Chapter 24: Q34P (page 666)

(a) The term that is 0 for an open tubular column has to be explained with the reason.(b) The value of B must be stated in terms of a physical property that can be measured. (c) The value ofCmust be represented in terms of a physical attribute that can be measured. (d)The minimum plate height must be expressed in terms of quantifiable physical amounts of B and C.

Short Answer

Expert verified

(a) For an open tubular column, the term A is found to be zero using the Deemter equation. The term A refers to the various paths that can be taken. The multiple plat begins in a packed column when the liquid flow takes several pathways through the column.

(b) The value of B in terms of physical property is $B = 2 D_{m}$ .

(d) The minimum plate height is $H_{\min} = 2 \sqrt{\frac{4 k}{3 {(k + 1)}^{2}} \frac{d^{2} D_{m}}{D_{s}} + \frac{(1 + 6 k + 11 k) 2_{r}^{2}}{24 {(k + 1)}^{2}}}$ .

Step by step solution

Define the open tubular column

A chromatography column in which the stationary phase is either the inner tube wall or a liquid or active material held stationary on the tube wall, while

the mobile phase has an open, unrestricted route.

The term that is 0 for an open tubular column has to be explained with the reason.

(a)

The Deemter equation is given as,

$H \approx A + \frac{B}{u x_{x}} + C u_{x}$

$C u_{x}$ is equilibration time

Using the Deemter equation, the term for an open tubular column is found to be zero. The letter A denotes the many options available. In a packed column, the multiple plat begins when the liquid flow follows various paths through the column.

The value of B must be stated in terms of a physical property that can be measured.

(b)

The Deemter equation is written as follows:

$H A + B x + C u x + C u x$

WhereA denotes multiple paths.

$\frac{B}{u z}$

Longitudinal diffusion is denoted by the symbol Cux.

To express the worth ofin terms of a physical attribute that can be measured

In terms of measurable physical property, the term B can be expressed as, $B = 2 D_{m}$ ,

where $D_{m}$ = diffusion coefficient of solute in mobile phase

Step 4: The value of C must be represented in terms of a physical attribute that can be measured.

(c)

The Deemter equation is given as,

$H \approx A + \frac{B}{U_{x}} + {Cu}_{x}$

Where A is multiple paths

$\frac{B}{u_{s}}$ is Longitudinal diffusion

$C u_{x}$ is equilibration time

To give the value of C in terms of measurable physical property

In terms of measurable physical property, the term C can be expressed as,

$C = C_{s} + C_{m}$

role="math" localid="1664886662003" $H e r e, C_{s} = \frac{2 k}{3 {(k + 1)}^{2}} \frac{d^{2}}{D_{s}} C_{m} = \frac{1 + 6 k + 11 k^{2}}{24 {(k + 1)}^{2}} \frac{r^{2}}{D_{m}}$

where $D_{m}$ = diffusion coefficient of solute in mobile phase

k= retention factor

d= thickness of stationary phase

r= radius of column

$D_{S} =$ diffusion coefficient of solute in stationary phase

The minimum plate height must be expressed in terms of quantifiable physical amounts of B and C.

(d)

The Deemter equation is given as,

$H \approx A + \frac{B}{u_{x}} + C u_{x}$

Where A is multiple paths

$\frac{B}{u_{z}}$ is Longitudinal diffusion

$C u_{x}$ is equilibration time

To give an for the minimum plate height in terms of measurable physical quantities of B and C

$H = \frac{B}{u_{x}} + C u_{x}$

Where $u_{x} =$ linear velocity

At optimum velocity, the plate height is minimum

$\frac{d H}{d u_{x}} = - \frac{B}{u_{s^{2}}} + c = 0 u_{x} = \sqrt{\frac{B}{C}}$

The minimum height of the plate is estimated by substituting the values of $u_{x}$ (optimum) back into the van Deemter equation,

$H_{m i n} = \frac{B}{u_{x}^{2}} + C u_{x} = B \sqrt{\frac{C}{B}} + C \sqrt{\frac{B}{C}} \sqrt{B C} = 2 \sqrt{B + (C_{s} + C_{m})} H_{m i n} = 2 \sqrt{(2 D_{m}) (\frac{2 k}{3 {(k + 1)}^{2}} \frac{d^{2}}{D_{s}} + \frac{1 + 6 k + 11 k}{24 {(k + 1)}^{2}} \frac{r^{2}}{D_{m}})} H_{m i n} = 2 \sqrt{\frac{4 K}{3 {(k + 1)}^{2}} \frac{d^{2} D_{m}}{D_{s}} + \frac{(1 + 6 k + 11 k) 2_{r}^{2}}{24 {(k + 1)}^{2}}}$

Thus the minimum plate height is $H_{m i n} = 2 \sqrt{\frac{4 K}{3 {(k + 1)}^{2}} \frac{d^{2} D_{m}}{D_{s}} + \frac{(1 + 6 k + 11 k) 2_{r}^{2}}{24 {(k + 1)}^{2}}}$ .