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Skoog/Holler/Crouch Chapter 26 Principles of Instrumental Analysis, 6th ed. Instructor’s Manual
CHAPTER 26
26-1. (a) Elution is a process in which species are washed through a chromatographic column by the flow or addition of fresh solvent. (b) The mobile phase in chromatography is the one the moves over or through an immobilized phase that is fixed in place in a column or on the surface of a flat plate. (c) The stationary phase in a chromatographic column is a solid or liquid that is fixed in place. The mobile phase then passes over or through the stationary phase. (d) The distribution constant K in chromatography is the ratio of the concentration (strictly acitivity) of the analyte in the stationary phase to its concentration (activity) in the mobile phase when equilibrium exists between the two phases. (e) The retention time for an analyte is the time interval between its injection onto a column and the appearance of its peak at the other end of the column. (f) The retention factor k is defined by the quation k = K A V S/ V M where K A is the distribution constant for species A and V S and V M are the volumes of the stationary and mobile phases respectively.
(g) The selectivity factor α of a column toward species A and B is given by α = K B/ K A,
where K B is the distribution constant of the more strongly held species and K A is the distribution constant for the less strongly held species. (h) The plate height H of a chromatographic column is defined by the relationship
H = σ^2 /L
where σ^2 is the variance obtained from the Gaussian shaped chromatographic peak and L
is the length of the column in cm. (i) Longitudinal diffusion is a source of band broadening in a column in which a solute diffuses from the concentrated center of the band to the more dilute regions on either side. (j) Eddy diffusion is a phenomenon in which molecules of an analyte reach the end of a column at different times as a result of traveling through the column by pathways that differ in length. (k) The resolution R s of a column toward two species A and B is given by the equation R s = 2Δ Z /( W A + W B) where Δ Z is the distance (in units of time) between the peaks for the two species and W A and W B are the widths (also in units of time) of the peaks at their bases. (l) The eluent in chromatography is the fresh mobile phase that carries the analyte through the column. 26-2. The general elution problem arises whenever chromatograms are obtained on samples that contain species with widely different distribution constants. When conditions are such that good separations of the more stongly retained species are realized, lack of resolution among the weakly held species is observed. Conversely when conditions are chosend that give satisfactory separations of the weakly retained compounds, severe band broadening and long retention times are encountered for the strongly bound species. The general elution problem is often solved in liquid chromatography by gradient elution and in gas chromatography by temperature programming.
26-10. Longitudinal diffusion is much more important in GC that in LC. Longitudinal diffusion is a large contribution to H at low flow rates. The initial decreases in H in plots of plate height vs. flow rate are thus largely the result of longitudinal diffusion.. Because gaseous diffusion coefficients are orders of magnitude larger than liquid values, the phenomenon becomes noticeable at higher flow rates in GC than in LC. The minimum is sometimes not observed at all in LC. 26-11. Gradient elution is a method of performing liquid chromatography in which the composition of the mobile phase is change continuously or in steps in order to optimize separations. 26-12. Zone separation is influenced by (1) packing that produce distribution coefficients that differ significantly; (2) increases in the column length; (3) variations in mobile phase composition (LC); (4) optimizing column temperature (GC); (5) changes in the pH of the mobile phase (LC); (6) incorporation of a species in the stationary phase that selectively complexes certain analytes (LC). 26-13. Slow sample introduction leads to band broadening. 26-14. N = 16( t R/ W )^2 (Equation 26-21) (a) For A, N = 16 × (5.4/0.41)^2 = 2775.49 or 2775 For B, N = 16 × (13.3/1.07)^2 = 2472.04 or 2472 For C, N = 16 × (14.1/1.16)^2 = 2363.97 or 2364 For D, N = 16 × (21.6/1.72)^2 = 2523.31 or 2523 (b) N = (2775.49 + 2472.04 + 2363.97 + 2523.31)/4 = 2533.70 or 2500 s = 174 or 200
(c) H = L / N (Equation 26-16 rearranged) H = 24.7 cm/ 2534 plates = 9.749 × 10 –3^ cm = 0.0097 cm 26-15. (a) k = ( t R – t M)/ t M (Equation 26-12) For A, k A = (5.4 – 3.1)/3.1 = 0. For B, k B= (13.3 – 3.1)/3.1 = 3. For C, k C = (14.1 – 3.1)/3.1 = 3. For D, k D = (21.6 – 3.1)/3.1 = 6. (b) Rearranging Equation 26-9, yields K = k ( V M/ V S) Substituting the equation in part (a) and the numerical data for V M and V S gives K = [( t R – t M)/ t M] × 1.37/0.164 = [( t R – t M)/ t M] × 8. KA = (5.4 – 3.1)/3.1 × 8.35 = 6. K B = (13.3 – 3.1)/3.1 × 8.35 = 27 K C = (14.1 – 3.1)/3.1 × 8.35 = 30 K D = (21.6 – 3.1)/3.1 × 8.35 = 50
26-16. (a) R s = 2 ⎡⎣(^ t^ R W^ )B^ C^ +− W (^ t CR)B⎤⎦ (Equation 26-25)
R s = 2(14.1 – 13.3)/(1.07 + 1.16) = 0.
