selective instability scan is used most commonly In this procedure, a change in operating voltages is used to cause trapped ions of a particular m/z ratio to adopt unstable trajectories By scanning the amplitude of the rf voltage applied to the ring electrode, ions of successively increasing m/z are made to adopt unstable trajectories and to exit the ion trap, where they can be detected by using an externally mounted electron multiplier Other methods for mass analysis have been described.11 11 R G Cooks et al., Chem Eng News 1991(March 25):26 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MASS SPECTROMETRY MASS SPECTROMETRY 10.7 10.3.6 Additional Mass Analyzers Space precludes more than mention of the more sophisticated mass analyzers, such as the Fouriertransform (ion-trap) mass spectrometer,12,13 tandem mass spectrometers,14 triple quadrupole mass spectrometer,15 and inductively coupled plasma–mass spectrometer.16 Triple quadrupole instruments are now routinely used in protein structure determinations, pesticide residue analysis, and drug metabolism studies 10.3.7 Resolving Power The most important parameter of a mass analyzer is its resolving power Using the 10% valley definition, two adjacent peaks (whose mass differences are ∆m) are said to be separated when the valley between them is 10% or less of the peak height (and the peak heights are approximately equal) For this condition, ∆m/m equals the peak width at a height that is 5% of the individual peak height A resolution of part in 800 adequately distinguishes between m/z values 800 and 801 so long as the peak intensity ratio is not greater than 10 to However, if one wanted to distinguish between the parent peaks of 2,2-naphthylbenzothiophene (260.0922) and 1,2-dimethyl-4-benzoylnaphthalene (260.1201), the required resolving power is m 260 = = 9319 ∆ m 260.1201 − 260.0922 (10.3) 10.4 DETECTORS After leaving a mass analyzer, the resolved ion beams sequentially strike some type of detector The electron multiplier, either single or multichannel, is most commonly used 10.4.1 Electron Multiplier In the electron multiplier the ion beam strikes a conversion dynode, which converts the ion beam to an electron beam A discrete dynode multiplier has 15 to 18 individual dynodes arranged in a venetian blind configuration and coated with a material that has high secondary-electron-emission properties A magnetic field forces the secondary electrons to follow circular paths, causing them to strike successive dynodes A microchannel plate is a solid-state electron multiplier composed of a hexagonal closepacked array of millions of independent, continuous, single-channel electron multipliers all fused together in a rigid parallel array With channel densities on the order of 106 per cm2, these devices are one of the highest pixel density sensors known Pore diameters range from 10 to 25 mm The inside of each pore, or channel, is coated with a secondary-electron-emissive material; thus each channel constitutes an independent electron multiplier The onset of ion feedback within the channel can be staved off by curving each channel in the plate but at the cost of considerable spatial distortion 12 M V Buchanan and R L Hettich, “Fourier Transform Mass Spectrometry of High-Mass Biomolecules,” Anal Chem 65:245A (1993) 13 A G Marshall and L Schweikhard, Int J Mass Spectrom Ion Proc 118/119:37 (1992) 14 J V Johnson and R A Yost, “Tandem Mass Spectrometry for Trace Analysis,” Anal Chem 57:758A (1985) 15 R A Yost and C G Enke, “Triple Quadrupole Mass Spectrometry for Direct Mixture Analysis and Structure Elucidation,” Anal Chem 51:1251A (1979) 16 R S Houk, “Mass Spectrometry of Inductively Coupled Plasma,” Anal Chem 58:97A (1986) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MASS SPECTROMETRY 10.8 