Scaling Column Length—How Does Resolution Change? When a chromatographic column's length is doubled (all other conditions kept constant), by what factor does the theoretical resolution increase?

Introduction / Context:
Chromatographic resolution depends on plate number (N), selectivity (α), and retention. Plate number scales with column length (L), and resolution scales with the square root of N. Therefore, changing column length has a predictable, sublinear effect on resolution.

Given Data / Assumptions:

• Stationary phase chemistry, particle size/film thickness, and mobile phase conditions remain constant.
• Linear velocity is adjusted to maintain similar efficiency per unit length.
• Peak shapes and selectivity do not change with length.

Concept / Approach:
Since N ∝ L, doubling L doubles N. Resolution follows Rs ∝ sqrt(N) when α and k are constant. Thus, doubling L increases Rs by sqrt(2), about 1.41×, not twofold.

Step-by-Step Solution:

Verification / Alternative check:
Empirical method translation tools reproduce the 1.41× gain when only length is doubled under matched conditions.

Why Other Options Are Wrong:

• 2×, 3×, 4×: overestimate gains; resolution grows with sqrt(N), not linearly with L.
• No change: contradicts theory and practice.

Common Pitfalls:
Expecting linear improvement, which leads to unnecessary pressure and time costs for modest resolution gains.

Final Answer:
2^0.5 (approximately 1.41×)