(b) α C,B= ((^^ tt RR^ ))CB^ −− t^ t^ MM (Equation 26-15)
α (^) C,B= (^) 13.314.1 −−3.13.1= 1. (c) Proceeding as in Example 26-1d, we write
Skoog/Holler/Crouch Chapter 27 Principles of Instrumental Analysis, 6th ed. Instructor’s Manual
CHAPTER 27
27-1. In gas-liquid chromatography , the stationary phase is a liquid that is immobilized on a solid. Retention of sample constituents involves equilibria between a gaseous and a liquid phase. In gas-solid chromatography , the stationary phase is a solid surface that retains analytes by physical adsorption. Here separations involve adsorption/desorption equilibria. 27-2. In a soap bubble meter, a soap film is formed in a gas buret through which the effluent from a GC column is flowing. The flow rate is then determined from the time required for the film to travel between two of the graduations in the buret. 27-3. Temperature programming involves increasing the temperature of a GC column as a function of time. This technique is particularly useful for samples that contain constituents whose boiling points differ significantly. Low boilin point constituents are separated initially at temperatures that provide good resolution. As the separation proceeds, the column temperature is increased so that the higher boilin constituents come off the column with good resolution and at reasonable lengths of time. 27-4. (a) Retention volume V R is defined by the equation V R = t R F where t R is the retention time and F is the volumetric flow rate. (b) The corrected retention volume is the retention volume after correctionto the average pressure within the column. It is given by
V R^0
V R^0 = jt F R
where j is the pressure correction factor given by Equation 27-5. (c) The specific retention volume V g is defined tye the equation R^0 M^0 V g = V^ m^ −S^ V ×^273 T C where V M is the retention volume of an unretained species, m S is the mass of the stationary phase, and T C is the column temperature in kelvins. 27-5. A concentration-sensitive detector responds to the concentration of the analyte in the mobile phase, whereas a mass-sensitive detector responds to the number of analyte molecules or ions that come in contact with the detector. Peak areas for a concentration- sensitive detector increase as the flow rate decreases because the analyte is in contact with the detector for a longer period. Peak areas for a mass-sensitive detector are not greatly affected by flow rate. Using CS for concentration sensitive and MS for mass sensitive, we find for each of the detectors listed: (a) thermal conductivity (CS), (b) atomic emission (MS), (c) thermionic (MS), (d) electron capture (CS), (e) flame photometric (MS), (f) flame ionization (MS). 27-6. (a) The thermal conductivity detector is based on the decrease in thermal conductivity of the helium or hydrogen carrier gas brought about by the presence of analyte molecules. (b) The atomic emission detector is based on the intensity of atomic emission lines generated from certain of the elements contained in analyte molecules. Atomization of the analyte and excitation of atomic emission is brought about by passing the eluent through an energetic microwave field.
(e) Advantages, flame photometric: selectivity toward S and P containing analytes, good sensitivity. Disadvantages: destructive, limited applicability. (f) Advantages, flame ionization: general applicability, large linear range, good sensitivity, low noise, low sensitivity toward most carrier gases and water, simplicity, ease of use. Disadvantage: destructive 27-8. A total ion chromatogram is obtained by summing the ion abundances in each mass spectrum and plotting versus time. A mass chromatogram is obtained by monitoring one m/z value during the chromatography experiment and plotting the ion abundance versus time. 27-9. The combination of GC with MS allows the identification of species eluting from the chromatographic column. The total ion chromatogram gives information similar to a conventional GC chromatogram. By monitoring selected ions, information about specific species can be obtained. By scanning the mass spectrum during the chromatography experiment, species eluting at various times can be identified. Gas chromatography coupled with tandem mass spectrometry allows even more specific identifications to be made. 27-10. Hyphenated methods couple GC with a different instrumental technique such as mass spectrometry, FTIR, NMR spectroscopy, or electrochemical methods. The effluent from the GC column is either continuously monitored by the second technique or collected and measured. 27-11. The packing material most often used is diatomaceous earth particles having diameters ranging from 250 to 170 μm or 170 to 149 μm.
