Question

Calculation of number of theoretical plates is done by using which of the following equation?

• A. \( N = 4 \left( \frac{t_R}{W} \right)^2 \)
• B. \( N = 16 \left( \frac{t_R}{W} \right)^2 \)
• C. \( N = 16 \left( \frac{t_R}{W} \right) \)
• D. \( N = 4 \left( \frac{t_R}{W^2} \right) \)

Hint:

Remember the "16" when using the peak width at the base (the wider part) to calculate theoretical plates.

Answer 1

The Correct Option is B

The number of theoretical plates (N) is a measure of the efficiency of a chromatographic column. It relates the retention time (\( t_R \)) of an analyte to the width of its peak (W) at the base. The most commonly used equation for calculating the number of theoretical plates based on peak width at the base is: $$ N = 16 \left( \frac{t_R}{W} \right)^2 $$ where \( t_R \) is the retention time and W is the width of the peak at its base, measured in the same units as \( t_R \). Another less common formula uses the peak width at half-height (\( W_{1/2} \)): $$ N = 5.54 \left( \frac{t_R}{W_{1/2}} \right)^2 $$ Given the options, the formula using the peak width at the base with a factor of 16 is the standard one presented.