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chemical engineering

Quantitative Chemical Analysis 8th edition Daniel C. Harris - Solutions

The molecular ion region in the mass spectrum of a large molecule, such as a protein, consists of a cluster of peaks differing by 1 Da. This pattern occurs because a molecule with many atoms has a high probability of containing one or several atoms of 13C, 15N, 18O, 2H, and 34S. In fact, the
Define the unit dalton. From this definition, compute the mass of 1 Da in grams. The mean of 60 measurements of the mass of individual E. coli cells vaporized by MALDI and measured with a quadrupole ion trap was 5.03 (± 0.14) × 1010 Da. Express this mass in femtograms.
Phytoplankton at the ocean surface maintain the fluidity of their cell membranes by altering their lipid (fat) composition when the temperature changes. When the ocean temperature is high, plankton synthesize relatively more 37:2 than 37:3.46After they die, plankton sink to the ocean floor and end
Chlorate (CO-3), chlorite (CO-2) , bromate (BrO-3), and iodate (IO-3) can be measured in drinking water at the 1-ppb level with 1% precision by selected reaction monitoring. Chlorate and chlorite arise from ClO2 used as a disinfectant. Bromate and iodate can be formed from Br-or I- when water is
In isotope dilution, a known amount of an unusual isotope (called the spike) is added to an unknown as an internal standard for quantitative analysis. After the mixture has been homogenized, some of the element of interest must be isolated. The ratio of the isotopes is then measured. From this
Nickel has two major and three minor isotopes. For the purpose of this problem, suppose that the only isotopes are 58Ni and 60Ni. The atomic mass of 58Ni is 57.935 3 Da and the mass of 60Ni is 59.9332 Da. From the amplitude of the peaks in the following spectrum, calculate the atomic mass of Ni and
Measure the width at half-height of the tallest peak in the spectrum below and calculate the resolving power of the spectrometer from the expression m/m1/2. Would you expect to be able to distinguish two peaks at 10000 and 10001 Da?
The two peaks near m/z 31.00 in Figure 21-9 differ in mass by 0.010 Da. Estimate the resolving power of the spectrometer from the expression m/∆m without making any measurements in the figure.Figure 21-9
The highest resolution mass spectra are obtained by Fourier transform ion cyclotron resonance mass spectrometry. Molecular ions of two peptides (chains of seven amino acids) differing in mass by 0.000 45 Da were separated with a 10% valley between them. The ions each have a mass of 906.49 Da and a
The mass of a fragment ion in a high-resolution spectrum is 83.086 5 Da. Which composition, C5H7O+ or C6H+11, better atches the observed mass?
Calculate the theoretical masses of the species in Figure 21-9 and compare your answers with the values observed in the figure.Figure 21-9
Consider the extraction of Mn+ from aqueous solution into organic solution by reaction with protonated ligand, HL:Rewrite Equation 22-13 in terms of Kextraction and express Kextraction in terms of the constants in Equation 22-13. Give a physical reason why each constant increases or decreases
Butanoic acid has a partition coefficient of 3.0 (favoring benzene) when distributed between water and benzene. Find the formal concentration of butanoic acid in each phase when 100 mL of 0.10 M aqueous butanoic acid is extracted with 25 mL of benzene (a) At pH 4.00 and (b) At pH 10.00.
