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The Van Deemter equation relates mobile-phase linear velocity to band broadening in a chromatographic column.
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Formula
H and A in mm · u in cm/s · B in mm·cm/s · C in mm·s/cm
| Symbol | Meaning | Unit |
|---|---|---|
| Height equivalent to a theoretical plate, a measure of band broadening | mm | |
| Multipath contribution to plate height | mm | |
| Longitudinal-diffusion contribution | mm·cm/s | |
| Mass-transfer-resistance contribution | mm·s/cm | |
| Linear mobile-phase velocity | cm/s |
H=A+\frac{B}{u}+CuThe model separates plate height into multipath, longitudinal diffusion and mass-transfer contributions. At fixed column length L, a smaller H gives more theoretical plates N=L/H. The classical form is an approximation for packed columns over a limited flow range; its coefficients depend on the column, particles, analyte and mobile phase. It does not directly determine selectivity or resolution between two compounds.
An approximation for a column and flow range where the three classical plate-height contributions are meaningful.
Plate height is the sum of multipath, diffusion and mass-transfer contributions.
Velocity at the minimum
Applies when B and C in the classical form are positive.
Given A=0.50 mm, B=0.20 mm·cm/s, C=0.05 mm·s/cm, u=2.0 cm/s and L=200 mm, find H and N.
H=0.50+0.10+0.10=0.70 mm; N=200/0.70≈286.
Using Van Deemter as a direct resolution equation.
It describes column efficiency; resolution also depends on retention and selectivity.
Formula cluster
A smaller H corresponds to more theoretical plates under the same conditions.
Let A=0.50 mm, B=0.20 mm·cm/s, C=0.05 mm·s/cm and u=2.0 cm/s. Then H=0.50+0.20/2+0.05·2=0.70 mm. For L=200 mm, N≈L/H=286. Check: every term has units of mm; at a fixed column length, reducing H increases plate count.
Optimize column flow and explain chromatographic efficiency as a function of linear velocity
Here is how to work through a typical Van Deemter Equation (H = A + B/u + Cu) task step by step:
Task
Given A=0.50 mm, B=0.20 mm·cm/s, C=0.05 mm·s/cm, u=2.0 cm/s and L=200 mm, find H and N.
Solution path
H=0.50+0.10+0.10=0.70 mm; N=200/0.70≈286.
The relation describes how flow velocity contributes to chromatographic band broadening. Its output is plate height H and, for a known column length, the plate count N.. A smaller H corresponds to more theoretical plates under the same conditions. It answers a bounded question and places Van Deemter Equation in a defined measurement or model context. It does not replace a complete process or system description. State the reference quantity and conditions before interpreting the number; only then can you tell whether it represents an amount, correction or efficiency.
The quantities are A represents multipath, B longitudinal diffusion, C mass transfer and u linear velocity. Their units are Each term A, B/u and Cu must have the same length unit as H.. Use values on the same reference basis; a ratio across inconsistent phases, time intervals or standards would not be meaningful. Check the dimension of every term before calculating and keep conversions visible. This shows whether the result should be dimensionless or carry a unit. Dimensional analysis cannot repair a bad measurement, but it catches many calculation errors early.
The stated validity is: the coefficients are empirical and not universally transferable. The calculation requires the column, mobile phase, analyte and relevant flow range are specified.. Outside this range, additional interactions, changed reference states or different geometries can alter the relation. If an assumption fails, do not transfer the result without qualification; name the limitation and use a more suitable model or measurement. This matters especially when comparing metrics collected under different experimental conditions. This assumption determines which samples and states the calculated value actually represents, so report it alongside the numerical result.
A representative case is: The values give H=0.70 mm and about 286 plates for L=200 mm. The check gives: Every term has units of mm; also verify N=L/H.. Write substituted values with units, then put the result back into the original relation or balance. A successful check still depends on the model assumptions. Also test whether limiting cases behave plausibly, for example whether an ideal limit is recovered or a balance returns the overall composition. These checks are more informative than merely rounding to several decimal places. For an additional plausibility check, change one input at a time and confirm that the result moves in the expected direction.
A nearby concept is chromatographic resolution.. The key difference is that Van Deemter models plate height; resolution compares two peaks and also depends on selectivity. Both relations may appear in related problems, but they answer different questions and do not automatically use the same data. Choose the equation by the requested output: A smaller H corresponds to more theoretical plates under the same conditions. If a problem asks for chromatographic resolution. instead, use that definition. This distinction prevents similarly named metrics or models from being treated as interchangeable. This distinction also determines which measurements, reference states and intermediate steps must be documented for a reproducible analysis.
Quanta exam set
Curated exam set for "Van Deemter Equation":
Question (front)
Which formula describes Van Deemter Equation?
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Question (front)
How do you rearrange Van Deemter Equation for Velocity at the minimum?
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Question (front)
Which common mistake happens with Van Deemter Equation?
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Create a curated FSRS exam set for H = A + B/u + Cu: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
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