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

(b) Why do ${\mathbf{H}}_{\mathbf{2}}$ and He allow more rapid linear velocities in gas chromatography than${\mathbf{N}}_{\mathbf{2}}$ does, without loss of column efficiency (Figure 24-11)?

(a)

One characteristic of an ideal carrier gas is that it must have high optimal velocity to achieve good separation between compounds being analyzed. The carrier gas must also have a high diffusion coefficient so that solutes can diffuse more rapidly and thus result to a better resolution. The velocities of the carrier gas should also be 1.5-2 times greater than the optimum velocity at the minimum of the van Deemter curve, to provide maximum efficiency per unit time. Furthermore, the carrier gas should have high quality because impurities can damage the stationary phase

(b)

${\mathrm{H}}_2$and He allow more rapid linear velocities in gas chromatography than ${\mathrm{N}}_2$without loss of column efficiency, because solutes diffuse more rapidly through ${\mathrm{H}}_2$ than through role="math" localid="1654769938173" $N_2$In the van Deemter equation, a small value of the mass transfer term $\left(C{U}_x\right)$ results to a solute with faster diffusion between phases.

$H=A+\frac{B}{u_x}+C{u}_x$

where:

$$\begin{gathered} -\mathrm{H}=\mathrm{plate}\mathrm{height} \\ -{\mathrm{u}}_{\mathrm{x}}+\mathrm{linear}\mathrm{velocity} \\ -\mathrm{A},\mathrm{B},\mathrm{and}\mathrm{C}=\mathrm{constants}\mathrm{for}\mathrm{a}\mathrm{given}\mathrm{column}\mathrm{and}\mathrm{stationary}\mathrm{phase} \end{gathered}$$

For a thin stationary phase$(^0.5\mathrm{\mu m})$, the mass transfer is dominated by slow diffusion through the mobile phase $\left({\mathrm{C}}_{\mathrm{m}}\right)$ than through the stationary phase$\left(C_s\right)$.

That is,$C_s<<C_m$.

$$\begin{gathered} C_M=\frac{1+6k+11K^2}{24{(k+1)}^2}\times \frac{r^2}{D_m} \\ {C}_s=\frac{2K}{3(K+1^2}\times \frac{d^2}{D_s} \end{gathered}$$

where:

$$\begin{gathered} .\mathrm{k}=\mathrm{retention}\mathrm{factor} \\ .\mathrm{r}=\mathrm{column}\mathrm{radius} \\ .\mathrm{d}=\mathrm{thickness}\mathrm{of}\mathrm{stationary}\mathrm{phase} \\ .{\mathrm{D}}_{\mathrm{m}}=\mathrm{diffusion}\mathrm{coefficient}\mathrm{of}\mathrm{solutien}\mathrm{mobile}\mathrm{phase} \\ .{\mathrm{D}}_{\mathrm{s}}=\mathrm{diffusion}\mathrm{coefficient}\mathrm{of}\mathrm{solutien}\mathrm{stationary}\mathrm{phase} \end{gathered}$$

For a given column with fixed values of r and k, the only variable that can affect the rate of mass transfer in the mobile phase is the diffusion coefficient. Comparing the diffusion coefficients of the three gases, they follow the order:${\mathrm{H}}_2>\mathrm{H}>{\mathrm{N}}_2$.

Thus,role="math" localid="1654773241068" ${\mathrm{H}}_2\mathrm{and}\mathrm{H}$ provide ease of diffusion for solutes.