# Calculating Width at Half‑Height of an HPLC Peak

## Question:

Based on the data provided, how can we calculate the width at half‑height of a peak eluting from an HPLC column?

## Answer:

The width at half‑height of a peak eluting from an HPLC column can be calculated using the plate height, column length, retention time, and number of theoretical plates. In this case, with a plate height of 8.68 μm, column length of 17.7 cm, and retention time of 11.1 min, the width at half‑height would be 10.98 seconds.

## Calculating Width at Half‑Height:

**Plate Height (H):** The plate height can be calculated using the formula H = L/N, where H is the plate height (8.68 μm), L is the column length (17.7 cm), and N is the number of theoretical plates. By solving for N, we find that N = 20392 plates.

**Calculating Number of Theoretical Plates (N):** We then use the formula N = 5.54*((tr/W₀.₅)^2), where tr is the retention time (11.1 min or 666s) and W₀.₅ is the width at half-height. By plugging in the values for N and solving for W₀.₅, we find that W₀.₅ = 10.98 seconds.

Therefore, the width at half‑height of the peak eluting from the HPLC column would be 10.98 seconds.