SECTION TEN 10.4.2 Faraday Cup Collector The Faraday cup collector consists of a cup with suitable suppressor electrodes, to suppress secondary-ion emission, and guard electrodes It is placed in the focal plane of the mass spectrometer 10.5 CORRELATION OF MASS SPECTRA WITH MOLECULAR STRUCTURE 10.5.1 Molecular Identification In the identification of a compound, the most important information is the molecular weight The mass spectrometer is able to provide this information, often to four decimal places One assumes that no ions heavier than the molecular ion form when using electron-impact ionization The chemical ionization spectrum will often show a cluster around the nominal molecular weight Several relationships aid in deducing the empirical formula of the parent ion (and also molecular fragments) From the empirical formula hypothetical molecular structures can be proposed using the entries in the formula indices of Beilstein (Beilsteins Handbuch der Organischen Chemie) and Chemical Abstracts 10.5.2 Natural Isotopic Abundances The relative abundances of natural isotopes produce peaks one or more mass units larger than the parent ion (Table 10.1a) For a compound CwHxNyOz, there is a formula that allows one to calculate the percentage of the heavy isotope contributions from a monoisotopic peak PM to the PM +1 peak: 100 PM +1 PM = 0.015 x + 1.11w + 0.37 y + 0.037z (10.4) TABLE 10.1 Isotopic Abundances and Masses of Selected Elements (a) Abundances of some polyisotopic elements, % Element 1H 2H 12C 13C 14N 15N Abundance 99.985 0.015 98.892 1.108 99.63 0.37 Element Abundance Element Abundance 16O 99.76 0.037 0.204 92.18 4.71 3.12 33S 0.76 4.22 75.53 24.47 50.52 49.48 17O 18O 28Si 29Si 30Si 34S 35Cl 37Cl 79Br 81Br (b) Selected isotope masses Element Mass Element Mass 1H 1.0078 12.0000 14.0031 15.9949 18.9984 27.9769 31P 30.9738 31.9721 34.9689 55.9349 78.9184 126.9047 12C 14N 16O 19F 28Si 32S 35Cl 56Fe 79Br 127I Source: J A Dean, ed., Lange’s Handbook of Chemistry, 14th ed., McGraw-Hill, New York, 1992 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MASS SPECTROMETRY MASS SPECTROMETRY 10.9 Tables of abundance factors have been calculated for all combinations of C, H, N, and O up to mass 500.17 Compounds that contain chlorine, bromine, sulfur, or silicon are usually apparent from prominent peaks at masses 2, 4, 6, and so on, units larger the nominal mass of the parent or fragment ion For example, when one chlorine atom is present, the P + mass peak will be about one-third the intensity of the parent peak When one bromine atom is present, the P + mass peak will be about the same intensity as the parent peak The abundance of heavy isotopes is treated in terms of the binomial expansion (a + b)m, where a is the relative abundance of the light isotope, b is the relative abundance of the heavy isotope, and m is the number of atoms of the particular element present in the molecule If two bromine atoms are present, the binomial expansion is ( a + b) = a + ab + b (10.5) Now substituting the percent abundance of each isotope (79Br and 81Br) into the expansion: (0.505) + 2(0.505)(0.495) + (0.495) gives 0.255 + 0.500 + 0.250 which are the proportions of P:(P + 2):(P + 4), a triplet that is slightly distorted from a 1:2:1 pattern When two elements with heavy isotopes are present, the binomial expansion ( a + b ) m (c + d ) n is used Sulfur-34 enhances the P + peak by 4.22%; silicon-29 enhances the P + peak by 4.71% and the P + peak by 3.12% 10.5.3 Exact Mass Differences If the exact mass of the parent or fragment ions is ascertained with a high-resolution mass spectrometer, this relationship is often useful for combinations of C, H, N, and O (Table 10.1b): Exact mass difference from nearest integral mass + 0.0051z − 0.0031y = number of hydrogens 