Morphine and morphine 3-b-d-glucuronide were separated on two different 50 3 4.6 mm columns with 3-mm particles.61 Column A was C18-silica run at 1.4 mL/min and column B was bare silica run at 2.0 mL/min.

(a) Estimate the volume,${\mathbf{V}}_{\mathbf{m}}$, and time,${\mathbf{t}}_{\mathbf{m}}$, at which unretained solute would emerge from each column. The observed times are 0.65 min for column A and 0.50 min for column B.

(b) Column A was eluted with 2 vol% acetonitrile in water containing 10 mM ammonium formate at pH 3. Morphine 3-$\mathrm{\beta }$-d-glucuro-nide emerged at 1.5 min and morphine at 2.8 min. Explain the order of elution.

(c) Find the retention factor k for each solute on column A, using${\mathrm{t}}_{\mathrm{m}}$5 0.65 min.

(d) Column B was eluted with a 5.0-min gradient beginning at 90 vol% acetonitrile in water and ending at 50 vol% acetonitrile in water. Both solvents contained 10 mM ammonium formate, pH 3. Morphine emerged at 1.3 min and morphine 3-b-d-glucuronide emerged at 2.7 min. Explain the order of elution. Why does the gradient go from high to low acetonitrile volume fraction?

(e) From Equation 25-12 in Box 25-4, estimate k* on Column B assuming S = 4 and with${\mathrm{t}}_{\mathrm{m}}$5 0.50 min.

Part (a)

First, we calculate the volume at which solvent front appears:

Then we calculated${\mathrm{t}}_{\mathrm{m}}$:

${\mathrm{t}}_{\mathrm{m}}=\frac{\mathrm{L}.{\mathrm{d}}_{\mathrm{c}}^2}{2.\mathrm{F}}$

Or:

${\mathrm{t}}_{\mathrm{m}}=\frac{\mathrm{Vm}}{\mathrm{F}}$

For column A:

$$\begin{gathered} {\mathrm{t}}_{\mathrm{m}}=\frac{0.529{\mathrm{cm}}^3}{1.4{\mathrm{cm}}^3/\min } \\ {\mathrm{t}}_{\mathrm{m}}=0.378\min \end{gathered}$$

For column B:

$$\begin{gathered} {\mathrm{t}}_{\mathrm{m}}=\frac{0.529{\mathrm{cm}}^3}{2{\mathrm{cm}}^3/\min } \\ {\mathrm{t}}_{\mathrm{m}}=0.265\min \end{gathered}$$

Part (b)

The morphine-3-$\mathrm{\beta }$-D-glucuronide would elute before morphine because it is more polar (it has more hydroxy groups and one carboxylic acid). So, because the reversed phase column is nonpolar the polar compound would less be retained.

Part (c)

The retention factor can be calculated using the formula:

$\mathrm{k}=\frac{{\mathrm{t}}_{\mathrm{r}}-{\mathrm{t}}_{\mathrm{m}}}{{\mathrm{t}}_{\mathrm{m}}}$

For morphine-3-$\mathrm{\beta }$-D-glucuronide, the retention factor is:

$$\begin{gathered} {\mathrm{k}}_1=\frac{\left(1.5-0.65\right)\min }{0.65\min } \\ {\mathrm{k}}_1=1.31 \end{gathered}$$

For morphine, the retention factor is:

$$\begin{gathered} {\mathrm{k}}_2=\frac{\left(2.8-0.65\right)\min }{0.65\min } \\ {\mathrm{k}}_2=3.31 \end{gathered}$$

Part (d)

Column B has bare silica which is polar. Morphine should be retained less than morphine-3-$\mathrm{\beta }$-D-glucuronide because it is less polar. The gradient goes from high to low acetonitrile volume fraction because it tends to increase concentration of water, so that the polarity can be increased. Because of that, the more polar compound can be removed.

Part (e)

The average retention factor is calculated using the equation:

${\mathrm{k}}^{*}=\frac{{\mathrm{t}}_{\mathrm{G}}.\mathrm{F}}{∆\mathrm{ɸ}.{\mathrm{V}}_{\mathrm{m}}.\mathrm{S}}$

First, we need to calculate the volume of mobile phase in the column:

$$\begin{gathered} {\mathrm{V}}_{\mathrm{m}}=\mathrm{F}.{\mathrm{t}}_{\mathrm{m}} \\ {\mathrm{V}}_{\mathrm{m}}=2\mathrm{m}\mathrm{L}/\min .0.5\min \\ {\mathrm{V}}_{\mathrm{m}}=1\mathrm{mL} \end{gathered}$$

The ${\mathrm{k}}^{*}$is:

$$\begin{gathered} {\mathrm{k}}^{*}=\frac{5\min .2\mathrm{mL}/\min }{0.4.1\mathrm{mL}.4} \\ {\mathrm{k}}^{*}=6.25 \end{gathered}$$

Here, the final result of part(a), part(b), part(c), part(d), part(e) is

$$\begin{gathered} a){\mathrm{V}}_{\mathrm{m}}=0.529{\mathrm{cm}}^3{\mathrm{t}}_{\mathrm{m}}=0.378\min {\mathrm{t}}_{\mathrm{m}}=0.265\min \\ b)Thepolarcompoundwouldlessberetained \\ c){\mathrm{k}}_1=1.31{\mathrm{k}}_2=3.31 \\ d)Themorepolarcompoundcanberemoved. \\ e){\mathrm{k}}^{*}=6.25 \end{gathered}$$