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.

a. By examining Figure 24-7, the retention time $\left({\mathrm{t}}_{\mathrm{r}}^{\text{'}}\right)$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):

b. By examining Figure 24-7, the retention time $\left({\mathrm{t}}_{\mathrm{r}}^{\text{'}}\right)$of Ar is approximately 1.9 min while that of is around 2.1 min.

Computing for the $∆{\mathrm{t}}_{\mathrm{r}}$:

$∆{\mathrm{t}}_{\mathrm{r}}=2.1\min -1.9=0.2\min$

The width of the bases of Ar and ${\mathrm{O}}_2$are almost equal and can be approximated to 0.15 . Thus, the average width of the two peaks $({\mathrm{W}}_{\mathrm{av}})$is 0.15 min.

Calculating for the resolution between ${\mathrm{A}}_{\mathrm{r}}$and ${\mathrm{O}}_2$:

$$\begin{gathered} \mathrm{Resolution}=\frac{∆{\mathrm{t}}_{\mathrm{r}}}{{\mathrm{w}}_{\mathrm{av}}} \\ =\frac{0.2\min }{0.15\min }=1.33\mathrm{n} \end{gathered}$$