Capacity factor and its significance MCQs With Answer

Capacity factor and its significance MCQs With Answer

Introduction: The capacity factor (k’) is a central concept in chromatographic separation, reflecting how long an analyte interacts with the stationary phase compared to the mobile phase. For M. Pharm students, a clear grasp of k’ helps optimize column selection, mobile phase composition, temperature, and flow rate to achieve efficient, reproducible separations. This quiz collection explores definitions, mathematical relations, practical calculation examples, and how k’ influences resolution, selectivity and analysis time in both liquid and gas chromatography. Detailed conceptual and calculation-based MCQs emphasize practical strategies to adjust k’ for improved method development and troubleshooting in pharmaceutical analysis.

Q1. What is the definition of the capacity factor (k’) in chromatographic terms?

• The ratio of peak height to peak width
• The time an analyte spends in the mobile phase only
• The ratio of the time an analyte is retained by the stationary phase to the time spent in the mobile phase
• The difference between retention time and dead time expressed in minutes

Correct Answer: The ratio of the time an analyte is retained by the stationary phase to the time spent in the mobile phase

Q2. Which equation correctly expresses k’ using retention time (tR) and dead time (t0)?

• k’ = t0 / (tR – t0)
• k’ = (tR – t0) / t0
• k’ = tR / t0
• k’ = (tR + t0) / t0

Correct Answer: k’ = (tR – t0) / t0

Q3. In terms of volumes, how is capacity factor expressed using retention volume VR and dead volume V0?

• k’ = VR / (VR – V0)
• k’ = (VR – V0) / V0
• k’ = V0 / (VR – V0)
• k’ = (VR + V0) / VR

Correct Answer: k’ = (VR – V0) / V0

Q4. If an analyte has tR = 5.2 min and t0 = 0.8 min, what is its k’?

• 0.15
• 5.0
• 4.5
• 6.5

Correct Answer: 5.0

Q5. Which range of k’ is typically considered optimal for efficient chromatographic separations?

• k’ < 0.5
• 0.5 to 1.0
• 1 to 10 (optimally 2–5)
• > 20

Correct Answer: 1 to 10 (optimally 2–5)

Q6. How does a very low k’ value (e.g., k’ < 0.5) affect chromatographic separation?

• Peaks are excessively broad with long retention times
• Analytes elute close to dead time causing poor resolution and co-elution
• Retention increases and analysis time becomes very long
• Column efficiency (N) increases dramatically

Correct Answer: Analytes elute close to dead time causing poor resolution and co-elution

Q7. What practical change would most directly increase k’ for a neutral compound in reversed-phase HPLC?

• Increase the percentage of organic modifier in the mobile phase
• Decrease the percentage of organic modifier in the mobile phase
• Increase the flow rate dramatically
• Shorten column length

Correct Answer: Decrease the percentage of organic modifier in the mobile phase

Q8. Which expression shows how capacity factor affects resolution Rs via the retention term?

• Resolution is proportional to (1 + k’)/k’
• Resolution contains the factor k’/(1 + k’)
• Resolution is independent of k’
• Resolution is proportional to (1 – k’)

Correct Answer: Resolution contains the factor k’/(1 + k’)

Q9. For two solutes with k’1 = 1.2 and k’2 = 2.4, what is the selectivity (α) assuming same t0?

• 0.5
• 1.0
• 2.0
• 1.2

Correct Answer: 2.0

Q10. Which of the following changes will generally decrease k’ for ionizable compounds in reversed-phase LC?

• Adjusting pH to a value where the analyte is more ionized
• Using a more hydrophobic stationary phase
• Reducing column temperature
• Decreasing mobile phase organic content

Correct Answer: Adjusting pH to a value where the analyte is more ionized

Q11. Which statement correctly describes the significance of k’ with regard to method reproducibility?

• k’ has no impact on reproducibility because only peak area matters
• Low and highly variable k’ values reduce reproducibility of retention and identification
• Only extremely large k’ values affect reproducibility
• Reproducibility is governed solely by detector sensitivity

Correct Answer: Low and highly variable k’ values reduce reproducibility of retention and identification

Q12. In gas chromatography, which parameter is most often changed to modify k’ for volatile analytes?

• Detector wavelength
• Carrier gas flow rate and column temperature
• Stationary phase particle size only
• Mobile phase composition (organic solvent percent)

Correct Answer: Carrier gas flow rate and column temperature

Q13. Given VR = 12.0 mL and V0 = 2.0 mL, what is the capacity factor?

• k’ = 6.0
• k’ = 5.0
• k’ = 0.17
• k’ = 2.0

Correct Answer: k’ = 5.0

Q14. How does k’ influence the contribution of column efficiency (N) to resolution?

• Higher k’ always negates the benefit of higher N
• The effect of N on Rs is weighted by k’/(1 + k’), so moderate k’ maximizes the benefit
• Resolution depends only on N and not on k’
• Lower k’ increases the weight of N in resolution

Correct Answer: The effect of N on Rs is weighted by k’/(1 + k’), so moderate k’ maximizes the benefit

Q15. Which strategy is least effective to increase k’ for a hydrophobic analyte in reversed-phase LC?

• Decrease mobile phase organic solvent
• Use a longer column
• Use a less hydrophobic stationary phase
• Lower column temperature moderately

Correct Answer: Use a less hydrophobic stationary phase

Q16. If two peaks have identical k’ values but different t0 due to instrument differences, what is true about their chromatographic selectivity (α)?

• α will be different because k’ depends on t0
• α equals 1 because identical k’ implies no selectivity between them
• α is the ratio of tR values, independent of k’
• α cannot be determined without peak widths

Correct Answer: α equals 1 because identical k’ implies no selectivity between them

Q17. Why is k’ preferred over absolute retention time for describing retention behavior across different systems?

• k’ includes detector response corrections
• Absolute retention time varies with flow and column geometry, while k’ is a normalized dimensionless measure
• Retention time cannot be measured accurately
• k’ is easier to measure than retention time

Correct Answer: Absolute retention time varies with flow and column geometry, while k’ is a normalized dimensionless measure

Q18. Which of the following is a direct consequence of very high k’ values (e.g., >15)?

• Very fast analyses with high throughput
• Shorter column life due to high pressure
• Long retention times, broad peaks, and sometimes excessive peak dispersion
• Improved peak symmetry and reduced tailing

Correct Answer: Long retention times, broad peaks, and sometimes excessive peak dispersion

Q19. For two analytes, k’1 = 0.8 and k’2 = 1.6. Which change would most improve their resolution without changing selectivity?

• Decrease column temperature to increase k’ of both equally
• Change stationary phase to alter α
• Increase flow rate to shorten tR
• Use gradient elution to reduce k’ difference

Correct Answer: Decrease column temperature to increase k’ of both equally

Q20. The Van Deemter optimization often aims to balance which relationship involving k’ for best practical chromatography?

• Minimize k’ to reduce retention time regardless of resolution
• Maximize k’ at the expense of plate number (N)
• Optimize linear velocity to achieve good plate height while maintaining a k’ that gives acceptable resolution and analysis time
• Keep k’ constant by using an isocratic mobile phase only

Correct Answer: Optimize linear velocity to achieve good plate height while maintaining a k’ that gives acceptable resolution and analysis time

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