For a given value of [HL]org in Equation 22-13, over what pH range (how many pH units) will D change from 0.01 to 100 if n = 2?Equation 22-13
For the extraction of Cu2+ by dithizone in CCl4, KL= 1.1 × 104, KM = 7 × 104, Ka = 3 × 10-5, β = 5 × 1022, and n = 2.(a) Calculate the distribution coefficient for extraction of 0.1 μM Cu2+ into CCl4 by 0.1 mM dithizone at pH 1.0 and at pH 4.0.(b) If 100 mL of 0.1 μM aqueous Cu2+ are
Consider the extraction of 100.0 mL of M2+ (aq) by 2.0 mL of 1 × 10-5 M dithizone in CHCl3, for which KL = 1.1 × 104, KM = 7 × 104, Ka = 3 × 10-5, β = 5 × 1018, and n = 2. (a) Derive an expression for the fraction of metal ion extracted into the organic phase, in terms of the distribution
The theoretical limit for extracting solute S from phase 1 (volume V1) into phase 2 (volume V2) is attained by dividing V2 into an infinite number of infinitesimally small portions and conducting an infinite number of extractions. With a partition coefficient K = [S]2/[S]1, the limiting fraction of
(a) Write the meaning of the retention factor, k, in terms of time spent by solute in each phase.(b) Write an expression in terms of k for the fraction of time spent by a solute molecule in the mobile phase.(c) The retention ratio in chromatography is defined as Show that R is related to the
(a) A chromatography column with a length of 10.3 cm and inner diameter of 4.61 mm is packed with a stationary phase that occupies 61.0% of the volume. If the volume flow rate is 1.13 mL/min, find the linear flow rate in cm/min. (b) How long does it take for solvent (which is the same as unretained
An open tubular column is 30.1 m long and has an inner diameter of 0.530 mm. It is coated on the inside wall with a layer of stationary phase that is 3.1 μm thick. Unretained solute passes through in 2.16 min, whereas a particular solute has a retention time of 17.32 min. (a) Find the linear and
A chromatographic procedure separates 4.0 mg of unknown mixture on a column with a length of 40 cm and a diameter of 0.85 cm.(a) What size column would you use to separate 100 mg of the same mixture?(b) If the flow is 0.22 mL/min on the small column, what volume flow rate should be used on the
Solvent passes through a column in 3.0 min but solute requires 9.0 min.(a) Calculate the retention factor, k.(b) What fraction of time is the solute in the mobile phase in the column?(c)The volume of stationary phase is 1/10 of the volume of the mobile phase in the column (Vs = 0.10Vm). Find the
Solvent occupies 15% of the volume of a chromatography column whose inner diameter is 3.0 mm. If the volume flow rate is 0.2 mL/min, find the linear flow rate.
Consider a chromatography column in which Vs = Vm/5. Find the retention factor if K = 3 and if K = 30.
The retention volume of a solute is 76.2 mL for a column with Vm = 16.6 mL and Vs = 12.7 mL. Calculate the retention factor and the partition coefficient for this solute
An open tubular column has an inner diameter of 207 μm and the thickness of the stationary phase on the inner wall is 0.50 μm. Unretained solute passes through in 63 s and a particular solute emerges in 433 s. Find the partition coefficient for this solute and find the fraction of time spent in
Isotopic compounds are separated in Figure 22-15 by repeated passage through a pair of columns. Each cycle in the figure represents one pass through length L = 50 cm containing N theoretical plates. The unadjusted relative retention is γ = 1.018.
Chromatograms of compounds A and B were obtained at the same flow rate with two columns of equal length.(a) Which column has more theoretical plates? (b) Which column has a larger plate height?
Why does plate height depend on linear flow rate, not volume flow rate?
(a) Why is it difficult to extract the EDTA complex of aluminum into an organic solvent but easy to extract the 8-hydroxyquinoline complex? (b) If you need to bring the EDTA complex into the organic solvent, should you add a phase transfer agent with a hydrophobic cation or a hydrophobic anion?
Describe how nonlinear partition isotherms lead to non- Gaussian bandshapes. Draw the bandshape produced by an overloaded column and a column with tailing.
A separation of 2.5 mg of an unknown mixture has been optimized on a column of length L and diameter d. Explain why you might not achieve the same resolution for 5.0 mg on a column of length 2L and diameter d.
An infinitely sharp zone of solute is placed at the center of a column at time t = 0. After diffusion for time t1, the standard deviation of the Gaussian band is 1.0 mm. After 20 min more, at time t2, the standard deviation is 2.0 mm. What will be the width after another 20 min, at time t3?