0.0078 (10.6) One substitutes integral numbers (guesses) for z (oxygen) and y (nitrogen) until the divisor becomes an integral multiple of the numerator within 0.0002 mass unit For example, if the exact mass is 177.0426 for a compound containing only C, H, O, and N (note the odd mass which indicates an odd number of nitrogen atoms), thus 0.0426 + 0.0051z − 0.0031y = hydrogen atoms 0.0078 17 J H Beynon and A E Williams, Mass and Abundance Tables for Use in Mass Spectrometry, Elsevier, Amsterdam, 1963 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MASS SPECTROMETRY 10.10 SECTION TEN when z = and y = The empirical formula is C9H7NO3 since 177 − 7(1) − 1(14) − 3(16) = carbon atoms 12 10.5.4 Number of Rings and Double Bonds The total number of rings and double bonds can be determined from the empirical formula (CwHxIzNy) by the relationship 2( w − x + y + ) when covalent bonds comprise the molecular structure Remember the total number for a benzene ring is (one ring and three double bonds); for a triple bond it is 10.5.5 General Rules If the nominal molecular weight of a compound containing only C, H, O, and N is even, so is the number of hydrogen atoms it contains If the nominal molecular weight is divisible by 4, the number of hydrogen atoms is also divisible by When the nominal molecular weight of a compound containing only C, H, O, and N is odd, the number of nitrogen atoms must be odd 10.5.6 Metastable Peaks A further means of ion characterization is achieved by monitoring specific fragmentations of a chosen parent ion This approach involves monitoring of metastable peaks that correspond to fragmentation that occurs in the first field-free region of a double-focusing mass spectrometer (also of a 60° sector instrument) The field-free region is between the exit of the ion source and the entrance to the mass analyzer Signal detection is dictated by the mass-to-charge ratios of both parent and daughter ions Metastable peaks m* appear as a weak, diffuse (often humped-shaped) peak, usually at a nonintegral mass The one-step decomposition process takes the general form Original ion → daughter ion + neutral fragment (10.7) The relationship between the original ion and daughter ion is given by m* = ( mass of daugher ion) mass of original ion (10.8) For example, a metastable peak appeared at 147.9 mass units in a mass spectrum with prominent peaks at 65, 91, 92, 107, 108, 155, 172, and 200 mass units After trying all possible combinations in the above expression, the fit is given by 147.9 = (172) 200 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website SiO2 HNO3 + HCl + H2SO4 Na2CO3 fusion Na2CO3 fusion 31 126 188, 250 Ta, Nb, Ti, R.E., Th None Ti, Fe Cr Fusion with KHSO4 + NaF HNO3 + H2SO4 Na2CO3 + KNO3 fusion See R.E above 23, 53a, 116, 194, 252, 258, 260, 261 34, 98, 200, 215, 249, 271, 272 53a, 81, 170, 258, 262 131, 214 Tm U V H2S group Fe, Mo HNO3 + HCl + H2SO4 207, 229 Tl Ca SiO2 Salts and Ni SiO2 KOH fusion in Ni crucible 26, 274 Filtn Cupferron pptn of V (NH4)2CO3 sepn H2S sepn Cupferron–CHCl3 sepn Dehydration in H2SO4 soln and filtn Dehydration in HCl soln NH3 pptn NH3 pptn Filtn after dehydration Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website (Continued) To the H2SO4 soln add FeSO4 [→ V(IV)], then a sl excess of KMnO4 [→ V(V)], then NaNO2 (to red excess MnO−4), then urea (to destroy HNO2), and titr with std FeSO4 soln Filt the CO−3 soln., acidify the filtrate, and ppt V with cupferron Ignite ppt., fuse it with KHSO4, leach in dil H2SO4, and det V colorimetrically with H2O2 Ppt H2S group elements from H2SO4 soln., filt., b to expel H2S, and ox soln with KMnO4 Ppt Fe, Mo, etc., with cupferron and ext them into CHCl3 Evap aq phase to SO4 fumes, destroy org matter with HNO3, and evap several times with