As the inside radius of an open tubular column is decreased, the maximum possible column efficiency increases and sample capacity decreases. For a thin stationary phase that equilibrates rapidly with analyte, the minimum theoretical plate height is given by

where r is the inside radius of the column and k is the retention factor.
(a) Find the limit of the square-root term as (unretained solute) and as (infinitely retained solute).
(b) If the column radius is 0.10 mm, find Hmin for the two cases in (a).
(c) What is the maximum number of theoretical plates in a 50-m-long column with a 0.10-mm radius if k 5.0?
(d) The relation between retention factor k and partition coefficient K (Equation 22-19) can also be written k 2tK/r, where t is the thickness of the stationary phase in a wall-coated column and r is the inside radius of the column. Derive the equation k 2tK/r and find k if K 1 000, t 0.20 m, and r 0.10 mm.

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