A chromatogram with ideal Gaussian bands has tr = 9.0 min and w1/2 = 2.0 min. (a) How many theoretical plates are present? (b) Find the plate height if the column is 10 cm long.
(a) The asymmetric chromatogram in Figure 22-14 has a retention time equal to 15 min, and the values of A and B are 33 and 11 s, respectively. Find the number of theoretical plates. (b) The width of the Gaussian peak in Figure 22-9 at a height equal to 1/10 of the peak height is 4.297σ. Suppose
Why is the extraction of a metal ion into an organic solvent with 8-hydroxyquinoline more complete at higher pH?
A chromatographic band has a width, w, of 4.0 mL and a retention volume of 49 mL. What width is expected for a band with a retention volume of 127 mL? Assume that the only band spreading occurs on the column itself.
A band from a column eluted at 0.66 mL/min has a width at half-height, w1/2, of 39.6 s. The sample was applied as a sharp plug with a volume of 0.40 mL, and the detector volume is 0.25 mL. Find the variances introduced by injection and detection. What would w1/2 be if the only broadening occurred
Two compounds with partition coefficients of 15 and 18 are to be separated on a column with Vm/Vs = 3.0 and tm = 1.0 min. Calculate the number of theoretical plates needed to produce a resolution of 1.5.
(a) Calculate the number of theoretical plates needed to achieve a resolution of 2.0 for compounds with unadjusted relative retention times of t2/t1 = 1.01, 1.05, or 1.10.(b) How can you increase N and γ = t2/t1 in a chromatography experiment?
Consider the peaks for pentafluorobenzene and benzene in the chromatogram below. The elution time for unretained solute is 1.06 min. The open tubular column is 30.0 m in length and 0.530 mm in diameter, with a layer of stationary phase 3.0 m thick on the inner wall.(a) Find the adjusted retention
A layer with negligible thickness containing 10.0 nmol of methanol (D = 1.6 × 10-9 m2/s) was placed in a tube of water 5.00 cm in diameter and allowed to spread by diffusion. Using Equation 22-25, prepare a graph showing the Gaussian concentration profile of the methanol zone after 1.00, 10.0, and
A 0.25-mm-diameter open tubular gas chromatography column is coated with stationary phase that is 0.25 μm thick. The diffusion coefficient for a compound with a retention factor k = 10 is Dm = 1.0 × 10-5 m2/s in the gas phase and Ds = 1.0 10-9 m2/s in the stationary phase. Consider longitudinal
Consider two Gaussian peaks with relative areas of 4:1. Construct a set of graphs to show the overlapping peaks if the resolution is 0.5, 1, or 2.
The distribution coefficient for extraction of a metal complex from aqueous to organic solvents is D = [total metal]org/[total metal]aq. Give physical reasons why β and Ka appear in the numerator of Equation 22-13, but KL and [H+]aq appear in the denominator.Equation 22-13
Give a physical interpretation of Equations 22-6 and 22-7 in terms of the fractional composition equations for a monoprotic acid discussed in Section 9-5
Solute S has a partition coefficient of 4.0 between water (phase 1) and chloroform (phase 2) in Equation 22-1. (a) Calculate the concentration of S in chloroform if [S(aq)] is 0.020 M. (b) If the volume of water is 80.0 mL and the volume of chloroform is 10.0 mL, find the quotient (mol S in
The weak base B (Kb = 1.0 × 10-5) equilibrates between water (phase 1) and benzene (phase 2). (a) Define the distribution coefficient, D, for this system. (b) Explain the difference between D and K, the partition coefficient. (c) Calculate D at pH 8.00 if K = 50.0. (d) Will D be greater or less at
The weak base B (Kb = 1.0 10-5) equilibrates between water (phase 1) and benzene (phase 2). (a) Define the distribution coefficient, D, for this system. (b) Explain the difference between D and K, the partition coefficient. (c) Calculate D at pH 8.00 if K = 50.0. (d) Will D be greater or less at
(a) What is the advantage of temperature programming in gas chromatography?(b) What is the advantage of pressure programming?