intermittent addn of H2O to remove N oxides Dil., pass through a Jones reductor, aerate the red soln to ox U(III) to U(IV), and titr with std K2Cr2O7, using diphenylamine sulfonate as indicator Heat melt with H2SO4 to expel HF quant In subsequent (NH4)2CO3 sepns., U remains in filtrate, which is evapd., acidified with H2SO4, red in a Jones reductor, and titrd as in preceding meth Spectrographically Leach melt in H2O, acidify with HCl, ppt Ti with NH3, and ignite ppt Fuse in KHSO4, leach in dil H2SO4, pass through a Jones reductor, and titr with std Fe(III) soln Same Leach melt in H2O, acidify with HCl, ppt ZrO2, TiO2, etc., with NH3, and filt Fume ppt with HNO3 + H2SO4, filt off SiO2, and det Ti colorimetrically with H2O2 Det Ti colorimetrically in filtrate from SiO2 detn MINERAL ANALYSIS 23.25 Filtn Anion exchange Same Expulsion with HBr Fe, Mn, Al Pb Fe, Mn Cd Pb, insol matter Cu, V, Mn, Fe Same + Sn HF + H2SO4 HNO3 + H2SO4 HNO3 + H2SO4 HNO3 + H2SO4 Same See R.E above 102, 158a, 226, 229 49, 124, 266 104 115 81, 170, 212, 213 232 Yb Zn Filtn of PbSO4 NH3 pptn Anion exchange NH3 pptn Pptn with NH3 + (NH4)2S2O8 Fe, Mn, Al HNO3 + HCl See R.E above Y Fractional distn of liq air Anion exchange Mo HCl 202 Air Filtn of WO3 Extn of WO3 with aq NH3 Type of separation Ca, Fe, Mn, Mo Insol matter Separations required from HCl + HNO3(10:1) Decomposition with 99, 127, 216, 268 Mineral numbers Xe W Element determined TABLE 23.4 Procedures for the Analysis of Minerals (Continued) Evap the soln of samp to dryness several times with intermittent addn of HCl, add aq NH3 + (NH4)2S2O8 to ppt Al, Fe, and Mn, filt., and b to expel NH3 Remove Cu by treatment with met Pb and titr Zn with std K4Feoc soln.; or titr Zn with std EDTA after addn of CN− (to mask Cu) and HCHO (to demask Zn) Evap the H2SO4 soln of samp to dryness, dissolve residue in dil HCl, and continue with NH3 + (NH4)2S2O8, etc., as in preceding method Evap filtrate from the PbSO4 to dryness and continue as in preceding meth Pass a dil H2SO4-HI soln of samp through an anion-exchange column If present, remove Fe, etc., from the eluate with aq NH3 after evapn to dryness Det Zn in eluate by titrn with EDTA Evap filtrate from the PbSO4 or insol matter to dryness, dissolve the salts in 1M HCl, pass soln through an anion-exchange column to remove the elements indicated, elute Zn with 3M HNO3, and det it as above Same Mass spectroscopy Decomp samp by heating with 100 mL HCl, add 10 mL HNO3, and evap to 10 mL Dil., let stand, filt off WO3, dissolve it in aq NH3, and filt B the soln to expel NH3, ppt W with cinchonine, ignite, and weigh as WO2 In a 50:10 HCl–HF soln., Mo is retained on anion-exchange resin In the eluate, det W either grav with cinchonine as above, or photometrically with hydroquinone or dithiol Procedure MINERAL ANALYSIS 23.26 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Filtn SiO2 KOH fusion (see treatment for minerals 26 and 274) 214 Filtn of insol ZrSiO4 (see R.E.) R.E Heating with hot concd H2SO4 168, 271 NH3 pptn Dehydration and filtn (NH4)2S pptn in presence of H2Tart Salts and Ni SiO2 Fe KOH fusion in Ni crucible 26, 274 Source: L Meites, ed., Handbook of Analytical Chemistry, McGraw-Hill, New York, 1963 Zr Leach melt in H2O, acidify with HCl, and ppt Zr, etc., with aq NH3 Filt., evap ppt to fumes with HNO3 + H2SO4, dil., filt., add H2Tart, make soln ammoniacal, and ppt with H2S Filt., acidify the filtrate, and ppt Zr + Ti with cupferron Ignite and weigh the mixed oxides; correct for TiO2 (detd colorimetrically with H2O2) The zircon is not attacked by the H2SO4 treatment After filtn., fuse residue with KOH as in preceding meth and continue as described there Filt off SiO2 To the H2SO4 soln add excess H2O2, then g (NH4)2HPO4 Filt., ignite, and weigh as ZrP2O7 Or ppt Zr with