27-12. (a) A PLOT column is a porous layer open tubular column, which is also called a support coated open tubular (SCOT) column. The inner surface of a PLOT column is lined with a thin film of a support material, such as a diatomaceous earth. This type of column holds several times a much stationary phase as does a wall-coated column. (b) A WCOT column is simply a capillary tube fashioned from fused silica, stainless steel, aluminum, copper, plastic, or glass. Its inner walls are coated with a thin layer of the mobile phase. (c) The SCOT column is described in part (a) of this question. 27-13. Megabore columns are open tubular columns that have a greater inside diameter ( μm) than typical open tubular columns, which range in diameter from 150 to 320 μm. 27-14. Fused silica columns have greater physical strength and flexibility than glass open tubular columns and are less reactive toward analytes than either glass or metal columns. 27-15. Desirable properties of a stationary phase for GC include: low volatility, thermal stability,
chemical inertness, and solvent characteristics that provide suitale k and α values for the
analytes to be separated. 27-16. Film thickness influences the rate at which analytes are carried through the column, with the rate increasing as the thickness is decreased. Less band broadening is encountered with thin films. 27-17. Liquid stationary phases are generally bonded and/or cross-linked in order to provide thermal stability and a more permanent stationary phase that will not leach off the column. Bonding involves attaching a monomolecular layer of the stationary phase to the packing surface by means of chemical bonds. Cross linking involves treating the
= 500 + (log 2.58^ log1.59) 100 = 558 I (^) (log 3.66 log1.59)
− ×
27-22. From Handbook of Chemistry and Physics, P H O 2 = 18.88 torr at 21.2°C.
Substituting into Equation 27-3, T C = 102.0 + 273 = 375 K, F m = 25.3 mL/min, T = 273 + 21.2 = 294.2 K, P = 748 torr gives
= m C^ (^ H O^2 )= 24.3 375 (748^ 18.88)= 30.2 mL/min
F F T^ P^ P
T P
× × −^ × × −
(b) V M^0 = jt (^) M F and P i = 748 torr + 26.1 psi × 5.17 torr/psi = 883 torr 2 j = (^) 2[(883 / 748)3[(883/748)^3 −−1]1] = 0.915 (Equation 27-5) t M = 18.0 s/60s/min = 0.3 min V M^0 = jt (^) M F = 0.915 × 0.3 min × 30.2 mL/min = 8.3 mL ( V (^) R^0 ) 1 = 0.915 × 1.98 min × 30.2 mL/min = 54.7 mL ( V (^) R^0 ) 2 = 0.915 × 4.16 × 30.2 = 115.0 mL ( V (^) R^0 ) 3 = 0.915 × 7.93 × 30.2 = 219.1 mL (c) Substituting into Equation 27-6 gives ( V (^) g (^) ) 1 = 54.71.40^ −^ 8.3 × 273375 = (54.7 − 8.3) × 0.520 = 24.1 mL/g stationary phase ( V (^) g (^) ) 2 = (115.0 − 8.3) × 0.520 =55.5 mL/g ( V (^) g (^) ) 3 = (219.1 − 8.3) × 0.520 =109.6 mL/g
(d) We rearrange Equation 27-7 to give K = V g ρS T C/
K 1 = 24.1 mL/g × 1.02 g/mL × 375/273 = 24.1 ×1.40 = 33.
K 2 = 55.5 × 1.40 = 77.
K 3 = 109.6 × 1.40 = 154
(e) The spreadsheet follows:
The equation for the line is log t R′ = m × (# C atoms) + b = 0.3286 × (# C atoms) – 0. For 7 C atoms, log t R′ = 0.3286 × 7 – 0.7496 = 1. t R′ = 35.53 and t R = 35.53 + 0.30 = 35.83 min V R^0 = jt F R = 0.915 × 35.83 ×30.2 = 990 mL
27-27. (a) Increasing V S/ V M leads to an increase in the film thickness d f. This increases causes a marked increase in C S u (Table 26-3) and thus an increase in H. (b) Reducing the rate of sample injection will lead to band broadening because all the molecules do not start to traverse the column at the same instant. Reduced efficiency and an increase in H results. (c) Increasing the injection port temperature will tend to decrease H because the same evaporation rate will increase. Thus, the sample will be put on the column in a narrow band with less initial zone spreading.
(d) Increasing the flow rate may cause either increases or decreases in H depending on the flow rate as can be seen in Figure 26-8b. (e) Reducing particle size increases the surface area and thus decreases film thickness d f in the C S u term in Equations 26-23 and 26-24. A decrease in particle size also makes the C M u term smaller. Both effects lead to a smaller plate height (Table 26-3). (f) Decreasing temperature will decrease the diffusion rates D M and D S. In Table 26-3, it can be seen that the B / u term becomes smaller and the C S u and C M u terms become larger with decreasing diffusion coefficients. This can lead to an increase in H if the C S u and C M u terms dominate or a decrease in H if the B / u term dominates. In most cases, H increases as the temperature decreases. 27-28. Gas-solid chromatography is used primarily for separating low molecular mass gaseous species such as carbon dioxide, carbon monoxide and oxides of nitrogen. 27-29. Gas-solid chromatography has limited application because active or polar compounds are retained more or less permanently on the stationary phase. In addition, severe tailing is often observed due to the nonlinear characteristics of the physical adsorption process.