This problem reviews concepts from Chapter 22. An unretained solute passes through a chromatography column in 3.7 min and analyte requires 8.4 min. (a) Find the adjusted retention time and retention factor for the analyte. (b) The volume of the mobile phase is 1.4 times the volume of the stationary
Retention time depends on temperature, T, according to the equation log (a/T) b, where a and b are constants for a specific compound on a specific column. A compound is eluted from a gas chromatography column at an adjusted retention time 15.0 min when the column temperature is 373 K. At 363 K,
What is the purpose of derivatization in chromatography? Give an example.
(a) Explain how solid-phase microextraction works. Why is cold trapping necessary during injection with this technique? Is all the analyte in an unknown extracted into the fiber in solid-phase microextraction?(b) Explain the differences between stir-bar sorptive extraction and solid-phase
Why is splitless injection used with purge and trap sample preparation?
State the order of decisions in method development for gas chromatography.
(a) Why is it illogical to use a thin stationary phase (0.2 m) in a wide-bore (0.53-mm) open tubular column?(b) Consider a narrow-bore (0.25 mm diameter), thin-film (0.10 μm) column with 5 000 plates per meter. Consider also a wide-bore (0.53 mm diameter), thick-film (5.0 μm) column with 1 500
The graph shows van Deemter curves for n-nonane at 70°C in the 3.0-m-long microfabricated column in Box 23-2 with a 1- to 2-m-thick stationary phase.(a) Why would air be chosen as the carrier gas? What is the danger of using air as carrier gas? (b) Measure the optimum velocity and plate height
(a) What are the relative advantages and disadvantages of packed and open tubular columns in gas chromatography?(b) Explain the difference between wall-coated, support-coated, and porous-layer open tubular columns.(c) What is the advantage of bonding (covalently attaching) the stationary phase to
(a) When a solution containing 234 mg of pentanol (FM 88.15) and 237 mg of 2,3-dimethyl 2-butanol (FM 102.17) in 10.0 mL was separated, the relative peak areas were pentanol:2,3 dimethyl-2-butanol 0.913:1.00. Considering pentanol to be the internal standard, find the response factor for
A standard solution containing 6.3 × 10-8 M iodoacetone and 2.0 × 10-7 M p dichlorobenzene (an internal standard) gave peak areas of 395 and 787, respectively, in a gas chromatogram. A 3.00-mL unknown solution of iodoacetone was treated with 0.100 mL of 1.6 × 10-5 M p-dichlorobenzene and the
The gasoline additive methyl t-butyl ether (MTBE) has been leaking into groundwater ever since its introduction in the 1990s. MTBE can be measured at parts per billion levels by solid-phase microextraction from groundwater to which 25% (wt/vol) NaCl has been added (salting out, Problem 7-8). After
Here is a student procedure to measure nicotine in urine. A 1.00-mL sample of biological fluid was placed in a 12-mL vial containing 0.7 g Na2CO3 powder. After 5.00 Î¼g of the internal standard 5-aminoquinoline were injected, the vial was capped with a Teflon-coated silicone rubber septum. The
Nitric oxide (NO) is a cell-signaling agent in physiologic processes including vasodilation, inhibition of clotting, and inflammation. A sensitive chromatography-mass spectrometry method was developed to measure two of its metabolites, nitrite (NO2- ) and nitrate (NO3- ), in biological fluids.