bromomandelic acid and ignite to ZrO2 MINERAL ANALYSIS 23.27 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website MINERAL ANALYSIS Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Source: DEAN’S ANALYTICAL CHEMISTRY HANDBOOK SECTION 24 METHODS FOR DETERMINATION OF WATER IN GASES, LIQUIDS AND SOLIDS Table 24.1 Methods for the Determination of Water in Gases Table 24.2 Methods for the Determination of Water in Liquids Table 24.3 Methods for the Determination of Water in Solids 24.2 24.4 24.7 There is no single technique applicable to measure water in solid, liquid, and gaseous substances although the Karl Fischer titrimetric procedure is widely used and the method to which all other methods are often compared The analytical chemist must review need with respect to required precision and accuracy, water concentration, and skills available, as well as equipment on hand Often speed is the most important criterion, particularly in production facilities An excellent treatise on methods for the determination of water is the three-part monograph by Mitchell and Smith.1 There is also a much abbreviated treatment by Mitchell.2 Selected methods and techniques are outlined in Tables 24.1 through 24.3 Some comments on various methods are now given The Karl Fischer method is perhaps the most widely used procedure for the determination of water Although this method works well in many cases, the commercial reagents are rather costly, the visual titration end point is difficult to discern, and there are numerous interferences, including oxidizing agents, unsaturated compounds, and thio compounds Liang3 discusses automatic on-line monitoring by flow-injection sampling Infrared spectrometry is broadly useful for determining water in the gas, liquid, or solid phase Several absorption bands can be used; the most useful are located in the near-infrared region at about 1.9 mm and in the fundamental region at about 2.7 and mm The reviews by Kaye4 and Wheeler5 and the report by Keyworth6 provide useful information on the near-infrared region Procedures based on colorimetry usually employ CoCl2 (blue when anhydrous) or CoBr2 (green when anhydrous) that change to red for the fully hydrated salts Cobalt chloride in ethanol gives an absorption maximum at 671 nm Anhydrous ethanol can be used to extract water from the solid sample Other substances that have found specific uses as colorimetric reagents have been methylene blue for traces of water in jet fuels, halides, ketones, and hydrocarbons; cobalt bromide–impregnated strips for testing halogenated refrigerants, gasoline, and oils; fuchsine for estimating water in granulated sugar and refinery pastes; and chloranilic acid for organic solvents except those containing amino-nitrogen John Mitchell, Jr., and D M Smith, Aquametry, 2d ed., Wiley, New York, 1977–1980, Parts I–III J Mitchell, Jr., in F J Welcher, ed., Standard Methods of Chemical Analysis, 6th ed., Van Nostrand, New York, 1966, Vol 3, Part B, Chap 64 Y Y Liang, Anal Chem 62:2504 (1990) W Kaye, Spectrochim Acta 6:257 (1954); 7:181 (1955) O H Wheeler, Chem Rev 59:629 (1959) D A Keyworth, Talanta 8:461 (1961) 24.1 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Low ppm 0.5%–5% Pass through reagent at 100°C, absorb NH3 in standard H2SO4 [2] NH3 ≡≡ 3H2O Alcoholic extraction; measure absorbance at 671 nm [4] Pass gas through CaC2 at 180 to 200°C; pass C2H2 released through ammoniacal Cu2SO4 and determine as red-colored CuC2 [2,16] Pass through tared tube containing P2O5 or other suitable desiccant Increase in weight is proportional to H2O [2] Measure absorbance at suitable wavelength [2,5] Absorbance of moisture in air at 27.97 mm using a water vapor laser [13] Measure absorbance at 127 nm [6] Measure m/e = 18 [2] Separation through packed column