How to Calculate Theoretical Plates

You'll always want to make sure you take the right medicine. It's important to check that the pharmaceutical drugs that are sold meet standards and regulations. Gas chromatography, one way researchers check for contaminants in drugs and food additives, lets engineers do this. You can learn more about the methods of chromatography separation that let scientists and engineers check the quality of many different substances.

Chromatography Separation

When a chemist wants to make sure a sample of a substance is made of the appropriate proportions of components, she can perform chromatography experiments that separate substances by various properties.

One example, gas chromatography, separates components of a dissolved substance by determining how fast it reacts with silica liquid. The speed of the reaction or whatever other property is measured can be compared to known measurements to determine the identity of the substance's constituents.

These chromatography results produce graphs that display peaks and valleys that tell you how prevalent certain substances are. You can measure quantities such as the ​response factor​ for gas chromatography as the area of a peak divided by the concentration of the calibration. This is the concentration that a chromatography apparatus has been designed to or set to measure for a particular substance.

These graphs let you perform calculations that consider experimental observations while demonstrating how they relate to theory. The ​retention time​ describes the position of a the peak maximum for a certain compound. This depends on the forces between the gas particles and liquid ones as the substance separates itself.

In gas chromatography, the gas doesn't exert a force that can attract itself to the solute so this part of the chromatography experiment doesn't affect retention time.

Scientists compare theory to experiment in determining the presence of "​theoretical plates​," layers in the chromatographic column that discern between components of the sample. The number of theoretical plates is used to measure the performance of the chromatographic columns themselves.

Plate Height Chromatography Formula

The column that separates the components uses plates to measure the abundance of the components. This means using more plates can help you achieve more precise, better resolution results. You can even use the ​"height equivalent to a theoretical plate" (HETP)​ in the equation


for Eddy-diffusion term ​A​, longitudinal diffusion term ​B​, resistance to mass transfer coefficient ​C​ and linear velocity ​v​.

The ​Eddy-diffusion term​ accounts for how broad the band of the solute is on the graph, the ​longitudinal diffusion term​ measures how one component diffuses from the center to the edges of the plate. Resistance to mass determines how the liquid transfer resists the opposition of liquid flowing.

The width of these peaks increases based on the square root of the distance the peak has migrated on the graph the chromatogram produces. This lets you calculate

HETP=\frac{\sigma ^2}{L}

for the standard deviation of the distances "sigma" ​σ​ and the each distance traveled ​L​. The equation also ensures ​HETP​ measures a distance.

Other Forms of Chromatography

Other chromatography experiments can change these formula depending on what exactly they're measuring or considering as a result of the experimental setup. ​High-performance liquid chromatography​ (HPLC) uses a pump to transfer a liquid solvent under pressure through a column that absorbs the liquid at various levels. Resolution in HPLC is, then, how well two peaks can be differentiated and determined as:


for retention times ​tr​ and peak widths ​W​ of two peaks A and B.

Some areas of chromatography use a time scale for the peak so the equation would become


for the retention time ​tr​ and its corresponding standard deviation. In ​elution chromatography​, in which the peak develops on a time scale, an equivalent form of the above equation is shown, in which ​L​ is now the column length, ​tr​ the time of retention of the peak by the column, and ​σt​ the standard deviation of the peak measured in units of time.


About the Author

S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.