Question

an analyst does gas chromatography with a 30-m column. a peak elutes at 17.0 minutes with a peak width w of 12 seconds. based on this peak, how many theoretical plates does the column have? give answer to nearest theoretical plate with no decimals.

Answer 1

To calculate the number of theoretical plates for a chromatography column, convert the retention time and peak width to the same units, and apply the formula N = 16(t_R^2 / w^2). For a retention time of 17.0 minutes and a peak width of 0.2 minutes, the number of theoretical plates is calculated to be 115,600.

Step-by-step explanation:

To calculate the number of theoretical plates, N, for a chromatography column, we use the formula:
N = 16 \(\frac{t_R^2}{w^2}\)
where t_R is the retention time and w is the peak width.

In this case, the retention time (t_R) is 17.0 minutes and the peak width (w) is 12 seconds.

First, we need to convert the retention time and the peak width to the same unit. Since there are 60 seconds in a minute, the peak width in minutes is 0.2 minutes (12 seconds \(\div\) 60 seconds per minute).

Now, we can plug the values into the formula:
N = 16 \(\frac{17.0^2}{0.2^2}\) which is N = 16 \(\frac{289}{0.04}\). Simplifying further we get N = 16 \(\times\) 7225, and N = 115,600 theoretical plates.

Therefore, the number of theoretical plates for the column is 115,600, which we round down to the nearest whole plate as the question asks for no decimals.