of Carbowax 20M or Porapak Q at 150°C [2,7,12] Reaction of H2O with CaC2; separation of resulting C2H2 by gas–liquid (OV-11 or DC 710) or gas–solid (silica gel at 80°C) chromatography [2] Separation through packed column of Porapak N [17] Measure heat transfer [8] Pass gas sample through a cold trap containing CaC2 on which water is condensed; heat trap to 90°C and determine C2H2 produced [14] Measure temperature before and after passage of gas through CaH2 [2] Absorbed the released NH3 in H3BO3 and measure electrical conductivity [9] Magnesium nitride (volumetric) Cobalt(II) chloride (colorimetric) Calcium carbide (colorimetric) Absorption (gravimetric) Infrared spectrophotometry Vacuum ultraviolet Mass spectrometry Gas chromatography Thermal conductivity Mass spectrometry (indirect) Calcium hydride (thermometric) 24.2 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Magnesium nitride (conductometric) High ppm ppm ≥1 mg Several volume percent 2–100 ppm ppm to few percent 0.5%–5% ppm ppm 0.1%–1% 0.5% to several percent 0.5% to few percent 0.1% to few percent Pass gas through molten reagent at 60°C, absorb released HCl in water, and titrate with standard Na borate [3] H2O ≡≡ 2HCl Succinyl chloride (volumetric) ppm to several percent Range Condensation; alcohol, acid, or tert-amine extraction; titration to electrometric or visual end point [1] H2O ≡≡ I2 Procedure and references Karl Fischer (volumetric) Method and technique TABLE 24.1 Methods for the Determination of Water in Gases Other volatile bases or acids ROH, RCOCH3, RCHO, NH3 Hydrocarbons Other compounds with same retention time Other compounds with same retention time Other compounds contributing to m/e = 18 Substances absorbing 105–150 nm, such as CH4, H2S ROH, RNH2 Other components of air have negligible effect Other substances absorbed by desiccant ROH Colored substances Other volatile bases or acids ROH, RNH2, R2NH, acids RCHO, RSH Interferences METHODS FOR DETERMINATION OF WATER IN GASES, LIQUIDS AND SOLIDS Measure relative humidity with psychrometer or hygrometer [2,11] Hygrometry Measure pressure before and after removal of H2O [2] Vapor pressure (manometric) J Mitchell, Jr., and D M Smith, Aquametry, 2d ed., Wiley-Interscience, New York, 1977–1980, three volumes J Mitchell, Jr., in I M Kolthoff and P J Elving, eds, Treatise in Analytical Chemistry, Part II, Vol 1, Interscience, New York, 1961 C B Belcher, Thompson, and T S West, Anal Chim Acta, 19:148 (1958) Singliar and Zubák, Chem prumysl 6:426 (1956) Curcio and Petty, J Opt Soc Am 41:302 (1951) Garton, Webb, and Wildy, J Sci Instrum 34:496 (1957) S Dal Nogare and Safranski, in J Mitchell et al., eds., Organic Analysis, Interscience, New York, 1960, Vol R H Cherry, Anal Chem 20:958 (1948) Peck, Zedek, and Wittova, Chem prumysl 5:219 (1955) 10 F A Keidel, Anal Chem 31:2043 (1959) 11 Weaver, Hughes, and Diniak, J Res Natl Bur Stand (U.S.) 60:489 (1958) 12 V M Sakharov, G S Beskova, and A I Butusova, Zh Anal Khim 31:250 (1976) (English, p 214) 13 P B Lund and L Kinnunen, J Phys E Sci Instrum 9:528 (1976) 14 G L Carlson and W R Morgan, Appl Spectrosc 31:48 (1977) 15 H Gerber, Res Dev 28:17 (Nov 1977) 16 W Boller, Chemiker-Ztg 50:537 (1983) 17 F F Andrawes, Anal Chem 55:1869 (1983) 18 E Flaherty, C Herold, and D Murray, Anal Chem 58:1903 (1986) Pass over cooled polished metal surface; measure temperature at which dew forms, as observed photometrically or visually [2,18] Dew-point measurement Supersaturation hygrometer utilizing a thermo-optical system that senses growth of salt particles optically and controls their growth by heating the substrate with an infrared source Output of heater is a measure of ambient relative humidity [15] Pass through electrolyte cell containing P2O5 and measure current [10] Electrolysis