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Retension Ratio:The chromatographic behaviour of a solute can be described in terms of the retention ratio, \(R\). The retention ratio is the fraction of the total time spent by the solute in the mobile phase, $$R = \frac { { t }_{ M } }{ { t }_{ M } + { t }_{ S } } \qquad ...(1) $$ where \({ t }_{ M }\) and \({ t }_{ S }\), are the times spent by the solute in the mobile and stationary phases respectively. The ratio \(\frac { { t }_{ M } }{ { t }_{ S } } \), is the same as the ratio \(\frac { { Q }_{ M } }{ { Q }_{ S } }\).
where \({ Q }_{ M }\) and \({ Q }_{ S } \)are the quantities of solute in the mobile and stationary phases respectively at equilibrium, $$\therefore \frac { { t }_{ M } }{ { t }_{ S } } = \frac { { Q }_{ M } }{ { Q }_{ S } } $$ But, quantity \(Q = Concentration (C) \times Volume (V),\) $$ \therefore \frac { { t }_{ M } }{ { t }_{ S } } = \frac { { C }_{ M } \times V_{ M } }{ { C }_{ S } \times V_{ S } } $$ If the partition coefficient \(K\) is given by equation, $$K = \frac { { C }_{ S } }{ { C }_{ M } }$$ Above equation becomes, $$\frac { { t }_{ M } }{ { t }_{ S } } = \frac { V_{ M } }{ K \times V_{ M } } $$ Rearrangement then gives, $$\frac { { t }_{ M } }{ { t }_{ M } + { t }_{ S } } = \frac { V_{ M } }{ V_{ M } + KV_{ M } } $$ Thus from eq (1) $$ R = \frac { { t }_{ M } }{ { t }_{ M } + { t }_{ S } } = \frac { V_{ M } }{ V_{ M } + KV_{ M } } $$ And It can therefore be seen that the retention ratio \(R\) decreases with increase in partition coefficient \(K\).
By adjusting the stationary phase, mobile phase combination and other operating factors, the retention ratio can be changed to give an efficient separation.
Retention volume: for a solute is the volume of the mobile phase required to carry the solute through the column to elution. It is also a measure of the fraction of time spent by the solute in the mobile phase. When a solute peak maximum appears at the column exit, one half of the total solute has eluted in the retention volume \({ V }_{ R }\). and the other half remains in the mobile and the stationary phases, i.e., $${ V }_{ R }{ C }_{ M } = { V }_{ M }{ C }_{ M } + { V }_{ S }{ C }_{ S } $$ deviding by \( { C }_{ M }\) $$\frac { { V }_{ R }{ C }_{ M } }{ { C }_{ M } } = \frac { { V }_{ M }{ C }_{ M } }{ { C }_{ M } } + \frac { { V }_{ S }{ C }_{ S } }{ { C }_{ M } } $$ $$ \boxed { { V }_{ R } = { V }_{ M } + K{ V }_{ S } } $$ This is the fundamental equation in chromatography and is applicable to all types of chromatography.
Retension Time:The time required for a solute peak to appear at the column exit is called retention time. If the column length is \(L\), then, the migration velocity of the solute is \(\frac { L }{ { t }_{ R } }, \) where \({ t }_{ R }\) is the retention time.
The retention volume \({ V }_{ R }\) is related to the retention time \({ t }_{ R }\) by, $${ V }_{ R } = { t }_{ R }F$$ where \(F\) is the rate of flow of the mobile phase.
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