Equation 22-33 contains terms (A, B, and C) describing three band-broadening mechanisms. (a) Which term is 0 for an open tubular column? Why? (b) Express the value of B in terms of measurable physical properties. (c) Express the value of C in terms of measurable physical quantities. (d) The linear
As the inside radius of an open tubular column is decreased, the maximum possible column efficiency increases and sample capacity decreases. For a thin stationary phase that equilibrates rapidly with analyte, the minimum theoretical plate height is given bywhere r is the inside radius of the column
Consider the chromatography of n-C12H26 on a 25-m-long × 0.53-mm-diameter open tubular column of 5% phenyl-95% methyl polysiloxane with a stationary-phase thickness of 3.0 μm and He carrier gas at 125°C. The observed retention factor for n-C12H26 is 8.0. Measurements were made of plate height,
Equation 23-3 gives the mass of analyte extracted into a solid-phase microextraction fiber as a function of the partition coefficient between the fiber coating and the solution.(a) A commercial fiber with a 100-m-thick coating has a film volume of 6.9 × 10-4 mL.26 Suppose that the initial
(a) Why do open tubular columns provide greater resolution than packed columns in gas chromatography? (b) Why do H2 and He allow more rapid linear flow rates in gas chromatography than N2 does, without loss of column efficiency (Figure 23-12)?
Box 23-1 shows the separation of enantiomers with the formula C9H4N2Cl6.(a) Verify that the formula for rings double bonds (21-3) agrees with the structure.(b) Find the nominal mass of C9H4N2Cl6 (Box 21-1)(c) The high-mass region of the electron impact mass spectrum of one enantiomer is shown on
(a) When would you use split, splitless, or on-column injection in gas chromatography?(b) Explain how solvent trapping and cold trapping work in splitless injection.
To which kinds of analytes do the following gas chromatography detectors respond? (a Thermal conductivity (b) Flame ionization (c) Electron capture (d) Flame photometric (e) Nitrogen-phosphorus (f ) Photoionization (g) Sulfur chemiluminescence (h) Atomic emission (i) Mass spectrometer
Why does a thermal conductivity detector respond to all analytes except the carrier gas? Why isn't the flame ionization detector universal?
Explain what is displayed in a reconstructed total ion chromatogram, selected ion monitoring, and selected reaction monitoring. Which technique is most selective and which is least selective and why?
Use Table 23-3 to predict the elution order of the following compounds from columns containing (a) poly(dimethylsiloxane),(b) (diphenyl)0.35(dimethyl)0.65polysiloxane, and (c) poly(ethylene glycol): hexane, heptane, octane, benzene, butanol, 2-pentanone.
Use Table 23-3 to predict the elution order of the following compounds from columns containing (a) poly(dimethylsiloxane), (b) (diphenyl)0.35(dimethyl)0.65polysiloxane, and (c) poly(ethylene glycol): 1. 1-Pentanol (n-C5H11OH, b.p. 138°C) 2. 2-Hexanone (CH3C( O)C4H9, b.p. 128°C) 3. Heptane
(a) Why does eluent strength increase as solvent becomes less polar in reversed-phase chromatography, whereas eluent strength increases as solvent becomes more polar in normal-phase chromatography?(b) What kind of gradient is used in supercritical fluid chromatography?
(a) Sketch a graph of the van Deemter equation (plate height versus linear flow rate). What would the curve look like if the multiple path term were 0? If the longitudinal diffusion term were 0? If the finite equilibration time term were 0?(b) Explain why the van Deemter curve for 1.8-μm particles
The figure below shows the separation of two enantiomers on a chiral stationary phase.(a) From tr and w1/2, find N for each peak.
(a) According to Equation 24-2, if all conditions are constant, but particle size is reduced from 3 μm to 0.7 μm, by what factor must pressure be increased to maintain constant linear velocity? (b) If all conditions except pressure are constant, by what factor will linear velocity increase if
Use Figure 24-15 to suggest which type of liquid chromatography you could use to separate compounds in each of the following categories:(a) Molecular mass < 2 000, soluble in octane(b) Molecular mass < 2 000, soluble in dioxane(c) Molecular mass < 2 000, ionic(d) Molecular mass < 2 000,
Microporous silica particles with a density of 2.2 g/mL and a diameter of 10 μm have a measured surface area of 300 m2/g. Calculate the surface area of the spherical silica as if it were simply solid particles. What does this calculation tell you about the shape or porosity of the particles?
