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1 Show that for a capillary column, the average flow can be calculated from the following formula: (where ū represents the average linear velocity in a column of internal diameter ID).

2 A comparative study of the evolution of the retention factors of n‐undecane and n‐tridecane, as a function of the temperature of the GC column, at a constant carrier gas flow rate of 3 ml/min, gave the following results:n‐decane: logk1 = −6.58 + 2,450 ∙ T −1n‐tridecane: logk2 = −7.91 + 3,010 ∙ T −1Justify the general form: logk = −A + B/TAt what temperature T1 would these two solutes coelute? Which of the two would elute first if we work at a temperature T below T1? Same question if T is over T1?At what temperature T2 will the separation factor be equal to 2?Knowing that the column phase ratio is equal to 250, calculate the Nernst distribution factors K1 and K2 of the two solutes when we work at 150°C.

3 We propose determining the maximum efficiency of a capillary column, with the following characteristics:L = 12 m, ID = 200 μm, stationary phase: methyl‐phenyl polysiloxane, df = 0.33 μmOperating conditions: carrier gas: H2; injector temperature: 250°C; oven temp.: 100°C; FID temp.: 250°C; split flow rate: 30 ml/min.We conduct several injections of an n‐undecane solution in pentane (injected volume: 0.5 μl) while changing the carrier gas flow rate. Calculation software gives the Golay curve equation:H = 5.44/u + 0.004u where H is in mm and u in mm/s.For what value of u does the height equivalent of a theoretical plate go through a minimum? What is the value of Hmin ?Calculate the maximum efficiency value Nmax.Between what values of u can we work, if we tolerate efficiency being greater than 0.95 Nmax?

4 The table below contains values of the retention factor k for four refinery gases, studied at three different temperatures on the same capillary column (length L = 30 cm, internal diameter = 250 μm), whose stationary phase is of the SE‐30 type. The chromatograph is equipped with a cryogenic accessory.k valuesCompoundB.P. (°C)−35°C25°C40°Cethene−1040.2490.1020.0833ethane−890.4080.1480.117propene−471.8990.4320.324propane−422.1230.4810.352Can the polarity or nonpolarity of the SE‐30 phase be deduced from the elution order of the compounds?Calculate the selectivity factor α for the propene–propane pair at the three temperatures indicated.For a given compound, why does k decrease in response to an increase in temperature?What is the number of theoretical plates of the column for propane at 40°C, if it is known that at this temperature the resolution factor for the propene–propane pair is 2? Calculate the corresponding HETP.What would be the minimum theoretical value of HETP for propane at 40°C?

5  In a GC analysis series, we seek to determine the influence of the column’s length on several parameters of the chromatogram. All experiments are conducted under the same temperature and carrier gas flow rate conditions.L (m)a = √LtR (min)tR/LRR/a153.72.05307.52.916015.34.15Complete the table.To the nearest measurement uncertainties, what simple relationship can we consider between retention times and column length?To the nearest measurement uncertainties, what simple relationship can we consider between the resolution and the square root of the column length?If we assume that the two peaks used to determine the resolution have practically the same full width at half‐maximum (FWHM), deduce from the previous questions a relationship between the FWHM and the column length as well as a relationship between the theoretical efficiency of the column and its length.The two peaks used to calculate R have retention times respectively of 8.3 min and 9.7 min with the column length equal to 60 m. Calculate the FWHM value of these peaks (same approximation as in question d), as well as the theoretical efficiency of the column for the solute whose retention time is 8.3 min.Calculate the theoretical efficiency of 15 and 30 m columns for the same solute.

6 The chromatographic analysis of an unleaded gas is conducted under the following conditions:Column: L = 150 m, ID = 0.25 mm, df = 0.25 μm, nonpolar stationary phase ‘PDH 150’. Injector, 100:1 split ratio, T = 200°C; FID detector, T = 200°C; oven T = 35°C; carrier gas, He; u = 20 cm/s; column head pressure, 2.5 bar; injected volume = 1 μL.In the following table, the variations in the free enthalpy of dissolution are shown, at the experimental temperature, for the solutes observed on the chromatogram.Solute2,3‐dimethyl pentane2,4‐dimethyl pentane2‐methyl hexane3‐methyl hexanebenzeneΔG0308 (kJ/mol)−17.79−16.80−17.73−18.05v17.27The retention times of the various solutes are given according to peak No.Peak No.1011121314tR (min)48.0055.1763.9064.5968.28Calculate the hold‐up time tM associated with this analysis. Since methane is not retained by the stationary phase, determine its free enthalpy variation at the temperature of the experiment.Assign each peak to its corresponding solute and justify your answer.From the 2,3‐dimethyl pentane peak, whose FWHM is 25 s, determine the theoretical plate number of the column.Calculate the phase ratio of this column.Calculate the distribution coefficient K of benzene in two different ways:By using its variation of free enthalpy of dissolution.From its retention factor.

7 The best‐known method for estimating the hold‐up time, tM, consists of measuring the retention time of a compound not retained on the column. Described here is another method for calculating the hold‐up time, which involves the relationship used in establishing retention factors. Knowing that for a homologous series of organic compounds if the column temperature is constant, we can write: (where tR represents the total retention time of a compound having n atoms of carbon, while a and b are constants that depend upon the type of solute and the stationary phase chosen).Recall the chromatographic parameters for which it is essential to know the hold‐up time tM. Which compound is used in general to determine tM?Calculate tM from the following experiment, employing the method above: a mixture of linear alkanes, possessing six, seven and eight atoms of carbon, is injected into the chromatograph. The retention times for these compounds are respectively, 271 s, 311 s, and 399 s, at a constant temperature of 80°C (column length 25 m, ID = 0.2 mm, df = 0.2 μm and a polysiloxane‐based stationary phase).If the Kovats index for pyridine on squalane is 695, what is the McReynolds constant of this compound on the column in question, if it is known that under the conditions of the experiment, its retention time is 346 s?

8 In a GC experiment, a mixture of n‐alkanes (up to n carbon atoms, where n represents a variable number) and 1‐butanol (CH3CH2CH2CH2OH) is injected onto a column maintained at a constant temperature and whose stationary phase is of the dimethylpolysiloxane type. The equation of the Kovats straight line derived from the chromatogram is: (where is expressed in seconds).The adjusted retention time of butanol is 168 s. If it is known that the retention index for butanol on a squalane column is 590 s, then deduce its corresponding McReynolds constant on this column.

9 We study a chromatogram obtained under the following conditions: Column: DB‐Wax, L= 30 m; ID = 0.321 mm; df = 0.25 μm; oven T = 210°C; mobile phase: H2, u = 50 cm/s; volume injected 0.2 μl; detector: FID, T = 220°C.The chromatogram has three peaks with the following characteristics:peak 1: tR1 = 1.01 min.; δ = 0.151 min.peak 2: tR2 = 1.95 min.; δ = 0.0277 min.peak 3: tR3 = 2.01 min.; δ = 0.0284 min.Calculate the dead time of the column. What can we conclude from this?From this, deduce the mobile phase flow rate in ml/min.Calculate the column phase ratio.Calculate the HETP (H) for peak No.2.Calculate retention factors k for peaks 2 and 3.From this, deduce the distribution coefficients K of the two corresponding compounds.Calculate the selectivity factor α between compounds 2 and 3.Calculate the resolution between these two peaks. Is it enough? What could be a solution to improve the resolution?Kovats retention indexes for octane, toluene, and methyl pentanoate on this same column are respectively 800, 850, and 985. Classify these three solutes by increasing retention times on this stationary phase.What is the polarity of this stationary phase? Justify your answer.