Other compounds that condense Other substances that condense Low percent ROH, RCHO, NH3, CH3COCH3, HF 1–1000 ppm Several volume percent Area of 100% relative humidity ppm to 0.1% METHODS FOR DETERMINATION OF WATER IN GASES, LIQUIDS AND SOLIDS 24.3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website 0.1% to several percent ppm to few percent Hydrolyze with strong acid and catalyst Titrate sample and blank with standard NaOMe [3] After hydrolysis, add known excess aniline, and titrate sample and blank with standard HClO4 in HOAc [4] Titrate sample with acetic anhydride in HOAc, using strong acid as catalyst [2] Measure absorbance in near-infrared region, 14 286 to 5000 cm−1 [2] Acetic anhydride (volumetric) Measure proton resonance Chemical shift varies with water concentration and H bonding [2] Measure intensity of blue color from water absorption in paper impregnated with FeSO4 and K ferricyanide [6] Paper chromatography Measure absorbance in fundamental region at or near 3590 cm−1 A drying technique was established employing vacuum distillation onto 4A molecular sieves [14] Nuclear magnetic resonance spectroscopy Infrared spectrophotometry (spectrophotometric) Hydrolyze at 110°C and determine excess acetic anhydride by measuring absorbance at 252 nm [2,5] After reaction with reagent in Kjeldahl assembly, remove NH3 by steam distillation and determine acidimetrically [2] Magnesium nitride (volumetric) (conductometric) 0.1% to several percent 0.1% to several percent 0.01% to few percent 0.01% to few percent Reaction with reagent at room temperature, treatment of excess reagent with MeOH, and titration of sample and blank with standard base [1,2] Acetyl chloride (volumetric) 0.1% to few percent Several percent 0.05% to several percent 0.02% to several percent 0.001%–0.1% Water in organic solvents determined by flow injection and measurement at 546 nm [21] Karl Fischer (flow injection) ppm to 100% Range Titration in inert solvent (e.g., MeOH or pyridine) to electrometric or visual end point [1,2] Procedure and references Karl Fischer (volumetric) Method and technique TABLE 24.2 Methods for the Determination of Water in Liquids ROH, RNH2 ROH, RNH2 ROH, RNH2, R2NH Same as acetyl chloride method Same as acetyl chloride method ROH, RNH2, R2NH Steam-distillable bases or acids; high concentrations of MeOH HCOOH, RCHO, strong R3N, high concentrations of ROH, RNH2 or R2NH Ketals RCHO, RSH, NH2OH, (RCOO)2, quinone, ascorbic acid Interferences METHODS FOR DETERMINATION OF WATER IN GASES, LIQUIDS AND SOLIDS 24.4 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Use a preliminary distillation step with a low-efficiency column, heating up to 135–150°C, then cooling the two-phase distillate at −10 to −20°C The water will solidify and reject the dissolved hydrocarbons from the crystal matrix, which can then be decanted [12] Measure dielectric constant directly in solution using high-frequency technique [8] A microwave resonance method for water in oil emulsions uses the difference in dielectric properties between water and oil [15] Measure current flowing through electrodes at fixed potential [9] Titrant is LiH in dimethylsulfoxide for water in organic solvents [11] Distillation Dielectric constant Conductivity Conductometric titration Water in dimethylformamide and dimethylsulfoxide determined by luminescence lifetime measurements of Eu(III) [18] Measure temperature rise on mixing sample with acetic anhydride and HClO4 catalyst [7] Acetic anhydride (thermometric) Luminescence lifetime Molten salt (AlCl3–N-butylpyridinium chloride) and water generates HCl which is electrochemically reduced at a rotating Pt disk electrode [19] Voltammetry Measure pressure rise when sample and CaC2 react in closed vessel [2] Thin-film perfluorosulfonate