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This problem reviews concepts from Chapter 23 using

Figure 24-7.

(a) Calculate the number of theoretical plates (N in Equation 23-30)

and the plate height (H) for CO.

(b) Find the resolution (Equation 23-23) between argon and oxygen.

Short Answer

Expert verified

(a)N=1.42104H=2.11mm(b)Resolution=1.33n

Step by step solution

01

To find the number of theoretical plates (N) and plate height (H).

a. By examining Figure 24-7, the retention time tr'of is approximately 17 min . The width at the base (w) of the peak can be approximated to 0.57 min . It is stated in the plot that the column length (L) is 30 m and column width is 0.53 mm

Note: Perform approximations by measuring the length of a known retention time or any parameter in the graph and solve for the unknown values by measuring the length and applying ratio and proportion.

Apply Equation 23-30 to compute for the number of theoretical plates (N):

N=16tr2w2=1617min20.57min2=1.42104Computefortheplateheight(H):H=LN=30m1.42104=2.11mm
02

Step 2:To find the resolution between argon and oxygen.

b. By examining Figure 24-7, the retention time tr'of Ar is approximately 1.9 min while that of is around 2.1 min.

Computing for the tr:

tr=2.1min-1.9=0.2min

The width of the bases of Ar and O2are almost equal and can be approximated to 0.15 . Thus, the average width of the two peaks (Wav)is 0.15 min.

Calculating for the resolution between Arand O2:

Resolution=trwav=0.2min0.15min=1.33n

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Most popular questions from this chapter

(a) What are the characteristics of an ideal carrier gas?

(b) Why do H2 and He allow more rapid linear velocities in gas chromatography thanN2 does, without loss of column efficiency (Figure 24-11)?

Consider the chromatography of n-c12H26on a 25 m 脳 0.53 mm open tubular column of 5% phenyl鈥95% methyl polysiloxane with a stationary phase thickness of 3.0 渭尘and He carrier gas at 125潞C. The observed retention factor for n-c12H26is 8.0. Measurements were made of plate height, H, at various values of linear velocity,xm/s. A least-squares curve through the data points is given by

localid="1654864230381" H(m)=(6.010-5m2/s)/x+(2.0910-3s)xthecoefficientsofthevanDeemterequation,findthediffusioncoefficientofn-c12H26inthemobileandstationaryphases.Whyisoneofthesediffusioncoefficientssomuchgreaterthantheother?

Heptane, decane, and an unknown had adjusted retention times of 12.6min(heptane),22.9min(decane), and20.0min(unknown). The retention indexes for heptane and decane are 700 and 1000 , respectively. Find the retention index for the unknown.

Efficiency of solid-phase microextraction. Equation24-9gives 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 a100-渭尘-thickcoating has a film volume of6.910-4mL. Suppose that the initial concentration of analyte in solution is

c0=0.10渭驳/mL(100ppb).Use a spreadsheet to prepare a graph showing the mass of analyte extracted into the fiber as a function of solution volume for partition coefficients of 10000,5000,1000and100and. Let the solution volume vary from 0to100mL.

(b) Evaluate the limit of Equation24-9asVr gets big relative to KVf. Does the extracted mass in your graph approach this limit?

(c) What percentage of the analyte fromof solution is extracted into the fiber when and whenK=100andwhenk=10000?

(a) Use Trouton's rule, Hvap(88Jmol-1K-1)Tbp, to estimate the enthalpy of vaporization of octane (b.p. 126).

(b) Use the form of the Clausius-Clapeyron equation below to estimate the vapor pressure of octane at the column temperature in Figure 24-9(70C)

In(P1P2)=-(HvapR)(1T1-1T2)

(c) Calculate the vapor pressure for hexane (b.p. 69C) at70C

(d) What is the relationship between solute vapor pressure and retention?

(e) Why is the technique called "gas chromatography鈥 if retained analytes are only partially vaporized?

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