Question

From the data in Problem 26-14, calculate for A, B, C, and D

(a) the retention factor.

(b) the distribution constant.

Short answer

(a)

$$\begin{gathered} \mathrm{Retention}\mathrm{factor}\mathrm{for}\mathrm{A}=1.00 \\ \mathrm{Retention}\mathrm{factor}\mathrm{for}\mathrm{B}=3.3 \\ \mathrm{Retention}\mathrm{factor}\mathrm{for}\mathrm{C}=4.1 \\ \mathrm{Retention}\mathrm{factor}\mathrm{for}\mathrm{D}=6.0 \end{gathered}$$

(b)

$$\begin{gathered} \mathrm{Distribution}\mathrm{constant}\mathrm{for}\mathrm{A}=8.4 \\ \mathrm{Distribution}\mathrm{constant}\mathrm{for}\mathrm{B}=27.6 \\ \mathrm{Distribution}\mathrm{constant}\mathrm{for}\mathrm{C}=34 \\ \mathrm{Distribution}\mathrm{constant}\mathrm{for}\mathrm{D}=50 \end{gathered}$$

Step-by-step solution

Part (a) Step 1: Given information 

$$\begin{gathered} \mathrm{Length}\mathrm{of}\mathrm{packing}24.7\mathrm{cm} \\ \mathrm{Flow}\mathrm{rate}0.313\mathrm{mL}/\min \\ {V}_M\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}1.37\mathrm{mL} \\ {V}_S\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}0.164\mathrm{mL} \end{gathered}$$

A chromatogram of a mixture of species A, B, C, and D provided the following data:

Part (a) Step 2: Retention factor   

Retention factor is as follows:

$K=\frac{t_R-t_M}{t_M}.........\left(1\right)$

Here,

$$\begin{gathered} K=\mathrm{retention}\mathrm{factor} \\ {t}_R=\mathrm{retention}\mathrm{time} \\ {t}_M=\mathrm{nonretained}\mathrm{time} \end{gathered}$$

Part (a) Step 3: Calculate retention factor for A 

Substitute values for A in equation (1) as follows:

$$\begin{gathered} K_A=\frac{t_R-t_M}{t_M} \\ =\frac{6.2-3.1}{3.1} \\ =1.00 \end{gathered}$$

Part (a) Step 4: Calculate retention factor for B

Substitute values for B in equation (1) as follows:

$$\begin{gathered} K_B=\frac{t_R-t_M}{t_M} \\ =\frac{13.3-3.1}{3.1} \\ =3.3 \end{gathered}$$

Part (a) Step 5: Calculate retention factor for C

Substitute values for C in equation (1) as follows:

$$\begin{gathered} K_C=\frac{t_R-t_M}{t_M} \\ =\frac{15.7-3.1}{3.1} \\ =4.1 \end{gathered}$$

Part (a) Step 6: Calculate retention factor for D

Substitute values for D in equation (1) as follows:

$$\begin{gathered} K_D=\frac{t_R-t_M}{t_M} \\ =\frac{21.6-3.1}{3.1} \\ =6.0 \end{gathered}$$

Part (b) Step 1: Distribution constant  

Distribution constant is as follows:

$K=\frac{k{V}_M}{V_S}............\left(2\right)$

Here,$K$is the distribution constant,$k$is the retention factor,$V_M$is the volume in mobile phase and$V_S$is the volume in stationary phase.

Part (b) Step 2: Distribution constant for A

Substitute the values for A in equation (2) as follows:

$$\begin{gathered} K=\frac{k{V}_M}{V_S} \\ {K}_A=\frac{k_A{V}_M}{V_S} \\ =\frac{1.0\times 1.37}{0.164} \\ =8.4 \end{gathered}$$

Part (b) Step 3: Distribution constant for B

Substitute the values for B in equation (2) as follows:

$$\begin{gathered} K=\frac{k{V}_M}{V_S} \\ {K}_B=\frac{k_B{V}_M}{V_S} \\ =\frac{3.3\times 1.37}{0.164} \\ =27.6 \end{gathered}$$

Part (b) Step 4: Distribution constant for C

Substitute the values for C in equation (2) as follows:

$$\begin{gathered} K=\frac{k{V}_M}{V_S} \\ {K}_C=\frac{k_C{V}_M}{V_S} \\ =\frac{4.1\times 1.37}{0.164} \\ =34 \end{gathered}$$

Part (b) Step 5: Distribution constant for D

Substitute the values for D in equation (2) as follows:

$$\begin{gathered} K=\frac{k{V}_M}{V_S} \\ {K}_D=\frac{k_D{V}_M}{V_S} \\ =\frac{6.0\times 1.37}{0.164} \\ =50 \end{gathered}$$