ionomer sensors overcoated with cellulose triacetate, polyvinyl alcohol–H3PO4 composite films operated in a pulsed voltammetric mode Water in sample equilibrates with sensing film between pulses and is then electrolyzed by the pulse [17] Voltammetric sensor Measure volume H2 evolved when sample and CaH2 react in gas-volumetric apparatus [9] Water and alcohols in gasoline blends separated on HPLC ion exclusion columns (Ultrastyragel 100 and 500 Å) with toluene as mobile phase [20] Size exclusion and adsorption chromatography Calcium hydride (gasometric) Columns using microparticulate normal phase, reversed phase, and ion exchange with NaCl in eluant and using a conductivity detector [22] HPLC Calcium carbide (manometric) Column packed with Porapak Q and kept at 150°C Reaction with 2,2-dimethoxypropane and a solid acid catalyst (Nafion resin) for min, followed by capillary column GC for acetone formed [16] Instantaneous reaction with a 0.5 nM ortho ester (triethyl orthoformate) and catalyst (methanesulfonic acid) followed by capillary column GC for ethanol formed [17] Gas chromatography 0.05–5 mol % Several percent Several percent 0.3% to several percent 1% to high percent 0.5% to few percent Linear up to 50 mM 0.04–0.2 mL 2.5 ppm up to 50% 0.03%–2% As low as 0.001% or 13.4 ppm As low as 0.001% or 13.4 ppm (Continued) ROH, RCHO, NH3 ROH Other conducting substances Other compounds having high dielectric constant ROH, RNH2, R2NH METHODS FOR DETERMINATION OF WATER IN GASES, LIQUIDS AND SOLIDS Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website 24.5 Measure specific gravity directly in known system where water is only variable [2] Measure refractive index of known system where water is only variable [2] b -Rays passed through sample and measured with appropriate counter [10] Density or specific gravity Refractometry Radiochemical (b -ray absorption) Range 0.1%–1% Variable Variable 0.3% to few percent J Mitchell, Jr., and D M Smith, Aquametry, 2d ed., Wiley-Interscience, New York, 1977–1980, in three parts J Mitchell, Jr., in I M Kolthoff and P J Elving, eds., Treatise on Analytical Chemistry, Interscience, New York, 1961, Part II, Vol Toennies and Elliott, J Am Chem Soc., 57:2136 (1935); 59:902 (1967) Das, J Indian Chem Soc 34:247 (1957) S Bruckenstein, Anal Chem 28:1920 (1956) Stringer, Nature, 167:1071 (1951) L H Greathouse, H J Janssen, and C H Haydel, Anal Chem 28:356 (1956) Oehme, Angew Chem 68:457 (1956) Perryman, Analyst 70:45 (1945) 10 Friedman, Zisman, and Sullivan, U.S Patent No 2,487,797 (1949) 11 C Yoshimura, K Miyamoto, and K Tamura, Bunseki Kagaku 27:310 (1978); Chem Abstr 89: 16126 (1978) 12 T H Gouw, Anal Chem 49:1887 (1977) 13 J Kovarik, Chem Abstr 86:56052 (1977) 14 A Barbetta and W Edgell, Appl Spectrosc 32:93 (1978) 15 D A Doherty, Anal Chem 49:690 (1977) 16 K D Dix, P A Sakkinen, and J S Fritz, Anal Chem 61:1325 (1989) 17 H Huang and P K Dasgupta, Anal Chem 64:2406 (1992) 18 S Lis and G R Choppin, Anal Chem 63:2542 (1991) 19 S Sakami and R A Osteryoung, Anal Chem 55:1970 (1983) 20 M Zinbo, Anal Chem 56:244 (1984) 21 I Norden-Andersson and A Edergren, Anal Chem 57:2571 (1985) 22 T S Stevens and K M Chritz, Anal Chem 59:1716 (1971) Measure turbidity or cloud point on titration with water-immiscible liquid (e.g., xylene or mineral oil) [2] Procedure and references Turbidity Method and technique TABLE 24.2 Methods for the Determination of Water in Liquids (Continued) ROH Unknown constituents Unknown constituents Other compounds only slightly soluble in sample solution Interferences METHODS FOR DETERMINATION OF WATER IN GASES, LIQUIDS AND SOLIDS 24.6 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Few to several percent Several percent 0.1% to several percent

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