Questions: Chromatography: Principles and Theoretical Plate Model

Question 1

A chemist doubles the column length. How does this affect the number of theoretical plates N and the resolution R between two peaks?

• A. N doubles, R doubles
• B. N doubles, R increases by a factor of √2
• C. N stays the same, R doubles
• D. Both N and R increase by a factor of √2

Answer: (B)

N is proportional to column length (N = L/H, where H is plate height), so doubling L doubles N. Resolution R is proportional to √N, so doubling N increases R by √2 ≈ 1.41. The practical implication: to double resolution, you must quadruple column length, which means gains from longer columns are subject to diminishing returns — and increasing selectivity (α) is almost always a more efficient path to better resolution.

Question 2

Two compounds with identical partition coefficients can be baseline-separated by using a sufficiently long column with high plate count.

• T. True
• F. False

Answer: False

Resolution depends on both efficiency (N) and selectivity (α = k₂/k₁). If two compounds have identical partition coefficients, α = 1 — they interact identically with both phases and migrate at exactly the same speed. No increase in N will separate them because there is no differential migration. Separation requires changing α by altering mobile phase composition, stationary phase chemistry, or temperature to create a difference in how the compounds interact with the system.

Question 3

What does a large retention factor (k >> 1) tell you about an analyte's interaction with the stationary and mobile phases?

Model answer: A large k means the analyte spends much more time in the stationary phase than in the mobile phase — it has strong affinity for the stationary phase relative to the mobile phase, based on favorable intermolecular interactions (e.g., hydrogen bonding, London dispersion). The analyte migrates slowly through the column and elutes late, with a broad, dilute peak.

k = (time in stationary phase)/(time in mobile phase). If k = 10, the analyte spends 10 times as long sorbed onto the stationary phase as it does moving with the mobile phase. Practical chromatography aims for k values between 1 and 10: too small and compounds elute too quickly for good separation; too large and peaks are very broad and take a long time to elute, wasting time and increasing detection limits.