# What is Retention Ratio, Retention Volume and Retention Time.

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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