(a) Nonpolar aromatic compounds were separated by HPLC on an octadecyl (C18) bonded phase. The eluent was 65 vol% methanol in water. How would the retention times be affected if 90% methanol were used instead?(b) Octanoic acid and 1-aminooctane were passed through the same column described in part
Consider the chromatogram of deuterated benzenes in Box 24-1. (a) Unretained thiourea, is eluted in 41.7 min. Find the linear velocity ux (mm/s). (b) Find the retention factor k for C6D6. (c) Find the plate number N and plate height for C6D6.
The antitumor drug gimatecan is available as nearly pure (S)-enantiomer. Neither pure (R) enantiomer nor a racemic (equal) mixture of the two enantiomers are available. To measure small quantities of (R)-enantiomer in nearly pure (S)-gimatecan, a preparationPreparation was subjected to normal-phase
Suppose that an HPLC column produces Gaussian peaks. The detector measures absorbance at 254 nm. A sample containing equal moles of compounds A and B was injected into the column. Compound A (ε254] = 2.26 × 104M-1 cm-1) has a height h = 128 mm and a halfwidth w1/2 = 10.1 mm. Compound B (ε254 =
Retention factors for three solutes separated on a C8 nonpolar stationary phase are listed in the table on the next page. Eluent was a 70:30 (vol/vol) mixture of 50 mM citrate buffer (adjusted to pH with NH3) plus methanol. Draw the dominant species of each compound at each pH in the table and
Morphine and morphine 3-Î²-D-glucuronide were separated on two different 4.6-mm diameter Ã— 50-mm-long columns with 3-Î¼m particles.39 Column A was C18-silica run at 1.4 mL/min, and column B was bare silica run at 2.0 mL/min.(a) Estimate the volume, Vm, and time,
The rate at which heat is generated inside a chromatography column from friction of flowing liquid is power (watts, W = J/s) = volume flow rate (m3/s) × pressure drop (pascals, Pa = kg/[m ∙ s2]).(a) Explain the analogy between heat generated in a chromatography column and heat generated in an
Cocaine metabolism in rats can be studied by injecting the drug and periodically withdrawing blood to measure levels of metabolites by HPLC-mass spectrometry. For quantitative analysis, isotopically labeled internal standards are mixed with the blood sample. Blood was analyzed by reversed-phase
HPLC separation of enantiomers of the drug Ritalin on a chiral stationary phase was shown in Problem 24-11.(a) Detection is by atmospheric pressure chemical ionization with selected reaction monitoring of the m/z 234 †’ 84 transition. Explain how this detection works and propose structures for
(a) Explain how to measure k and resolution.(b) State three methods for measuring tm in reversed-phase chromatography.(c) Estimate tm for a 0.46 × 15 cm column containing 5-μm particles operating at a flow rate of 1.5 mL/min. Estimate tm if the particle size were 3.5 μm instead.
What is the difference between dead volume and dwell volume? How do each of these volumes affect a chromatogram?
What does it mean for a separation procedure to be "rugged" and why is it desirable?
What are criteria for an adequate isocratic chromatographic separation?
Explain how to use a gradient for the first run to decide whether isocratic or gradient elution would be more appropriate.
What are the general steps in developing an isocratic separation for reversed-phase chromatography with one organic solvent?
Why are the relative eluent strengths of solvents in adsorption chromatography fairly independent of solute?
What are the general steps in developing an isocratic separation for reversed-phase chromatography with two organic solvents?
What are the general steps in developing an isocratic separation for reversed-phase chromatography with one organic solvent and temperature as variables?

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