Chapter 23: Q19P (page 630)

(a) Write the meaning of the retention factor,k, in terms of time spent by solute in each phase. (b) Write an expression in terms of kfor the fraction of time spent by a solute molecule in the mobile phase. (c) The retention ratio in chromatography is defined as $R = \frac{time for solvent}{time for solute to pass through column} = \frac{t_{m}}{t_{r}}$ Show that is related to the retention factor by the equation $R = 1 / k + 1$

Short Answer

Expert verified

$a) k = \frac{t_{s}}{t_{m}} b) \Rightarrow \frac{1}{1 + k} c) R = \frac{1}{1 + k}$

Step by step solution

Define Retention Factor:

The retention factor, also known as the capacity factor (k), in column chromatography is defined as the ratio of time an analyte is retained in the stationary phase to time

To find the retention Factor :

a) To calculate the retention factor as k

$k = \frac{t (solute in the stationary phase)}{t (solute in the mobile phase)}$

$k = \frac{t_{r} - t_{m}}{t_{m}} k = \frac{t_{s}}{t_{m}}$

$t_{r}$ is actually the retention time of solute of interest

To find the fraction of time spent in the mobile phase:

b) Fraction of time spent in the mobile phase $t_{m}$ would be

$\frac{t_{m}}{t_{m} + t_{s}}$

$k = \frac{t_{s}}{t_{m}} t_{s} = k \times t_{m}$

Substitute the expression

$\Rightarrow \frac{t_{m}}{t_{m} + t_{s}} \Rightarrow \frac{t_{m}}{t_{m} + k \times t_{m}} \Rightarrow \frac{t_{m}}{t_{m} + k \times t_{m}} \Rightarrow \frac{1}{1 + k \times 1} \Rightarrow \frac{1}{1 + k}$

To find the retention Factor in chromatography:

c) The retention ration in chromatography is defined as

$R = \frac{time for solvent}{time for solute to pass through column}$

$R = \frac{t_{m}}{t_{r}} R = \frac{t_{m}}{t_{m} + t_{s}} R = \frac{1}{1 + k}$

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Short Answer

Step by step solution

Define Retention Factor:

To find the retention Factor :

To find the fraction of time spent in the mobile phase:

To find the retention Factor in chromatography:

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